├── LICENSE
├── README.md
├── example
├── BTMF
│ ├── btmf_net.pdf
│ ├── slide1.png
│ ├── slide2.png
│ ├── slides.pdf
│ └── slides.tex
├── MF-TF-SFR
│ ├── graphics
│ │ ├── MF_convergence_over_gd_and_als_within_1000iter.pdf
│ │ ├── MF_convergence_over_gd_and_als_within_1000iter_Seattle.pdf
│ │ ├── MF_convergence_over_gd_and_als_within_100iter.pdf
│ │ ├── MF_convergence_over_gd_and_als_within_200iter_Seattle.pdf
│ │ ├── Polytechnique_signature-RGB-gauche_FR.png
│ │ ├── Portland_traffic_speed.png
│ │ ├── fluid_flow_heatmap_2_times_4.png
│ │ ├── gaint_panda_gray.png
│ │ ├── gaint_panda_gray_missing_rate_90.png
│ │ ├── gaint_panda_gray_recovery_90_mf_rank_50_lmbda_0.png
│ │ ├── gaint_panda_gray_recovery_90_mf_rank_50_lmbda_10.png
│ │ ├── ivado_logo.jpg
│ │ ├── lijun_sun.jpg
│ │ ├── matrix_element.pdf
│ │ ├── matrix_factorization_illustration.pdf
│ │ ├── nicolas_saunier.png
│ │ ├── portland_sensor_stations.png
│ │ ├── smoothing_matrix_factorization_illustration.pdf
│ │ ├── speed_field_80_missing_data.png
│ │ ├── speed_field_HTF_rec_tau_10.png
│ │ ├── speed_field_HTF_rec_tau_15.png
│ │ ├── speed_field_MF_als_rec.png
│ │ ├── speed_field_MF_gd_rec.png
│ │ ├── speed_field_MF_sgd_rec.png
│ │ ├── speed_field_SMF_rec_lambda_10.png
│ │ ├── speed_field_SMF_rec_lambda_100.png
│ │ ├── speed_field_fully_data.png
│ │ ├── tensor_element.pdf
│ │ ├── third_order_Hankel_tensor.pdf
│ │ ├── third_orderr_CP_factorization_simple_notation.pdf
│ │ └── xinyu_chen.png
│ └── slides.tex
├── missing-data-patterns
│ ├── slide.pdf
│ ├── slide.png
│ └── slide.tex
├── parent-functions
│ ├── slide.pdf
│ ├── slide.png
│ └── slide.tex
├── ridesharing-innovation
│ ├── images
│ │ ├── README.md
│ │ ├── didi_logo.png
│ │ ├── lyft_logo.png
│ │ ├── ridesharing_allocation.jpg
│ │ ├── ridesharing_illustration.jpg
│ │ ├── ridesharing_interface.png
│ │ └── uber_brand.png
│ ├── slide.pdf
│ ├── slide.png
│ └── slide.tex
├── social-learning
│ ├── images
│ │ ├── Bandura.jpg
│ │ ├── Chomsky.png
│ │ ├── README.md
│ │ ├── Skinner.jpg
│ │ ├── bobo_doll.png
│ │ └── bobo_doll_experiment.jpg
│ ├── slide.pdf
│ ├── slide.tex
│ ├── slide1.png
│ └── slide2.png
└── tensor-factorization
│ ├── slide1.png
│ ├── slide2.png
│ ├── slides.pdf
│ └── slides.tex
└── reading-notes
├── NYC_transportation
├── graphics
│ ├── Empire_State_Building.jpg
│ ├── Midtown_Manhattan.jpg
│ ├── bronx_bus_map.png
│ ├── brooklyn_bus_map.png
│ ├── citibike.png
│ ├── citibike2.png
│ ├── citibike_monthly_trips.png
│ ├── citibike_popular_road.png
│ ├── cv_technology.png
│ ├── find_a_bike.png
│ ├── lady_liberty.jpg
│ ├── manhattan_bus_map.png
│ ├── mobility1.png
│ ├── mobility2.png
│ ├── modal_share.png
│ ├── nyc_bus.png
│ ├── nyc_ghg.png
│ ├── nyc_ghg_transport.png
│ ├── nyc_map.png
│ ├── nyc_mobility_stat1.png
│ ├── nyc_mobility_stat2.png
│ ├── shared_mobility.png
│ └── subway_map.png
├── main.pdf
└── main.tex
├── deblurring-images-slides
├── graphics
│ ├── book-cover.png
│ ├── exact-vs-blurred-images.png
│ └── sharp-vs-blurred-images.png
└── main.tex
└── social-learning-slides
├── .DS_Store
├── graphics
├── Bandura.jpg
├── Chomsky.png
├── Skinner.jpg
├── bobo_doll.png
├── bobo_doll_experiment.jpg
├── congested_taxi.jpeg
├── use_chopsticks.png
└── wechat.png
├── main.pdf
└── main.tex
/LICENSE:
--------------------------------------------------------------------------------
1 | MIT License
2 |
3 | Copyright (c) 2020 Xinyu Chen
4 |
5 | Permission is hereby granted, free of charge, to any person obtaining a copy
6 | of this software and associated documentation files (the "Software"), to deal
7 | in the Software without restriction, including without limitation the rights
8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 |
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 |
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 |
--------------------------------------------------------------------------------
/README.md:
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1 | # awesome-beamer
2 | Creating presentation slides by using Beamer in LaTeX. [[What is Beamer in LaTeX?](https://en.wikipedia.org/wiki/Beamer_(LaTeX))]
3 |
4 | ### Beamer Examples
5 |
6 | [**Example 1**] Social learning (background & example)
7 |
8 |
9 | 
10 | 
11 |
12 |
13 | If you want to reproduce these slides on [overleaf.com](https://www.overleaf.com), please follow these steps:
14 |
15 | - Upload the file `slide.tex` (check out `slide.tex` at [here](https://github.com/xinychen/awesome-beamer/blob/main/example/social-learning/slide.tex)).
16 | - Upload the image folder `../social-learning/images/` (check out the folder at [here](https://github.com/xinychen/awesome-beamer/tree/main/example/social-learning/images), please upload all images).
17 | - Recompile `slide.tex` on your Overleaf project.
18 |
19 | [**Example 2**] Ridesharing (innovation history)
20 |
21 |
22 | 
23 |
24 |
25 | If you want to reproduce this slide on [overleaf.com](https://www.overleaf.com), please follow these steps:
26 |
27 | - Upload the file `slide.tex` (check out `slide.tex` at [here](https://github.com/xinychen/awesome-beamer/blob/main/example/ridesharing-innovation/slide.tex)).
28 | - Upload the image folder `../ridesharing-innovation/images/` (check out the folder at [here](https://github.com/xinychen/awesome-beamer/tree/main/example/ridesharing-innovation/images), please upload all images).
29 | - Recompile `slide.tex` on your Overleaf project.
30 |
31 | [**Example 3**] Math parent function (a list)
32 |
33 | > This slide is created by referring to [this tutorial](https://www.youtube.com/watch?v=0fsWGg81RwU&list=PL1D4EAB31D3EBC449&index=12).
34 |
35 |
36 | 
37 |
38 |
39 | If you want to reproduce this slide on [overleaf.com](https://www.overleaf.com), please follow these steps:
40 |
41 | - Upload the file `slide.tex` (check out `slide.tex` at [here](https://github.com/xinychen/awesome-beamer/blob/main/example/parent-functions/slide.tex)).
42 | - Recompile `slide.tex` on your Overleaf project.
43 |
44 | [**Example 4**] Missing data patterns
45 |
46 |
47 | 
48 |
49 |
50 | If you want to reproduce this slide on [overleaf.com](https://www.overleaf.com), please follow these steps:
51 |
52 | - Upload the file `slide.tex` (check out `slide.tex` at [here](https://github.com/xinychen/awesome-beamer/blob/main/example/missing-data-patterns/slide.tex)).
53 | - Recompile `slide.tex` on your Overleaf project.
54 |
55 | [**Example 5**] Bayesian temporal matrix factorization (BTMF)
56 |
57 |
58 | 
59 | 
60 |
61 |
62 | If you want to reproduce these slides on [overleaf.com](https://www.overleaf.com), please follow these steps:
63 |
64 | - Upload the image `btmf_net.pdf` and the file `slides.tex` (check out them at the folder [../example/BTMF](https://github.com/xinychen/awesome-beamer/tree/main/example/BTMF)).
65 | - Recompile `slides.tex` on your Overleaf project.
66 |
67 | > The whole slides are avaiable on [Zenodo](https://doi.org/10.5281/zenodo.4693404).
68 |
69 | [**Example 6**] Tensor factorization with Bayesian treatment
70 |
71 |
72 | 
73 | 
74 |
75 |
76 | If you want to reproduce these slides on [overleaf.com](https://www.overleaf.com), please follow these steps:
77 |
78 | - Upload the file `slides.tex` (check out it at [here](https://github.com/xinychen/awesome-beamer/blob/main/example/tensor-factorization/slides.tex)).
79 | - Recompile `slides.tex` on your Overleaf project.
80 |
81 | > The whole slides are avaiable on [Zenodo](https://doi.org/10.5281/zenodo.4693404).
82 |
83 | ### Helpful Questions & Answers
84 |
85 | 1. [How do I align an image to centre?](https://tex.stackexchange.com/questions/53862) [350k+ views]
86 | 2. [Blocks in Beamer](https://tex.stackexchange.com/q/174257/227605) [240+k views]
87 | 3. [How to scale a tikzpicture including texts?](https://tex.stackexchange.com/questions/26846) [200k+ views]
88 | 4. [LaTeX beamer presentation-package 16:9 aspect ratio?](https://tex.stackexchange.com/questions/14336) [140k+ views]
89 | 5. [How to insert a background image in a beamer frame?](https://tex.stackexchange.com/questions/7916) [130k+ views]
90 | 6. [Positioning content at the top of a beamer slide (by default)](https://tex.stackexchange.com/questions/9889) [100k+ views]
91 | 7. [logo in the first page only](https://tex.stackexchange.com/questions/61051) [90k+ views]
92 | 8. [Add space between paragraphs in Beamer](https://tex.stackexchange.com/questions/11622) [90k+ views]
93 | 9. [Animation on beamer](https://tex.stackexchange.com/questions/177057/animation-on-beamer) [85+ views]
94 | 10. [Design a custom Beamer theme from scratch](https://tex.stackexchange.com/questions/146529) [80k+ views]
95 | 11. [Where to find custom beamer themes](https://tex.stackexchange.com/questions/5828) [60k+ views]
96 | 12. [How to overlap images in a beamer slide?](https://tex.stackexchange.com/questions/34921) [60k+ views]
97 | 13. [How to include existing PDF slides into my Beamer presentation?](https://tex.stackexchange.com/questions/57441) [40k+ views]
98 | 14. [Using pause without increasing page number](https://tex.stackexchange.com/questions/191218) [10k+ views]
99 | 15. [Add Overlays in beamer \tableofcontents items](https://tex.stackexchange.com/q/67218/227605) [10k+ views]
100 |
101 | ### Helpful Material
102 |
103 | - [The TikZ and PGF Packages Manual](https://www.bu.edu/math/files/2013/08/tikzpgfmanual.pdf), created by Till Tantau.
104 |
105 | - [LaTeX Tutorials](https://www.michellekrummel.com/tutorials), created by Michelle Krummel.
106 |
107 | - [Drawing with the tikz-3dplot Package](https://latex.net/tikz-3dplot/), created by Jeff Hein.
108 |
109 | - [Three Dimensional Plot Types](https://tikz.dev/pgfplots/reference-3dplots).
110 |
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1 | \documentclass{beamer}
2 |
3 | \usepackage[utf8]{inputenc}
4 | \usefonttheme{professionalfonts}
5 | \usepackage{tikz}
6 | \newcommand{\topline}{
7 | \tikz[remember picture, overlay] {
8 | \draw[gray, thick] ([xshift = 1cm, yshift = -1.2cm]current page.north west)
9 | -- ([xshift = -1cm, yshift = -1.2cm, xshift = \paperwidth]current page.north west);}}
10 |
11 | \setbeamertemplate{frametitle}[default][center]
12 | \setbeamertemplate{navigation symbols}{}
13 | \setbeamerfont{footline}{series = \bfseries}
14 | \setbeamertemplate{footline}[page number]
15 |
16 | \begin{document}
17 |
18 | \begin{frame}
19 | \frametitle{\color{black}\textbf{Bayesian Temporal Matrix Factorization}}
20 | \topline
21 |
22 | \footnotesize
23 | Model description\footnote{\scriptsize $\mathcal{N}(\cdot)$: Gaussian/Normal distribution; $\mathcal{W}(\cdot)$: Wishart distribution; $\mathcal{MN}(\cdot)$: Matrix normal distribution; $\mathcal{IW}(\cdot)$: Inverse Wishart distribution; $\text{Gamma}(\cdot)$: Gamma distribution.}:
24 | \scriptsize
25 | \begin{itemize}
26 | \item[\color{black}\textbullet] Assumption over observations:
27 | \begin{equation}
28 | y_{it}\sim\mathcal{N}\left(\boldsymbol{w}_i^\top\boldsymbol{x}_t,\tau_i^{-1}\right),\quad \left(i,t\right)\in\Omega
29 | \end{equation}
30 | \item[\color{black}\textbullet] Prior setting of factor matrices and precision:
31 | \begin{align}
32 | &\boldsymbol{w}_i\sim\mathcal{N}\left(\boldsymbol{\mu}_{w},\Lambda_w^{-1}\right),\\
33 | &\boldsymbol{x}_{t}\sim\begin{cases}
34 | \mathcal{N}\left(\boldsymbol{0},I_R\right),&\text{if $t\in\left\{1,2,\ldots,h_d\right\}$}, \\
35 | \mathcal{N}\left(A^\top \boldsymbol{v}_{t},\Sigma\right),&\text{otherwise},
36 | \end{cases} \\
37 | &\tau_i\sim\text{Gamma}\left(\alpha,\beta\right).
38 | \end{align}
39 | \item[\color{black}\textbullet] Prior setting of hyperparameters:
40 | \begin{align}
41 | &\boldsymbol{\mu}_w | \Lambda_w \sim\mathcal{N}\left(\boldsymbol{\mu}_0,(\beta_0\Lambda_w)^{-1}\right),\,\Lambda_w\sim\mathcal{W}\left(W_0,\nu_0\right), \\
42 | &A\sim\mathcal{MN}_{(Rd)\times R}\left(M_0,\Psi_0,\Sigma\right),\,\Sigma \sim\mathcal{IW}\left(S_0,\nu_0\right),
43 | \end{align}
44 | \end{itemize}
45 |
46 | \end{frame}
47 |
48 | \begin{frame}
49 | \frametitle{\color{black}\textbf{Bayesian Temporal Matrix Factorization}}
50 | \topline
51 |
52 | \footnotesize
53 | Bayesian network:
54 | \begin{center}
55 | \includegraphics[scale=0.6]{graphics/btmf_net.pdf}
56 | \end{center}
57 | \scriptsize
58 | \begin{itemize}
59 | \item[\color{black}\textbullet] Graphical model of BTMF (time lag set: $\{1,2,\ldots,d\}$). The shaded node $(y_{i,t})$ are the observed data in $\Omega$.
60 | \end{itemize}
61 | \end{frame}
62 |
63 | \end{document}
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/example/MF-TF-SFR/slides.tex:
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1 | \documentclass{beamer}
2 | \usefonttheme{professionalfonts}
3 |
4 | \usepackage[utf8]{inputenc}
5 | \usepackage{graphicx, xcolor, color}
6 | \usepackage{amsmath, amsthm, amssymb, amsfonts}
7 | \usepackage{bbm}
8 | \usepackage{wasysym}
9 | \usepackage{pifont}
10 | \usepackage{emoji}
11 | \usepackage[absolute, overlay]{textpos}
12 |
13 | \usepackage{tikz}
14 | \usepackage{caption}
15 | \captionsetup[figure]{labelformat = empty}
16 | \usepackage{tabularx, booktabs}
17 | \usepackage{multicol}
18 |
19 | \usepackage{multirow}
20 | \DeclareMathOperator*{\argmax}{arg\,max}
21 | \DeclareMathOperator*{\argmin}{arg\,min}
22 |
23 | \usepackage{color}
24 | \usepackage{minted}
25 | \usepackage{caption}
26 | \captionsetup{font = scriptsize, labelfont = scriptsize}
27 | \setbeamerfont{frametitle}{size=\normalsize}
28 | \setbeamertemplate{section in toc}[ball unnumbered]
29 | % \setbeamertemplate{subsection in toc}[ball unnumbered]
30 |
31 | \setbeamertemplate{itemize items}[circle]
32 | \setbeamercolor{itemize item}{fg=black}
33 |
34 | \definecolor{light_red}{RGB}{209,105,81}
35 | \definecolor{fair_red}{RGB}{237,27,47}
36 | \definecolor{light_green}{RGB}{58,181,75}
37 | \definecolor{thick_blue}{RGB}{5,43,108}
38 | \definecolor{fair_blue}{RGB}{0,112,192}
39 | \definecolor{light_blue}{RGB}{0,153,228}
40 | \definecolor{light_brown}{RGB}{132, 60, 11}
41 | \usepackage{hyperref}
42 | \hypersetup{
43 | colorlinks=true,
44 | linkcolor=blue,
45 | urlcolor=gray
46 | }
47 | \setbeamercolor{block title}{fg = black, bg = light_blue!40}
48 | \setbeamercolor{block body}{fg = black, bg = white}
49 | \setbeamertemplate{blocks}[rounded][shadow]
50 | \setbeamercolor{block title example}{fg = black, bg = orange!40}
51 | \setbeamercolor{block body example}{fg = black, bg = white}
52 |
53 | \setbeamercolor{block title alerted}{fg = black, bg = light_red!40}
54 | \setbeamercolor{section number projected}{bg=gray}
55 | \setbeamercolor{section number projected}{bg=gray}
56 | \setbeamercolor{subsection number projected}{bg=gray}
57 | \hypersetup{colorlinks=false}
58 |
59 | \setbeamertemplate{frametitle}[default][center]
60 | \setbeamertemplate{navigation symbols}{}
61 | \setbeamerfont{footline}{series=\bfseries}
62 | \setbeamertemplate{footline}[frame number]{}
63 |
64 | \usefonttheme{professionalfonts}
65 | \usepackage{tikz}
66 | \newcommand{\topline}{
67 | \tikz[remember picture, overlay] {
68 | \draw[gray, thick] ([xshift = 1cm, yshift = -1cm]current page.north west)
69 | -- ([xshift = -1cm, yshift = -1cm, xshift = \paperwidth]current page.north west);}}
70 |
71 | \setbeamertemplate{frametitle}[default][center]
72 | \setbeamertemplate{navigation symbols}{}
73 | \setbeamerfont{footline}{series = \bfseries}
74 | \setbeamertemplate{footline}[page number]
75 |
76 | \begin{document}
77 |
78 | \begin{frame}[plain]
79 |
80 | \begin{tikzpicture}[remember picture, overlay]
81 | \node[xshift=2.7cm,yshift=-1.1cm] at (current page.north west) {\includegraphics[height = 2.25cm]{graphics/Polytechnique_signature-RGB-gauche_FR.png}};
82 | \end{tikzpicture}
83 |
84 | \begin{tikzpicture}[remember picture, overlay]
85 | \node[xshift=10.5cm,yshift=-1.1cm] at (current page.north west) {\includegraphics[height = 1.25cm]{graphics/ivado_logo.jpg}};
86 | \end{tikzpicture}
87 |
88 | {\color{white}title}
89 |
90 | \vspace{3em}
91 |
92 | \begin{center}
93 | {\color{black!80}\large\textbf{Low-Rank Matrix and Tensor Factorization}
94 |
95 | \vspace{0.2em}
96 |
97 | \textbf{for Speed Field Reconstruction}}
98 |
99 | \small
100 |
101 | \vspace{1.2em}
102 |
103 | \textbf{Xinyu Chen}
104 |
105 | \vspace{0.4em}
106 |
107 | {March 9, 2023}
108 |
109 | \vspace{0.5em}
110 |
111 | \begin{columns}
112 | \begin{column}{0.3\textwidth}
113 | \begin{figure}
114 | \centering
115 | \includegraphics[height = 2.0cm]{graphics/xinyu_chen.png}
116 | \caption*{\centering\scriptsize \textbf{Ph.D. candidate} \\Xinyu Chen\\ Polytechnique Montr\'eal}
117 | \end{figure}
118 | \end{column}
119 | \hspace{-3em}
120 | \begin{column}{0.3\textwidth}
121 | \begin{figure}
122 | \centering
123 | \includegraphics[height = 2cm]{graphics/nicolas_saunier.png}
124 | \caption*{\centering\scriptsize
125 | \textbf{Supervisor} \\
126 | Prof. Nicolas Saunier\\ Polytechnique Montr\'eal}
127 | \end{figure}
128 | \end{column}
129 | \hspace{-3em}
130 | \begin{column}{0.3\textwidth}
131 | \begin{figure}
132 | \centering
133 | \includegraphics[height = 2cm]{graphics/lijun_sun.jpg}
134 | \caption*{\centering\scriptsize
135 | \textbf{Co-supervisor} \\ Prof. Lijun Sun\\ McGill University}
136 | \end{figure}
137 | \end{column}
138 |
139 | \end{columns}
140 |
141 | \end{center}
142 |
143 | \end{frame}
144 |
145 | \begin{frame}[plain]
146 | \footnotesize
147 |
148 | \begin{itemize}
149 | \item[\color{black}\ding{202}] \textbf{Slides}: {\color{light_blue}\url{https://xinychen.github.io/slides/MF_TF_SFR.pdf}}
150 | \item[\color{black}\ding{203}] \textbf{Jupyter Notebook}: {\color{light_blue}\url{https://github.com/xinychen/transdim/blob/master/toy-examples/MF_TF_SFR.ipynb}}
151 | \end{itemize}
152 |
153 | \end{frame}
154 |
155 | \begin{frame}[plain]
156 | \frametitle{\color{black}\textbf{Outline}}
157 | \topline
158 | \footnotesize
159 |
160 | \tableofcontents
161 |
162 | \end{frame}
163 |
164 | \section{\color{black}\textbf{Motivation}}
165 |
166 | \begin{frame}{\color{black}\textbf{Motivation}}
167 | \topline
168 | \footnotesize
169 |
170 | \begin{itemize}
171 | \item Portland highway traffic speed data\footnote{\scriptsize\color{light_blue}\url{https://portal.its.pdx.edu/home}}
172 | \end{itemize}
173 |
174 | \begin{center}
175 | \begin{tikzpicture}
176 | \pgfdeclareimage[height = 4cm]{img}{graphics/portland_sensor_stations.png}
177 | \node (img) at (0, 0) {\pgfuseimage{img}};
178 | \node at (0, -2.3) {\color{gray}\scriptsize Highway network \& sensor locations};
179 |
180 | \pgfdeclareimage[height = 3.5cm]{img}{graphics/portland_speed_field_I5_NB.png}
181 | \node (img) at (5.5, 0) {\pgfuseimage{img}};
182 | \node at (5.5, -2) {\color{gray}\scriptsize Traffic speed field};
183 | \end{tikzpicture}
184 | \end{center}
185 |
186 | \begin{itemize}
187 | \item Speed field $\boldsymbol{Y}\in\mathbb{R}^{N\times T}$ ($N$ locations \& $T$ time steps)
188 | \item Speed field shows strong spatial/temporal dependencies
189 | \end{itemize}
190 |
191 | \end{frame}
192 |
193 | \begin{frame}{\color{black}\textbf{Motivation}}
194 | \topline
195 | \footnotesize
196 |
197 | \begin{center}
198 | \begin{tikzpicture}
199 | \pgfdeclareimage[height = 2.8cm]{img}{graphics/speed_field_80_missing_data.png}
200 | \node (img) at (0, 0) {\pgfuseimage{img}};
201 | \node at (0,-2) {\Large\color{gray}$\Downarrow$};
202 | \node at (-1.5,-1.8) {\scriptsize $200$-by-$500$ matrix};
203 | \node at (-1.5,-2.2) {\scriptsize (NGSIM)};
204 | \node at (2,-1.8) {\scriptsize Reconstruct speed field from};
205 | \node at (2,-2.2) {\scriptsize 20\% sparse trajectories?};
206 | \pgfdeclareimage[height = 2.8cm]{img}{graphics/speed_field_fully_data.png}
207 | \node (img) at (0, -4) {\pgfuseimage{img}};
208 | \end{tikzpicture}
209 | \end{center}
210 |
211 | \begin{itemize}
212 | \item How to learn from sparse spatiotemporal data?
213 | \item How to characterize spatial/temporal local dependencies?
214 | \end{itemize}
215 |
216 | \end{frame}
217 |
218 | \section{\color{black}\textbf{Matrix Factorization}}
219 |
220 | \subsection{\color{black}Optimization Problem}
221 |
222 | \begin{frame}{\color{black}\textbf{Matrix Factorization}}
223 | \topline
224 | \footnotesize
225 |
226 | \begin{itemize}
227 | \item Spatiotemporal data can be reconstructed by low-dimensional latent factors!
228 | \end{itemize}
229 |
230 | \begin{center}
231 | \begin{tikzpicture}
232 | \pgfdeclareimage[width=0.9\textwidth]{img}{graphics/matrix_factorization_illustration.pdf}
233 | \node (img) at (0, 0) {\pgfuseimage{img}};
234 |
235 | \node [rotate=90] at (-4.9, 0.3) {\color{gray}\scriptsize Spatial locations};
236 | \node at (-3.2, 1.5) {\color{gray}\scriptsize Time steps};
237 | \node at (0, 1.5) {\color{gray}\scriptsize Spatial factors};
238 | \node at (3.2, 1.2) {\color{gray}\scriptsize Temporal factors};
239 |
240 | \end{tikzpicture}
241 | \end{center}
242 |
243 | \vspace{-1.5em}
244 |
245 | \begin{itemize}
246 | \item MF optimization problem
247 | \begin{equation*}
248 | \min_{\boldsymbol{W},\boldsymbol{X}}~\frac{1}{2}\left\|\mathcal{P}_{\Omega}(\boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})\right\|_{F}^{2}+\frac{\rho}{2}\left(\|\boldsymbol{W}\|_{F}^{2}+\|\boldsymbol{X}\|_{F}^2\right)
249 | \end{equation*}
250 | with factor matrices $\boldsymbol{W}$ and $\boldsymbol{X}$. {\color{gray}\scriptsize($\|\cdot\|_{F}^2$ is the squared Frobenius norm.)}
251 | \begin{itemize}\scriptsize
252 | \item[\color{black}\circ] Objective function $f(\boldsymbol{W},\boldsymbol{X})$ or $f$;
253 | \item[\color{black}\circ] Rank $R\in\mathbb{N}^{+}$ ($R<\min\{N,T\}$);
254 | \item[\color{black}\circ] Orthogonal projection $\mathcal{P}_{\Omega}(\cdot)$.%:\mathbb{R}^{N\times T}\to\mathbb{R}^{N\times T}$
255 | \end{itemize}
256 | \end{itemize}
257 |
258 | \end{frame}
259 |
260 | \begin{frame}{\color{black}\textbf{Matrix Factorization}}
261 | \topline
262 | \footnotesize
263 |
264 | \begin{center}
265 | \begin{tikzpicture}
266 | \pgfdeclareimage[width=0.9\textwidth]{img}{graphics/matrix_factorization_illustration.pdf}
267 | \node (img) at (0, 0) {\pgfuseimage{img}};
268 |
269 | \node [rotate=90] at (-4.9, 0.3) {\color{gray}\scriptsize Spatial locations};
270 | \node at (-3.2, 1.5) {\color{gray}\scriptsize Time steps};
271 | \node at (0, 1.5) {\color{gray}\scriptsize Spatial factors};
272 | \node at (3.2, 1.2) {\color{gray}\scriptsize Temporal factors};
273 |
274 | \end{tikzpicture}
275 | \end{center}
276 |
277 | \vspace{-1em}
278 |
279 | \begin{itemize}
280 | \item MF optimization problem
281 | \end{itemize}
282 | \begin{equation*}
283 | \min_{\boldsymbol{W},\boldsymbol{X}}~\frac{1}{2}\left\|\mathcal{P}_{\Omega}(\boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})\right\|_{F}^{2}+\frac{\rho}{2}\left(\|\boldsymbol{W}\|_{F}^{2}+\|\boldsymbol{X}\|_{F}^2\right)
284 | \end{equation*}
285 |
286 | \begin{itemize}
287 | \item Orthogonal projection $\color{cyan!70!black}\mathcal{P}_{\Omega}:\mathbb{R}^{N\times T}\to\mathbb{R}^{N\times T}$?
288 | \begin{itemize}\scriptsize
289 | \item[\color{black}\circ] Simple example: $\color{cyan!70!black}\boldsymbol{Y}=\begin{bmatrix} 1 & 2 \\ 3 & 4 \\ \end{bmatrix}$ with $\color{cyan!70!black}\Omega=\{(1,1),(2,2)\}$, we have
290 | \begin{equation*}
291 | {\color{cyan!70!black}\mathcal{P}_{\Omega}(\boldsymbol{Y})=\begin{bmatrix}
292 | 1 & 0 \\ 0 & 4 \\
293 | \end{bmatrix}}
294 | \quad\quad
295 | \mathcal{P}_{\Omega}^{\perp}(\boldsymbol{Y})=\begin{bmatrix}
296 | 0 & 2 \\ 3 & 0 \\
297 | \end{bmatrix}\quad\text{(On the complement)}
298 | \end{equation*}
299 | \end{itemize}
300 | \item Role of regularization (with $\rho$): avoid overfitting.
301 | \end{itemize}
302 |
303 | \end{frame}
304 |
305 | \subsection{\color{black}GD vs. SGD vs. ALS}
306 |
307 | \begin{frame}{\color{black}\textbf{Matrix Factorization}}
308 | \topline
309 | \footnotesize
310 |
311 | \begin{itemize}
312 | \item MF optimization problem
313 | \end{itemize}
314 |
315 | \vspace{-1em}
316 |
317 | \begin{equation*}
318 | \min_{\boldsymbol{W},\boldsymbol{X}}~\frac{1}{2}\left\|\mathcal{P}_{\Omega}(\boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})\right\|_{F}^{2}+\frac{\rho}{2}\left(\|\boldsymbol{W}\|_{F}^{2}+\|\boldsymbol{X}\|_{F}^2\right)
319 | \end{equation*}
320 |
321 | \begin{itemize}
322 | \item Partial derivatives
323 | \end{itemize}
324 | \begin{equation*}
325 | \left\{
326 | \begin{aligned}
327 | \frac{\partial f}{\partial\boldsymbol{W}}
328 | &=-\boldsymbol{X}\mathcal{P}_{\Omega}^\top(\boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})+\rho\boldsymbol{W} \\
329 | \frac{\partial f}{\partial\boldsymbol{X}}
330 | &=-\boldsymbol{W}\mathcal{P}_{\Omega}(\boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})+\rho\boldsymbol{X} \\
331 | \end{aligned}\right.
332 | \end{equation*}
333 |
334 | \begin{itemize}
335 | \item Gradient descent (\textbf{GD}) vs. Steepest gradient descent (\textbf{SGD})
336 | \end{itemize}
337 | \begin{equation*}
338 | \left\{
339 | \begin{aligned}
340 | \boldsymbol{W}:&=\boldsymbol{W}-\alpha\frac{\partial f}{\partial\boldsymbol{W}} \\
341 | \boldsymbol{X}:&=\boldsymbol{X}-\alpha\frac{\partial f}{\partial\boldsymbol{X}} \\
342 | \end{aligned}\right.
343 | \quad\text{vs.}\quad
344 | \left\{
345 | \begin{aligned}
346 | \alpha:=&{\displaystyle\argmin_{\alpha}}~f(\boldsymbol{W}-\alpha \frac{\partial f}{\partial\boldsymbol{W}},\boldsymbol{X}) \\
347 | \boldsymbol{W}:=&\boldsymbol{W}-\alpha \frac{\partial f}{\partial\boldsymbol{W}} \\
348 | \beta:=&{\displaystyle\argmin_{\beta}}~f(\boldsymbol{W},\boldsymbol{X}-\beta \frac{\partial f}{\partial\boldsymbol{X}}) \\
349 | \boldsymbol{X}:=&\boldsymbol{X}-\beta \frac{\partial f}{\partial\boldsymbol{X}} \\
350 | \end{aligned}\right.
351 | \end{equation*}
352 |
353 | \begin{itemize}\scriptsize
354 | \item \textbf{Fixed} step size $\alpha$ (\textbf{GD}) vs. \textbf{optimal} step sizes $\{\alpha,\beta\}$ (\textbf{SGD})
355 | \end{itemize}
356 |
357 | \end{frame}
358 |
359 | \begin{frame}{\color{black}\textbf{Matrix Factorization}}
360 | \topline
361 | \footnotesize
362 |
363 | \begin{itemize}
364 | \item MF optimization problem
365 | \end{itemize}
366 |
367 | \vspace{-1em}
368 |
369 | \begin{equation*}
370 | \min_{\boldsymbol{W},\boldsymbol{X}}~\frac{1}{2}\left\|\mathcal{P}_{\Omega}(\boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})\right\|_{F}^{2}+\frac{\rho}{2}\left(\|\boldsymbol{W}\|_{F}^{2}+\|\boldsymbol{X}\|_{F}^2\right)
371 | \end{equation*}
372 |
373 | \begin{itemize}
374 | \item Partial derivatives
375 | \end{itemize}
376 | \begin{equation*}
377 | \left\{
378 | \begin{aligned}
379 | \frac{\partial f}{\partial\boldsymbol{W}}
380 | &=-\boldsymbol{X}\mathcal{P}_{\Omega}^\top(\boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})+\rho\boldsymbol{W} \\
381 | \frac{\partial f}{\partial\boldsymbol{X}}
382 | &=-\boldsymbol{W}\mathcal{P}_{\Omega}(\boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})+\rho\boldsymbol{X} \\
383 | \end{aligned}\right.
384 | \end{equation*}
385 |
386 | \begin{itemize}
387 | \item Alternating least squares (\textbf{ALS})
388 | \end{itemize}
389 | \begin{equation*}
390 | \left\{
391 | \begin{aligned}
392 | \frac{\partial f}{\partial\boldsymbol{W}}&=\boldsymbol{0} \\
393 | \frac{\partial f}{\partial\boldsymbol{X}}&=\boldsymbol{0} \\
394 | \end{aligned}\right.
395 | \Longrightarrow
396 | \left\{
397 | \begin{aligned}
398 | \boldsymbol{w}_i&:=\Bigl(\sum_{t:(i,t)\in\Omega}\boldsymbol{x}_t\boldsymbol{x}_t^\top+\rho\boldsymbol{I}_{R}\Bigr)^{-1}\sum_{t:(i,t)\in\Omega}\boldsymbol{x}_ty_{i,t} \\
399 | \boldsymbol{x}_t&:=\Bigl(\sum_{i:(i,t)\in\Omega}\boldsymbol{w}_i\boldsymbol{w}_i^\top+\rho\boldsymbol{I}_{R}\Bigr)^{-1}\sum_{i:(i,t)\in\Omega}\boldsymbol{w}_iy_{i,t} \\
400 | \end{aligned}\right.
401 | \end{equation*}
402 |
403 | \begin{itemize}
404 | \item Latent factors
405 | \begin{itemize}\scriptsize
406 | \item[\color{black}\circ] $\boldsymbol{w}_{i}\in\mathbb{R}^{R},\,i=1,2,\ldots,N$ are the columns of $\boldsymbol{W}$;
407 | \item[\color{black}\circ] $\boldsymbol{x}_{t}\in\mathbb{R}^{R},\,t=1,2,\ldots,T$ are the columns of $\boldsymbol{X}$.
408 | \end{itemize}
409 | \end{itemize}
410 |
411 | \end{frame}
412 |
413 | \begin{frame}{\color{black}\textbf{Matrix Factorization}}
414 | \topline
415 | \footnotesize
416 |
417 | \textbf{Speed field reconstruction}
418 | \begin{itemize}
419 | \item Objective function $f$ vs. iteration
420 | \begin{itemize}\scriptsize
421 | \item[\color{black}\circ] Set rank $R=10$, weight parameter $\rho=10$;
422 | \item[\color{black}\circ] Set GD step size $\alpha=10^{-4}$.
423 | \end{itemize}
424 | \end{itemize}
425 |
426 | \begin{center}
427 | \begin{tikzpicture}
428 | \pgfdeclareimage[height = 3.5cm]{img}{graphics/MF_convergence_over_gd_and_als_within_1000iter.pdf}
429 | \node (img) at (0, 0) {\pgfuseimage{img}};
430 | \pgfdeclareimage[height = 3.5cm]{img}{graphics/MF_convergence_over_gd_and_als_within_100iter.pdf}
431 | \node (img) at (5, 0) {\pgfuseimage{img}};
432 | \end{tikzpicture}
433 | \end{center}
434 |
435 | \end{frame}
436 |
437 | \begin{frame}[plain]
438 | \footnotesize
439 |
440 | \begin{center}
441 | \begin{tikzpicture}
442 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_80_missing_data.png}
443 | \node (img) at (0, 0) {\pgfuseimage{img}};
444 | \node at (0,-1.3) {\scriptsize Sparse speed field};
445 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_MF_gd_rec.png}
446 | \node (img) at (5.8, 0) {\pgfuseimage{img}};
447 | \node at (5.8,-1.3) {\scriptsize MF with GD};
448 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_MF_sgd_rec.png}
449 | \node (img) at (0, 0-3) {\pgfuseimage{img}};
450 | \node at (0,-1.3-3) {\scriptsize MF with SGD};
451 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_MF_als_rec.png}
452 | \node (img) at (5.8, 0-3) {\pgfuseimage{img}};
453 | \node at (5.8,-1.3-3) {\scriptsize MF with ALS};
454 | \end{tikzpicture}
455 | \end{center}
456 |
457 | \begin{itemize}
458 | \item Reconstruction errors
459 | \end{itemize}
460 |
461 | \scriptsize
462 | \begin{equation*}
463 | \text{MAPE}=\begin{cases}
464 | 50.66\%\quad\text{(GD)} \\ 45.13\% \quad\text{(SGD)} \\ 45.84\% \quad\text{(ALS)}
465 | \end{cases}\quad\quad
466 | \text{RMSE}=\begin{cases}
467 | 2.33\quad\text{(GD)} \\ 2.79\quad\text{(SGD)} \\ 2.80\quad\text{(ALS)}
468 | \end{cases}\text{(mph)}
469 | \end{equation*}
470 |
471 | \end{frame}
472 |
473 | \begin{frame}{\color{black}\textbf{Matrix Factorization}}
474 | \topline
475 | \footnotesize
476 |
477 | \textbf{Seattle freeway traffic speed dataset} {\scriptsize\color{gray}(randomly mask 60\% entries)}
478 | \begin{itemize}
479 | \item Dataset: 323 loop detectors \& 8,064 time steps (288 per day)
480 | \item Objective function $f$ vs. iteration
481 | \begin{itemize}\scriptsize
482 | \item[\color{black}\circ] Set rank $R=10$, weight parameter $\rho=10^2$;
483 | \item[\color{black}\circ] Set GD step size $\alpha=2\times10^{-5}$.
484 | \end{itemize}
485 | \end{itemize}
486 |
487 | \begin{center}
488 | \begin{tikzpicture}
489 | \pgfdeclareimage[height = 3.5cm]{img}{graphics/MF_convergence_over_gd_and_als_within_1000iter_Seattle.pdf}
490 | \node (img) at (0, 0) {\pgfuseimage{img}};
491 | \pgfdeclareimage[height = 3.5cm]{img}{graphics/MF_convergence_over_gd_and_als_within_200iter_Seattle.pdf}
492 | \node (img) at (5, 0) {\pgfuseimage{img}};
493 | \end{tikzpicture}
494 | \end{center}
495 |
496 | \vspace{-1em}
497 |
498 | \begin{itemize}
499 | \item[\color{black}\circ] Reconstruction errors
500 | \end{itemize}
501 |
502 | \scriptsize
503 | \begin{equation*}
504 | \text{MAPE}=\begin{cases}
505 | 9.14\%\quad\text{(GD)} \\ 9.12\% \quad\text{(SGD)} \\ 9.13\% \quad\text{(ALS)}
506 | \end{cases}\quad\quad
507 | \text{RMSE}=\begin{cases}
508 | 5.24\quad\text{(GD)} \\ 5.24\quad\text{(SGD)} \\ 5.24\quad\text{(ALS)}
509 | \end{cases}\text{(mph)}
510 | \end{equation*}
511 |
512 | \end{frame}
513 |
514 | \section{\color{black}\textbf{Smoothing Matrix Factorization}}
515 |
516 | \subsection{\color{black}Spatial/Temporal Smoothing}
517 |
518 | \begin{frame}{\color{black}\textbf{Smoothing Matrix Factorization}}
519 | \topline
520 | \footnotesize
521 |
522 | \begin{itemize}
523 | \item Spatial/temporal local dependencies are also important!
524 | \end{itemize}
525 |
526 | \begin{center}
527 | \begin{tikzpicture}
528 | \pgfdeclareimage[width=0.9\textwidth]{img}{graphics/smoothing_matrix_factorization_illustration.pdf}
529 | \node (img) at (0, 0) {\pgfuseimage{img}};
530 |
531 | \node [rotate=90] at (-4.9, 0.3) {\color{gray}\scriptsize Spatial locations};
532 | \node at (-3.2, 1.5) {\color{gray}\scriptsize Time steps};
533 | \node at (0, 1.5) {\color{gray}\scriptsize Spatial factors};
534 | \node at (3.2, 1.5) {\color{gray}\scriptsize Temporal factors};
535 |
536 | \end{tikzpicture}
537 | \end{center}
538 |
539 | \vspace{-1em}
540 |
541 | \begin{itemize}
542 | \item Formulate spatial/temporal dependencies
543 | \end{itemize}
544 |
545 | \begin{equation*}
546 | \begin{aligned}
547 | \boldsymbol{W}\boldsymbol{\Psi}_1^\top=
548 | &\begin{bmatrix}
549 | \mid & & \mid \\ \color{orange!70!black}\boldsymbol{w}_2-\boldsymbol{w}_1 & \cdots & \color{orange!70!black}\boldsymbol{w}_N-\boldsymbol{w}_{N-1} \\ \mid & & \mid \\
550 | \end{bmatrix} \\
551 | \boldsymbol{X}\boldsymbol{\Psi}_2^\top=
552 | &\begin{bmatrix}
553 | \mid & & \mid \\ \color{red!80!black}\boldsymbol{x}_2-\boldsymbol{x}_1 & \cdots & \color{red!80!black}\boldsymbol{x}_T-\boldsymbol{x}_{T-1} \\ \mid & & \mid \\
554 | \end{bmatrix}
555 | \end{aligned}
556 | \end{equation*}
557 |
558 | \end{frame}
559 |
560 | \subsection{\color{black}Alternating Minimization}
561 |
562 | \begin{frame}{\color{black}\textbf{Smoothing Matrix Factorization}}
563 | \topline
564 | \footnotesize
565 |
566 | \begin{itemize}
567 | \item Formulate spatial/temporal dependencies
568 | \end{itemize}
569 |
570 | \vspace{-1em}
571 |
572 | \begin{equation*}
573 | \boldsymbol{\Psi}=\begin{bmatrix}
574 | -1 & 1 & 0 & \cdots & 0 & 0 \\
575 | 0 & -1 & 1 & \cdots & 0 & 0 \\
576 | 0 & 0 & -1 & \cdots & 0 & 0 \\
577 | \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\
578 | 0 & 0 & 0 & \cdots & -1 & 1 \\
579 | \end{bmatrix}
580 | \Longrightarrow
581 | \left\{
582 | \begin{aligned}
583 | &\|\boldsymbol{W}\boldsymbol{\Psi}_1^\top\|_{F}^{2}\quad\text{with $\boldsymbol{\Psi}_1\in\mathbb{R}^{(N-1)\times N}$} \\
584 | &\|\boldsymbol{X}\boldsymbol{\Psi}_2^\top\|_{F}^{2}\quad\text{with $\boldsymbol{\Psi}_2\in\mathbb{R}^{(T-1)\times T}$}
585 | \end{aligned}\right.
586 | \end{equation*}
587 |
588 | \begin{itemize}
589 | \item SMF optimization problem
590 | \end{itemize}
591 | \begin{equation*}
592 | \begin{aligned}
593 | \min_{\boldsymbol{W},\boldsymbol{X}}~&\frac{1}{2}\left\|\mathcal{P}_{\Omega}(\boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})\right\|_{F}^{2}+\frac{\rho}{2}(\|\boldsymbol{W}\|_{F}^{2}+\|\boldsymbol{X}\|_{F}^{2}) \\
594 | &+\frac{\lambda}{2} (\|\boldsymbol{W}\boldsymbol{\Psi}_{1}^\top\|_{F}^{2}+\|\boldsymbol{X}\boldsymbol{\Psi}_{2}^\top\|_{F}^{2})
595 | \end{aligned}
596 | \end{equation*}
597 |
598 | \begin{itemize}
599 | \item \textbf{Alternating minimization}
600 | \end{itemize}
601 |
602 | \begin{equation*}
603 | \begin{aligned}
604 | \boldsymbol{W}:=\{\boldsymbol{W}\mid\frac{\partial f}{\partial\boldsymbol{W}}=\boldsymbol{0}\}\quad\quad
605 | \boldsymbol{X}:=\{\boldsymbol{X}\mid\frac{\partial f}{\partial\boldsymbol{X}}=\boldsymbol{0}\}
606 | \end{aligned}
607 | \end{equation*}
608 |
609 | \begin{itemize}
610 | \item Solve each matrix equation by the \textbf{conjugate gradient} method.
611 | \end{itemize}
612 |
613 | \end{frame}
614 |
615 | \begin{frame}{\color{black}\textbf{Smoothing Matrix Factorization}}
616 | \topline
617 | \footnotesize
618 |
619 | \begin{itemize}
620 | \item Speed field reconstruction
621 | \begin{itemize}\scriptsize
622 | \item[\color{black}\circ] Set rank $R=10$, weight parameter $\rho=10$.
623 | \item[\color{black}\circ] Recall that the reconstruction errors of MF:
624 | \begin{equation*}
625 | \text{MAPE}=\begin{cases}
626 | 50.66\%\quad\text{(GD)} \\ 45.13\% \quad\text{(SGD)} \\ 45.84\% \quad\text{(ALS)}
627 | \end{cases}\quad\quad
628 | \text{RMSE}=\begin{cases}
629 | 2.33\quad\text{(GD)} \\ 2.79\quad\text{(SGD)} \\ 2.80\quad\text{(ALS)}
630 | \end{cases}\text{(mph)}
631 | \end{equation*}
632 | \end{itemize}
633 | \end{itemize}
634 |
635 | \begin{center}
636 | \begin{tikzpicture}
637 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_SMF_rec_lambda_10.png}
638 | \node (img) at (0, 0) {\pgfuseimage{img}};
639 | \node at (0,1.3) {\scriptsize SMF ($\lambda=10$)};
640 | \node at (0,-1.3) {\scriptsize MAPE = \textbf{44.06\%}, RMSE = 2.16mph};
641 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_SMF_rec_lambda_100.png}
642 | \node (img) at (5.8, 0) {\pgfuseimage{img}};
643 | \node at (5.8,1.3) {\scriptsize SMF ($\lambda=10^2$)};
644 | \node at (5.8,-1.3) {\scriptsize MAPE = 48.00\%, RMSE = \textbf{1.60mph}};
645 | \end{tikzpicture}
646 | \end{center}
647 |
648 | \end{frame}
649 |
650 |
651 | \section{\color{black}\textbf{Tensor Factorization}}
652 |
653 | \subsection{\color{black}Basic Idea}
654 |
655 | \begin{frame}{\color{black}\textbf{Tensor Factorization}}
656 | \topline
657 | \footnotesize
658 |
659 | \begin{itemize}
660 | \item What is tensor? $\boldsymbol{X}\in\mathbb{R}^{m\times n}$ vs. $\boldsymbol{\mathcal{X}}\in\mathbb{R}^{m\times n\times t}$
661 | \end{itemize}
662 |
663 | \begin{center}
664 | \begin{tikzpicture}
665 | \pgfdeclareimage[width=2cm]{img}{graphics/matrix_element.pdf}
666 | \node (img) at (0, -0.2) {\pgfuseimage{img}};
667 | \pgfdeclareimage[width=2.5cm]{img}{graphics/tensor_element.pdf}
668 | \node (img) at (3.5, 0) {\pgfuseimage{img}};
669 | \end{tikzpicture}
670 | \end{center}
671 |
672 | \vspace{-1em}
673 |
674 | \begin{itemize}
675 | \item Tensors are everywhere!
676 | \end{itemize}
677 |
678 | \begin{center}
679 | \begin{tikzpicture}
680 | \pgfdeclareimage[height=2cm]{img}{graphics/gaint_panda_rgb.jpg}
681 | \node (img) at (0, -0.2) {\pgfuseimage{img}};
682 | \node at (0, -1.5) {\color{gray}\scriptsize Color image with};
683 | \node at (0, -1.9) {\color{gray}\scriptsize RGB channels};
684 |
685 | \pgfdeclareimage[height=2.5cm]{img}{graphics/fluid_flow_heatmap_2_times_4.png}
686 | \node (img) at (5.2, -0.2) {\pgfuseimage{img}};
687 | \node at (5.2, -1.7) {\color{gray}\scriptsize Dynamical system (fluid flow)};
688 | \end{tikzpicture}
689 | \end{center}
690 |
691 | \end{frame}
692 |
693 | \begin{frame}[plain]
694 |
695 | \begin{center}
696 | \resizebox{10.5cm}{!}{
697 | \begin{tikzpicture}
698 |
699 | \pgfdeclareimage[height = 3.6cm]{hitchcock}{graphics/Hitchcock.jpg}
700 | \draw (0, 2.3) node {\color{light_red}\textbf{\large{Higher-Order SVD}}};
701 | \node (hitchcock) at (0, -0.4) {\pgfuseimage{hitchcock}};
702 | \draw (0, -2.7) node {\large\textbf{Frank Lauren Hitchcock}};
703 |
704 | \node [circle, line width = 1mm, draw = light_blue, fill = white, minimum size = 0.4cm] (node1) at (0, 3.2) {};
705 | \draw (0, 4) node {\Large\textbf{1927}};
706 |
707 | \node [circle, line width = 1mm, draw = light_blue, fill = white, minimum size = 0.4cm] (node2) at (5, 3.2) {};
708 | \draw (5, 4) node {\Large\textbf{1960s}};
709 | \draw (5, 2.3) node {\color{light_red}\textbf{\large{Tucker Decomposition}}};
710 | \draw (5, 1.1) node {\large\textbf{Ledyard R. Tucker}};
711 |
712 | \path [line width = 1mm, draw = light_blue, -] (node1) edge (node2);
713 |
714 | \node [circle, line width = 1mm, draw = light_blue, fill = white, minimum size = 0.4cm] (node3) at (10, 3.2) {};
715 | \draw (10, 4) node {\Large\textbf{1970}};
716 | \draw (10, 2.3) node {\color{light_red}\textbf{\large{CP Decomposition}}};
717 | \draw (10, 1.1) node {\large\textbf{J. Douglas Carroll}};
718 | \draw (10, 0.5) node {\large\textbf{Jih-Jie Chang}};
719 | \draw (10, -0.1) node {\large\textbf{Richard A. Harshman}};
720 |
721 | \draw [line width = 1mm, draw = light_blue] (5.2, 3.2) -- (7.5, 3.2) -- (7.6, 3.5) -- (7.8, 2.9) -- (7.9, 3.2) -- (9.8, 3.2);
722 |
723 | \pgfdeclareimage[height = 3.6cm]{Kolda}{graphics/Kolda.jpg}
724 | \node (Kolda) at (15, -0.4) {\pgfuseimage{Kolda}};
725 | \node [circle, line width = 1mm, draw = light_blue, fill = white, minimum size = 0.4cm] (node4) at (15, 3.2) {};
726 | \draw (15, 4) node {\Large\textbf{2009}};
727 | \draw (15, 2.5) node {\color{light_red}\textbf{\large{Tensor Decompositions}}};
728 | \draw (15, 2.0) node {\color{light_red}\textbf{\large{and Applications}}};
729 | \draw (15, -2.7) node {\large\textbf{Tamara G. Kolda}};
730 |
731 | \draw [line width = 1mm, draw = light_blue] (5.2 + 5, 3.2) -- (7.5 + 5, 3.2) -- (7.6 + 5, 3.5) -- (7.8 + 5, 2.9) -- (7.9 + 5, 3.2) -- (9.8 + 5, 3.2);
732 |
733 | \pgfdeclareimage[height = 3.6cm]{Oseledets}{graphics/Oseledets.jpg}
734 | \node (Oseledets) at (20, -0.4) {\pgfuseimage{Oseledets}};
735 | \node [circle, line width = 1mm, draw = light_green, fill = white, minimum size = 0.4cm] (node5) at (20, 3.2) {};
736 | \draw (20, 4) node {\Large\textbf{2011}};
737 | \draw (20, 2.5) node {\color{light_red}\textbf{\large{Tensor-Train}}};
738 | \draw (20, 2) node {\color{light_red}\textbf{\large{Decomposition}}};
739 | \draw (20, -2.7) node {\large\textbf{Ivan Oseledets}};
740 |
741 | \draw [line width = 1mm, draw = light_blue] (5.2 + 10, 3.2) -- (7.5 + 10, 3.2) -- (7.6 + 10, 3.5) -- (7.8 + 10, 2.9) -- (7.9 + 10, 3.2) -- (9.8 + 10, 3.2);
742 |
743 | \draw [line width = 1mm, draw = light_green] (5.2 + 15, 3.2) -- (6.5 + 15, 3.2) -- (6.6 + 15, 3.5) -- (6.8 + 15, 2.9) -- (6.9 + 15, 3.2) -- (7.8 + 15, 3.2);
744 |
745 | \end{tikzpicture}
746 | }
747 | \end{center}
748 |
749 | \end{frame}
750 |
751 | \subsection{\color{black}CP Tensor Factorization}
752 |
753 | \begin{frame}{\color{black}\textbf{CP Tensor Factorization}}
754 | \topline
755 | \footnotesize
756 |
757 | \begin{itemize}
758 | \item Factorize $\boldsymbol{\mathcal{Y}}$ into the combination of three rank-$R$ factor matrices (i.e., low-dimensional latent factors).
759 | \end{itemize}
760 |
761 | \begin{center}
762 | \includegraphics[width=0.6\textwidth]{graphics/third_orderr_CP_factorization_simple_notation.pdf}
763 | \end{center}
764 |
765 | \begin{itemize}
766 | \item Understanding CP factorization\footnote{\scriptsize CANDECOMP/PARAFAC (CP) decomposition.}$^,$\footnote{\scriptsize The symbol $\otimes$ denotes the outer product.}:
767 | \begin{equation*}
768 | \left\{
769 | \begin{aligned}
770 | &y_{i,j,t}\approx\sum_{r=1}^{R}u_{i,r}v_{j,r}x_{t,r}
771 | \quad\quad\text{(sum of latent factors)} \\
772 | &\boldsymbol{\mathcal{Y}}\approx\sum_{r=1}^{R}\boldsymbol{u}_{r}\otimes\boldsymbol{v}_{r}\otimes\boldsymbol{x}_{r}
773 | \quad\quad\text{(sum of rank-one tensors)}
774 | \end{aligned}\right.
775 | \end{equation*}
776 | \end{itemize}
777 |
778 | \end{frame}
779 |
780 | \subsection{\color{black}Hankel Tensor and Its Factorization}
781 |
782 | \begin{frame}{\color{black}\textbf{Hankel Tensor and Its Factorization}}
783 | \topline
784 | \footnotesize
785 |
786 | \begin{itemize}
787 | \item Hankel matrix
788 | \begin{itemize}\scriptsize
789 | \item[\color{black}\circ] Given $\boldsymbol{y}=(1,2,3,4,5)^\top$ and window length $\tau=2$, we have
790 | \begin{equation*}
791 | \mathcal{H}_{\tau}(\boldsymbol{y})=\begin{bmatrix}
792 | 1 & 2 \\ 2 & 3 \\ 3 & 4 \\ 4 & 5 \\
793 | \end{bmatrix}\in\mathbb{R}^{4\times 2}
794 | \end{equation*}
795 |
796 | \item[\color{black}\circ] On time series $\boldsymbol{y}=(y_1,y_2,\ldots,y_5)^\top$ with $\tau=2$:
797 | \begin{equation*}
798 | \begin{aligned}
799 | &\mathcal{H}_{\tau}(\boldsymbol{y})=\begin{bmatrix}
800 | y_1 & y_2 \\ y_2 & y_3 \\ y_3 & y_4 \\ y_4 & y_5 \\
801 | \end{bmatrix}\approx\begin{bmatrix}
802 | {\color{cyan!70!black}v_1} \\
803 | {\color{cyan!70!black}v_2} \\ {\color{cyan!70!black}v_3} \\ {\color{cyan!70!black}v_4} \\
804 | \end{bmatrix}\otimes\begin{bmatrix}
805 | {\color{orange!70!black}x_1} \\
806 | {\color{orange!70!black}x_2} \\
807 | \end{bmatrix} \\
808 | \Longrightarrow\quad\hat{\boldsymbol{y}}=\begin{bmatrix}
809 | \hat{y}_1 \\
810 | \hat{y}_2 \\
811 | \hat{y}_3 \\
812 | \hat{y}_4 \\
813 | \hat{y}_5 \\
814 | \end{bmatrix}=&\mathcal{H}_{\tau}^{-1}\left(\begin{bmatrix}
815 | v_1x_1 & v_1x_2 \\
816 | v_2x_1 & v_2x_2 \\
817 | v_3x_1 & v_3x_2 \\
818 | v_4x_1 & v_4x_2 \\
819 | \end{bmatrix}\right)=\begin{bmatrix}
820 | {\color{cyan!70!black}v_1}{\color{orange!70!black}x_1} \\ ({\color{cyan!70!black}v_1}{\color{orange!70!black}x_2}+{\color{cyan!70!black}v_2}{\color{orange!70!black}x_1})/2 \\ ({\color{cyan!70!black}v_2}{\color{orange!70!black}x_2}+{\color{cyan!70!black}v_3}{\color{orange!70!black}x_1})/2 \\ ({\color{cyan!70!black}v_3}{\color{orange!70!black}x_2}+{\color{cyan!70!black}v_4}{\color{orange!70!black}x_1})/2 \\ {\color{cyan!70!black}v_4}{\color{orange!70!black}x_2} \\
821 | \end{bmatrix}
822 | \end{aligned}
823 | \end{equation*}
824 | \item[\color{black}\circ] Automatic temporal modeling.
825 | \end{itemize}
826 | \end{itemize}
827 |
828 | \end{frame}
829 |
830 | \begin{frame}{\color{black}\textbf{Hankel Tensor and Its Factorization}}
831 | \topline
832 | \footnotesize
833 |
834 | \begin{itemize}
835 | \item (Hankelization) Hankel tensor $\mathcal{H}_{\tau}(\boldsymbol{Y})$
836 | \begin{itemize}\scriptsize
837 | \item[\color{black}\circ] Tensor size: $N\times (T-\tau+1)\times \tau$;
838 | \item[\color{black}\circ] Slices: $\boldsymbol{Y}_{k}=\begin{bmatrix}
839 | \mid & \mid & & \mid \\
840 | \color{orange!70!black}\boldsymbol{y}_{k} & \color{orange!70!black}\boldsymbol{y}_{k+1} & \cdots & \color{orange!70!black}\boldsymbol{y}_{T-\tau+k} \\
841 | \mid & \mid & & \mid \\
842 | \end{bmatrix},\, k=1,2,\ldots,\tau$;
843 | \item[\color{black}\circ] Slice size: $\color{orange!70!black}N\times(T-\tau+1)$.
844 | \end{itemize}
845 | \end{itemize}
846 |
847 | \begin{center}
848 | \includegraphics[scale=0.8]{graphics/third_order_Hankel_tensor.pdf}
849 | \end{center}
850 |
851 | \end{frame}
852 |
853 | \begin{frame}{\color{black}\textbf{Hankel Tensor and Its Factorization}}
854 | \topline
855 | \footnotesize
856 |
857 | \begin{itemize}
858 | \item HTF optimization problem
859 | \end{itemize}
860 | \begin{equation*}
861 | \begin{aligned}
862 | \min_{\boldsymbol{U},\boldsymbol{V},\boldsymbol{X}}~&\frac{1}{2}\Bigl\|\mathcal{P}_{\tilde{\Omega}}\Bigl(\mathcal{H}_{\tau}(\boldsymbol{Y})-\sum_{r=1}^{R}\boldsymbol{u}_{r}\otimes\boldsymbol{v}_{r}\otimes\boldsymbol{x}_{r}\Bigr)\Bigr\|_{F}^{2} \\
863 | \end{aligned}
864 | \end{equation*}
865 |
866 | \begin{itemize}
867 | \item HTF's advantage/disadvantage over MF:
868 | \begin{itemize}\scriptsize
869 | \item[\color{black}\ding{51}] Automatic temporal modeling\quad\quad\ding{55}\, High memory consumption
870 | \end{itemize}
871 | \end{itemize}
872 |
873 | \begin{itemize}
874 | \item Speed field reconstruction
875 | \begin{itemize}\scriptsize
876 | \item[\color{black}\circ] Set rank $R=10$;
877 | \item[\color{black}\circ] Recall that SMF: MAPE = 48.00\% \& RMSE = 1.60mph.
878 | \end{itemize}
879 | \end{itemize}
880 |
881 | \begin{center}
882 | \begin{tikzpicture}
883 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_HTF_rec_tau_10.png}
884 | \node (img) at (0, 0) {\pgfuseimage{img}};
885 | \node at (0,1.3) {\scriptsize HTF ($\tau=10$)};
886 | \node at (0,-1.3) {\scriptsize MAPE = \textbf{41.40\%}, RMSE = \textbf{1.42mph}};
887 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_HTF_rec_tau_15.png}
888 | \node (img) at (5.8, 0) {\pgfuseimage{img}};
889 | \node at (5.8,1.3) {\scriptsize HTF ($\tau=15$)};
890 | \node at (5.8,-1.3) {\scriptsize MAPE = 43.97\%, RMSE = \textbf{1.42mph}};
891 | \end{tikzpicture}
892 | \end{center}
893 |
894 | \end{frame}
895 |
896 | \section{\color{black}\textbf{Discussion}}
897 |
898 | \subsection{\color{black}Which Model Is Better?}
899 |
900 | \begin{frame}{\color{black}\textbf{Which Model Is Better?}}
901 | \topline
902 | \footnotesize
903 |
904 | \begin{center}
905 | \begin{tikzpicture}
906 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_80_missing_data.png}
907 | \node (img) at (0, 0) {\pgfuseimage{img}};
908 | \node at (0,-1.3) {\scriptsize Sparse speed field};
909 |
910 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_MF_als_rec.png}
911 | \node (img) at (5.8, 1) {\pgfuseimage{img}};
912 | \node at (5.8,2.1) {\scriptsize MF (ALS)};
913 |
914 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_fully_data.png}
915 | \node (img) at (0, 0-3) {\pgfuseimage{img}};
916 | \node at (0,-1.3-3) {\scriptsize Ground truth speed field};
917 |
918 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_SMF_rec_lambda_100.png}
919 | \node (img) at (5.8, 1.5-3) {\pgfuseimage{img}};
920 | \node at (5.8,2.6-3) {\scriptsize SMF};
921 |
922 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_HTF_rec_tau_10.png}
923 | \node (img) at (5.8, -1-3) {\pgfuseimage{img}};
924 | \node at (5.8,0.1-3) {\scriptsize HTF};
925 | \end{tikzpicture}
926 | \end{center}
927 |
928 |
929 | \end{frame}
930 |
931 |
932 | \begin{frame}{\color{black}\textbf{Which Model Is Better?}}
933 | \topline
934 | \footnotesize
935 |
936 | \begin{center}
937 | \begin{tikzpicture}
938 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_80_missing_data.png}
939 | \node (img) at (0, 0) {\pgfuseimage{img}};
940 | \node at (0,-1.3) {\scriptsize Sparse speed field};
941 |
942 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_MF_als_rec.png}
943 | \node (img) at (5.8, 1) {\pgfuseimage{img}};
944 | \node at (5.8,2.1) {\scriptsize MF (ALS)};
945 | \draw [ultra thick, red] (3.8,1.3) rectangle (4.5,1.95);
946 | \draw [ultra thick, blue] (7,0.4) rectangle (7.7,1.95);
947 |
948 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_fully_data.png}
949 | \node (img) at (0, 0-3) {\pgfuseimage{img}};
950 | \node at (0,-1.3-3) {\scriptsize Ground truth speed field};
951 | \draw [ultra thick, red] (3.8-5.8,1.3-4) rectangle (4.5-5.8,1.95-4);
952 | \draw [ultra thick, blue] (7-5.8,0.4-4) rectangle (7.7-5.8,1.95-4);
953 |
954 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_SMF_rec_lambda_100.png}
955 | \node (img) at (5.8, 1.5-3) {\pgfuseimage{img}};
956 | \node at (5.8,2.6-3) {\scriptsize SMF};
957 | \draw [ultra thick, red] (3.8,1.8-3) rectangle (4.5,2.45-3);
958 | \draw [ultra thick, blue] (7,0.9-3) rectangle (7.7,2.45-3);
959 |
960 | \pgfdeclareimage[height = 2.2cm]{img}{graphics/speed_field_HTF_rec_tau_10.png}
961 | \node (img) at (5.8, -1-3) {\pgfuseimage{img}};
962 | \node at (5.8,0.1-3) {\scriptsize HTF};
963 | \draw [ultra thick, red] (3.8,-0.7-3) rectangle (4.5,-0.05-3);
964 | \draw [ultra thick, blue] (7,-1.6-3) rectangle (7.7,-0.05-3);
965 | \end{tikzpicture}
966 | \end{center}
967 |
968 |
969 | \end{frame}
970 |
971 | \begin{frame}{\color{black}\textbf{Which Model Is Better?}}
972 | \topline
973 | \footnotesize
974 |
975 | \begin{itemize}
976 | \item Seattle freeway traffic speed data
977 | \begin{itemize}\scriptsize
978 | \item[\color{black}\circ] Randomly mask 60\% entries;
979 | \item[\color{black}\circ] SMF: set $R=10$, $\rho=10^2$, $\lambda=2\times 10^2$;
980 | \item[\color{black}\circ] HTF: set $\tau=6$, $R=10$;
981 | \item[\color{black}\circ] Reconstruction errors
982 | \begin{equation*}
983 | \text{MAPE}=\begin{cases}
984 | 9.13\% &\text{(MF)} \\
985 | 9.01\% &\text{(SMF)} \\
986 | \boldsymbol{8.67\%} &\text{(HTF)} \\
987 | \end{cases}\quad\quad
988 | \text{RMSE}=\begin{cases}
989 | 5.24 &\text{(MF)} \\
990 | 5.14 &\text{(SMF)} \\
991 | \boldsymbol{5.02} &\text{(HTF)} \\
992 | \end{cases}\text{(mph)}
993 | \end{equation*}
994 | \end{itemize}
995 |
996 | \end{itemize}
997 |
998 | \end{frame}
999 |
1000 | \begin{frame}{\color{black}\textbf{Which Model Is Better?}}
1001 | \topline
1002 | \footnotesize
1003 |
1004 | \begin{itemize}
1005 | \item Gray image inpainting
1006 | \begin{itemize}\scriptsize
1007 | \item[\color{black}\circ] Randomly mask 90\% pixels;
1008 | \item[\color{black}\circ] MF: set $R=50$, $\rho=10^{-1}$;
1009 | \item[\color{black}\circ] SMF: set $R=50$, $\rho=10^{-1}$, $\lambda=10$.
1010 | \end{itemize}
1011 | \end{itemize}
1012 |
1013 | \vspace{-1em}
1014 |
1015 | \begin{center}
1016 | \begin{tikzpicture}
1017 | \pgfdeclareimage[height=2.2cm]{img}{graphics/gaint_panda_gray_missing_rate_90.png}
1018 | \node (img) at (0, 0) {\pgfuseimage{img}};
1019 | \node at (0, -1.4) {\scriptsize Incomplete image};
1020 |
1021 | \pgfdeclareimage[height=2.2cm]{img}{graphics/gaint_panda_gray_recovery_90_mf_rank_50_lmbda_0.png}
1022 | \node (img) at (2.8, 0) {\pgfuseimage{img}};
1023 | \node at (2.8, -1.4) {\scriptsize MF};
1024 |
1025 | \pgfdeclareimage[height=2.2cm]{img}{graphics/gaint_panda_gray_recovery_90_mf_rank_50_lmbda_10.png}
1026 | \node (img) at (5.6, 0) {\pgfuseimage{img}};
1027 | \node at (5.6, -1.4) {\scriptsize SMF};
1028 |
1029 | \pgfdeclareimage[height=2.2cm]{img}{graphics/gaint_panda_gray.png}
1030 | \node (img) at (8.4, 0) {\pgfuseimage{img}};
1031 | \node at (8.4, -1.4) {\scriptsize Ground truth};
1032 |
1033 | \end{tikzpicture}
1034 | \end{center}
1035 |
1036 | \end{frame}
1037 |
1038 | \section{\color{black}\textbf{Conclusion}}
1039 |
1040 | \begin{frame}{\color{black}\textbf{Conclusion}}
1041 | \topline
1042 | \footnotesize
1043 |
1044 | \begin{itemize}
1045 | \item How to reconstruct sparse speed field?
1046 | \begin{itemize}\scriptsize
1047 | \item[\color{black}\ding{51}] Matrix factorization ({\color{red!80!black}\textbf{MF}}) \quad\ding{51} Tensor factorization ({\color{red!80!black}\textbf{TF}})
1048 | \end{itemize}
1049 | \item The importance of spatiotemporal modeling in low-rank methods?
1050 | \begin{itemize}\scriptsize
1051 | \item[\color{black}\circ] Spatial/temporal {\color{red!80!black}\textbf{smoothing}} regularization:
1052 | \end{itemize}
1053 | \end{itemize}
1054 | \scriptsize
1055 | \begin{equation*}
1056 | \begin{aligned}
1057 | \min_{\boldsymbol{W},\boldsymbol{X}}~&\frac{1}{2}\left\|\mathcal{P}_{\Omega}(\boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})\right\|_{F}^{2}+\frac{\rho}{2}(\|\boldsymbol{W}\|_{F}^{2}+\|\boldsymbol{X}\|_{F}^{2}) \\
1058 | &+\color{red!80!black}\frac{\lambda}{2} (\|\boldsymbol{W}\boldsymbol{\Psi}_{1}^\top\|_{F}^{2}+\|\boldsymbol{X}\boldsymbol{\Psi}_{2}^\top\|_{F}^{2})
1059 | \end{aligned}
1060 | \end{equation*}
1061 | \begin{itemize}
1062 | \begin{itemize}\scriptsize
1063 | \item[\color{black}\circ] Automatic temporal modeling via {\color{red!80!black}\textbf{Hankelization}}:
1064 | \end{itemize}
1065 | \end{itemize}
1066 | \begin{equation*}
1067 | \begin{aligned}
1068 | \min_{\boldsymbol{U},\boldsymbol{V},\boldsymbol{X}}~&\frac{1}{2}\Bigl\|\mathcal{P}_{\tilde{\Omega}}\Bigl({\color{red!80!black}\mathcal{H}_{\tau}(\boldsymbol{Y})}-\sum_{r=1}^{R}\boldsymbol{u}_{r}\otimes\boldsymbol{v}_{r}\otimes\boldsymbol{x}_{r}\Bigr)\Bigr\|_{F}^{2} \\
1069 | \end{aligned}
1070 | \end{equation*}
1071 |
1072 | \end{frame}
1073 |
1074 |
1075 | \begin{frame}[plain]
1076 | \begin{tikzpicture}[remember picture, overlay]
1077 | \node[xshift=2.7cm,yshift=-1.1cm] at (current page.north west) {\includegraphics[height = 2.25cm]{graphics/Polytechnique_signature-RGB-gauche_FR.png}};
1078 | \end{tikzpicture}
1079 |
1080 | \begin{tikzpicture}[remember picture, overlay]
1081 | \node[xshift=10.5cm,yshift=-1.1cm] at (current page.north west) {\includegraphics[height = 1.25cm]{graphics/ivado_logo.jpg}};
1082 | \end{tikzpicture}
1083 |
1084 | \vspace{2em}
1085 |
1086 | \begin{center}
1087 | \LARGE Thanks for your attention!
1088 |
1089 | \vspace{1em}
1090 |
1091 | \large Any Questions?
1092 | \end{center}
1093 |
1094 | \scriptsize
1095 |
1096 | \vspace{1em}
1097 |
1098 | \textbf{About me}:
1099 | \begin{itemize}
1100 | \item[\emoji{classical-building}] Homepage:~{\color{light_blue}\url{https://xinychen.github.io}}
1101 | \item[\emoji{technologist}] GitHub:~{\color{light_blue}\url{https://github.com/xinychen}} {\scriptsize(\textbf{3k+ stars})}
1102 | \item[\emoji{writing-hand}] Blog:~{\color{light_blue}\url{https://medium.com/@xinyu.chen}} {\scriptsize(\textbf{60k+ views})}
1103 | \item[\emoji{love-letter}] How to reach me:~{\color{light_blue}\url{chenxy346@gmail.com}}
1104 | \end{itemize}
1105 |
1106 | \end{frame}
1107 |
1108 | \end{document}
1109 |
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/example/missing-data-patterns/slide.pdf:
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/example/missing-data-patterns/slide.png:
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/example/missing-data-patterns/slide.tex:
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1 | \documentclass{beamer}
2 |
3 | \usepackage[utf8]{inputenc}
4 | \usefonttheme{professionalfonts}
5 | \usepackage{tikz}
6 | \newcommand{\topline}{
7 | \tikz[remember picture, overlay] {
8 | \draw[gray, thick] ([xshift = 1cm, yshift = -1.2cm]current page.north west)
9 | -- ([xshift = -1cm, yshift = -1.2cm, xshift = \paperwidth]current page.north west);}}
10 |
11 | \setbeamertemplate{frametitle}[default][center]
12 | \setbeamertemplate{navigation symbols}{}
13 | \setbeamerfont{footline}{series = \bfseries}
14 | \setbeamertemplate{footline}[page number]
15 |
16 | \usepackage{pgfplots}
17 | \begin{filecontents}{speed_no1.data}
18 | 1 42.61
19 | 2 45.43
20 | 3 45.99
21 | 4 45.37
22 | 5 42.24
23 | 6 36.90
24 | 7 32.65
25 | 8 34.37
26 | 9 37.09
27 | 10 33.09
28 | 11 25.20
29 | 12 16.55
30 | 13 24.89
31 | 14 33.48
32 | 15 38.96
33 | 16 43.39
34 | 17 45.01
35 | 18 45.28
36 | 19 44.65
37 | 20 42.97
38 | 21 41.04
39 | 22 38.08
40 | 23 39.45
41 | 24 40.41
42 | 25 39.41
43 | 26 37.30
44 | 27 35.57
45 | 28 36.46
46 | 29 39.85
47 | 30 42.33
48 | 31 41.85
49 | 32 44.51
50 | 33 45.05
51 | 34 44.45
52 | 35 41.47
53 | 36 36.30
54 | 37 32.72
55 | 38 34.45
56 | 39 36.68
57 | 40 33.00
58 | 41 25.99
59 | 42 18.61
60 | 43 25.82
61 | 44 33.59
62 | 45 39.40
63 | 46 42.70
64 | 47 45.33
65 | 48 46.20
66 | 49 45.23
67 | 50 42.03
68 | 51 37.69
69 | 52 33.43
70 | 53 35.75
71 | 54 37.17
72 | 55 32.57
73 | 56 24.98
74 | 57 18.33
75 | 58 26.58
76 | 59 33.05
77 | 60 40.26
78 | 61 41.29
79 | 62 44.32
80 | 63 45.39
81 | 64 45.11
82 | 65 42.16
83 | 66 36.90
84 | 67 32.92
85 | 68 33.84
86 | 69 36.24
87 | 70 33.15
88 | 71 25.93
89 | 72 19.16
90 | 73 24.25
91 | 74 30.92
92 | 75 38.17
93 | 76 41.60
94 | 77 44.24
95 | 78 45.49
96 | 79 45.28
97 | 80 43.17
98 | 81 39.65
99 | 82 34.20
100 | 83 34.34
101 | 84 36.82
102 | 85 32.93
103 | 86 28.15
104 | 87 25.24
105 | 88 28.93
106 | 89 33.23
107 | 90 39.34
108 | 91 41.93
109 | 92 44.50
110 | 93 45.79
111 | 94 45.61
112 | 95 43.76
113 | 96 40.76
114 | 97 35.56
115 | 98 35.55
116 | 99 37.76
117 | 100 33.38
118 | 101 28.69
119 | 102 27.10
120 | 103 30.10
121 | 104 33.98
122 | 105 39.77
123 | \end{filecontents}
124 |
125 | \begin{filecontents}{speed_no1_nm1.data}
126 | 1 42.61
127 | 2 45.43
128 | 3 45.99
129 | 4 45.37
130 | 5 42.24
131 | 6 36.90
132 | 7 32.65
133 | 8 34.37
134 | 9 37.09
135 | 10 33.09
136 | 11 25.20
137 | 12 16.55
138 | 13 24.89
139 | 14 33.48
140 | 15 38.96
141 | \end{filecontents}
142 |
143 | \begin{filecontents}{speed_no1_nm2.data}
144 | 30 42.33
145 | 31 41.85
146 | 32 44.51
147 | 33 45.05
148 | 34 44.45
149 | 35 41.47
150 | 36 36.30
151 | 37 32.72
152 | 38 34.45
153 | 39 36.68
154 | 40 33.00
155 | 41 25.99
156 | 42 18.61
157 | 43 25.82
158 | 44 33.59
159 | 45 39.40
160 | \end{filecontents}
161 |
162 | \begin{filecontents}{speed_no1_nm3.data}
163 | 75 38.17
164 | 76 41.60
165 | 77 44.24
166 | 78 45.49
167 | 79 45.28
168 | 80 43.17
169 | 81 39.65
170 | 82 34.20
171 | 83 34.34
172 | 84 36.82
173 | 85 32.93
174 | 86 28.15
175 | 87 25.24
176 | 88 28.93
177 | 89 33.23
178 | 90 39.34
179 | \end{filecontents}
180 |
181 | \begin{filecontents}{speed_no2.data}
182 | 1 36
183 | 2 37
184 | 3 37
185 | 4 37
186 | 5 34
187 | 6 30
188 | 7 26
189 | 8 28
190 | 9 31
191 | 10 28
192 | 11 32
193 | 12 34
194 | 13 32
195 | 14 29
196 | 15 30
197 | 16 33
198 | 17 36
199 | 18 36
200 | 19 34
201 | 20 31
202 | 21 29
203 | 22 26
204 | 23 27
205 | 24 28
206 | 25 27
207 | 26 25
208 | 27 23
209 | 28 24
210 | 29 27
211 | 30 30
212 | 31 29
213 | 32 32
214 | 33 33
215 | 34 32
216 | 35 29
217 | 36 24
218 | 37 20
219 | 38 22
220 | 39 24
221 | 40 21
222 | 41 13
223 | 42 8
224 | 43 13
225 | 44 21
226 | 45 27
227 | 46 30
228 | 47 33
229 | 48 34
230 | 49 33
231 | 50 30
232 | 51 25
233 | 52 21
234 | 53 23
235 | 54 25
236 | 55 20
237 | 56 12
238 | 57 8
239 | 58 14
240 | 59 21
241 | 60 28
242 | 61 29
243 | 62 32
244 | 63 33
245 | 64 33
246 | 65 30
247 | 66 24
248 | 67 20
249 | 68 21
250 | 69 24
251 | 70 21
252 | 71 13
253 | 72 8
254 | 73 12
255 | 74 18
256 | 75 26
257 | 76 29
258 | 77 32
259 | 78 33
260 | 79 33
261 | 80 31
262 | 81 27
263 | 82 21
264 | 83 22
265 | 84 24
266 | 85 20
267 | 86 16
268 | 87 13
269 | 88 16
270 | 89 21
271 | 90 23
272 | 91 26
273 | 92 28
274 | 93 32
275 | 94 33
276 | 95 33
277 | 96 31
278 | 97 27
279 | 98 24
280 | 99 21
281 | 100 13
282 | 101 8
283 | 102 12
284 | 103 18
285 | 104 26
286 | 105 29
287 | \end{filecontents}
288 |
289 | \begin{filecontents}{speed_no2_nm1.data}
290 | 60 28
291 | 61 29
292 | 62 32
293 | 63 33
294 | 64 33
295 | 65 30
296 | 66 24
297 | 67 20
298 | 68 21
299 | 69 24
300 | 70 21
301 | 71 13
302 | 72 8
303 | 73 12
304 | 74 18
305 | 75 26
306 | 76 29
307 | 77 32
308 | 78 33
309 | 79 33
310 | 80 31
311 | 81 27
312 | 82 21
313 | 83 22
314 | 84 24
315 | 85 20
316 | 86 16
317 | 87 13
318 | 88 16
319 | 89 21
320 | 90 23
321 | \end{filecontents}
322 |
323 | \begin{document}
324 |
325 | \begin{frame}
326 | \frametitle{\color{black}\textbf{Imputation Experiments}}
327 | \topline
328 |
329 | \footnotesize
330 | Missing data generation:
331 | \scriptsize
332 | \begin{itemize}
333 | \item[\color{black}\textbullet] Random missing (RM)
334 |
335 | {\tiny\color{gray}(Data are missing at random.)}
336 |
337 | \vspace{0.5em}
338 |
339 | \resizebox{7cm}{!}{
340 | \begin{tikzpicture}[domain = 0:110]
341 | \begin{axis}[
342 | height = 3cm,
343 | width = 7cm,
344 | axis x line = center,
345 | axis y line = center,
346 | xtick={15, 30, 45, 60, 75, 90, 105},
347 | ytick={0},
348 | xticklabels={\tiny$T$, \tiny$2T$, \tiny$3T$, \tiny$4T$, \tiny$5T$, \tiny$6T$, \tiny$7T$},
349 | yticklabels = {},
350 | xlabel style = {below left},
351 | ylabel style = {below right},
352 | xmin = 1,
353 | xmax = 115,
354 | ymin = 0,
355 | ymax = 60]
356 | \addplot[no marks, smooth, draw = cyan!60!blue, thick] file {speed_no1.data};
357 | \addplot+[only marks,
358 | mark = *,
359 | mark options = {scale = 0.9, fill = white},
360 | draw = gray!60, thick] plot coordinates{
361 | (6, 36.90) (13, 24.89) (25, 39.41) (29, 39.85) (55, 32.57) (76, 41.60) (83, 34.34) (89, 33.23) (95, 43.76)};
362 | \addplot[no marks, smooth, draw = orange!60!black, thick] file {speed_no2.data};
363 | \addplot+[only marks,
364 | mark = *,
365 | mark options = {scale = 0.9, fill = white},
366 | draw = gray!60, thick] plot coordinates{
367 | (14, 29) (19, 34) (39, 24) (45, 27) (70, 21) (83, 22)};
368 | \end{axis}
369 | \end{tikzpicture}}
370 |
371 | \vspace{0.5em}
372 |
373 | \item[\color{black}\textbullet] Non-random missing (NM)
374 |
375 | {\tiny\color{gray}(Data are missing continuously during few time periods.)}
376 |
377 | \vspace{0.5em}
378 |
379 | \resizebox{7cm}{!}{
380 | \begin{tikzpicture}[domain = 0:110]
381 | \begin{axis}[
382 | height = 3cm,
383 | width = 7cm,
384 | axis x line = center,
385 | axis y line = center,
386 | xtick = {15, 30, 45, 60, 75, 90, 105},
387 | ytick = {0},
388 | xticklabels = {\tiny$T$, \tiny$2T$, \tiny$3T$, \tiny$4T$, \tiny$5T$, \tiny$6T$, \tiny$7T$},
389 | yticklabels = {},
390 | xlabel style = {below left},
391 | ylabel style = {below right},
392 | xmin = 1,
393 | xmax = 115,
394 | ymin = 0,
395 | ymax = 60]
396 | \addplot[no marks, smooth, draw = cyan!60!blue, thick] file {speed_no1.data};
397 | \addplot[no marks, smooth, draw = gray!30, thick] file {speed_no1_nm1.data};
398 | \addplot[no marks, smooth, draw = gray!30, thick] file {speed_no1_nm2.data};
399 | \addplot[no marks, smooth, draw = gray!30, thick] file {speed_no1_nm3.data};
400 | \addplot[no marks, smooth, draw = orange!60!black, thick] file {speed_no2.data};
401 | \addplot[no marks, smooth, draw = gray!30, thick] file {speed_no2_nm1.data};
402 | \end{axis}
403 | \end{tikzpicture}}
404 |
405 | \end{itemize}
406 |
407 | \end{frame}
408 |
409 | \end{document}
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/example/parent-functions/slide.pdf:
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/example/parent-functions/slide.png:
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/example/parent-functions/slide.tex:
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1 | \documentclass{beamer}
2 | \usepackage{multicol}
3 | \usetheme{Dresden}
4 | \usecolortheme{beaver}
5 | \usefonttheme{professionalfonts}
6 |
7 | \begin{document}
8 | \begin{frame}{Parent function}
9 |
10 | Please check out the following parent function list.
11 | \begin{enumerate}
12 | \begin{multicols}{3}
13 | \item $y=x$
14 | \item $y=|x|$
15 | \item $y=x^{2}$
16 | \item $y=x^{3}$
17 | \item $y=x^{b}$
18 | \item $y=\sqrt{x}$
19 | \item $y=\sqrt[3]{x}$
20 | \item $y=\frac{1}{x}$
21 | \item $y=2^{x}$
22 | \item $y=e^{x}$
23 | \item $y=\ln x$
24 | \item $y=\frac{1}{1+e^{-x}}$
25 | \item $y=\sin x$
26 | \item $y=\cos x$
27 | \item $y=\tan x$
28 | \end{multicols}
29 | \end{enumerate}
30 |
31 | \end{frame}
32 | \end{document}
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/example/ridesharing-innovation/images/README.md:
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1 | Note that these images are from the following sources:
2 |
3 | - `ridesharing_interface.png`: [https://www.ecolane.com/blog/ride-hailing-vs.-ride-sharing-the-key-difference-and-why-it-matters](https://www.ecolane.com/blog/ride-hailing-vs.-ride-sharing-the-key-difference-and-why-it-matters)
4 | - `ridesharing_illustration.jpg` & `ridesharing_allocation.jpg`: [https://edu.gcfglobal.org/en/sharingeconomy/what-is-ridesharing/1/](https://edu.gcfglobal.org/en/sharingeconomy/what-is-ridesharing/1/)
5 | - Other images are from Google image.
6 |
7 | In addition, we refer to wiki for summarizing content: [https://en.wikipedia.org/wiki/Ridesharing_company](https://en.wikipedia.org/wiki/Ridesharing_company)
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/example/ridesharing-innovation/images/lyft_logo.png:
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/example/ridesharing-innovation/images/ridesharing_illustration.jpg:
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/example/ridesharing-innovation/images/ridesharing_interface.png:
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/example/ridesharing-innovation/images/uber_brand.png:
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/example/ridesharing-innovation/slide.pdf:
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/example/ridesharing-innovation/slide.tex:
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1 | \documentclass[aspectratio=169]{beamer}
2 |
3 | \usepackage[utf8]{inputenc}
4 |
5 | \usepackage{graphicx}
6 | \usepackage{xcolor}
7 | \definecolor{light_red}{RGB}{209,105,81}
8 | \definecolor{light_blue}{RGB}{0,153,228}
9 |
10 | \setbeamertemplate{frametitle}[default][center]
11 | \setbeamertemplate{navigation symbols}{}
12 |
13 | \usepackage{tikz}
14 | \newcommand{\topline}{%
15 | \tikz[remember picture, overlay] {%
16 | \draw[gray, thick] ([xshift = 1cm, yshift = -1.2cm]current page.north west) -- ([xshift = -1cm, yshift = -1.2cm, xshift = \paperwidth]current page.north west);}}
17 |
18 | \begin{document}
19 |
20 | \begin{frame}
21 | \frametitle{\color{black}\textbf{Ridesharing Innovation}}
22 | \topline
23 |
24 | \vspace{-0.5em}
25 |
26 | \begin{tikzpicture}
27 |
28 | \pgfdeclareimage[width = 1.8cm]{img}{images/uber_brand.png}
29 | \node (img) at (-3.5, 1.1) {\pgfuseimage{img}};
30 |
31 | \pgfdeclareimage[width = 2.5cm]{img}{images/lyft_logo.png}
32 | \node (img) at (-3.5, -0.2) {\pgfuseimage{img}};
33 |
34 | \pgfdeclareimage[width = 2cm]{img}{images/didi_logo.png}
35 | \node (img) at (-3.5, -1.5) {\pgfuseimage{img}};
36 |
37 | \draw[thick, gray, opacity = 0.9] (-2, -1.8) -- (-2, 1.2);
38 |
39 | \pgfdeclareimage[height = 2.5cm]{img1}{images/ridesharing_interface.png}
40 | \node (img1) at (0, 0) {\pgfuseimage{img1}};
41 |
42 | \draw (1.9, 0) node[rotate = 0] {{\color{light_blue}\LARGE$\Rightarrow$}};
43 |
44 | \draw (0, -1.8) node {\scriptsize\fbox{\color{light_blue}\textbf{Request the vehicle}}};
45 |
46 | \pgfdeclareimage[height = 3.5cm]{img2}{images/ridesharing_allocation.jpg}
47 | \node (img2) at (3.5, 0) {\pgfuseimage{img2}};
48 |
49 | \draw (3.5, -2.2) node {\scriptsize\fbox{\color{light_blue}\textbf{Allocation}}};
50 |
51 | \draw (5.2, 0) node[rotate = 0] {{\color{light_blue}\LARGE$\Rightarrow$}};
52 |
53 | \pgfdeclareimage[height = 2.0cm]{img3}{images/ridesharing_illustration.jpg}
54 | \node (img3) at (7.6, 0) {\pgfuseimage{img3}};
55 |
56 | \draw (7.6, -1.5) node {\scriptsize\fbox{\color{light_blue}\textbf{Accept the request}}};
57 |
58 | \end{tikzpicture}
59 |
60 | \vspace{-1.2em}
61 | \noindent\rule[0ex]{\linewidth}{0.2pt}
62 |
63 | \vspace{0.5em}
64 | \begin{columns}
65 | \begin{column}{0.35\textwidth}
66 | \footnotesize
67 | \textbf{\color{light_red}Ridematching} programs:
68 | \vspace{-0.3em}
69 | \begin{itemize}
70 | \item[\color{gray}\textbullet] Began migrating to the Internet in {\color{light_blue}the late 1990s}.\vspace{-0.2em}
71 | \item[\color{gray}\textbullet] Achieved daily response by Federal Transit Administration (US) in {\color{light_blue}2006}.
72 | \end{itemize}
73 | \end{column}
74 |
75 | \begin{column}{0.37\textwidth}
76 | \footnotesize
77 | \textbf{\color{light_red}Ridesharing} ideas:
78 | \vspace{-0.3em}
79 | \begin{itemize}
80 | \item[\color{gray}\textbullet] {\color{light_blue}2002}: Hailing a ride via mobile app.\vspace{-0.2em}
81 | \item[\color{gray}\textbullet] {\color{light_blue}2007}: Intercity carpooling.
82 | \item[\color{gray}\textbullet] [Benefits] Reducing congestion, environmental footprint...
83 | \end{itemize}
84 | \end{column}
85 |
86 | \begin{column}{0.35\textwidth}
87 | \footnotesize
88 | \textbf{\color{light_red}Ridesharing} companies:
89 | \vspace{-0.3em}
90 | \begin{itemize}
91 | \item[\color{gray}\textbullet] {\color{light_blue}2009}: Uber was founded.\vspace{-0.2em}
92 | \item[\color{gray}\textbullet] {\color{light_blue}2011}: Sidecar was launched.\vspace{-0.2em}
93 | \item[\color{gray}\textbullet] {\color{light_blue}2012}: Lyft was launched.\vspace{-0.2em}
94 | \item[\color{gray}\textbullet] {\color{light_blue}2013}: California - 1st state regulate such companies.
95 | \end{itemize}
96 | \end{column}
97 | \end{columns}
98 |
99 | \end{frame}
100 |
101 | \end{document}
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/example/social-learning/images/Bandura.jpg:
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/example/social-learning/images/README.md:
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1 | Note that these images are from the following sources:
2 |
3 | - `Bandura.jpg`: [https://en.wikipedia.org/wiki/Albert_Bandura](https://en.wikipedia.org/wiki/Albert_Bandura)
4 | - `Chomsky.png`: [https://en.wikipedia.org/wiki/Noam_Chomsky](https://en.wikipedia.org/wiki/Noam_Chomsky)
5 | - `Skinner.jpg`: [https://en.wikipedia.org/wiki/B._F._Skinner](https://en.wikipedia.org/wiki/B._F._Skinner)
6 | - `bobo_doll.png` & `bobo_doll_experiment.jpg`: [https://en.wikipedia.org/wiki/Bobo_doll_experiment](https://en.wikipedia.org/wiki/Bobo_doll_experiment)
7 |
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/example/social-learning/slide.tex:
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1 | \documentclass{beamer}
2 |
3 | \usepackage[utf8]{inputenc}
4 |
5 | \usepackage{graphicx}
6 | \usepackage{xcolor}
7 | \definecolor{light_red}{RGB}{209,105,81}
8 | \definecolor{light_green}{RGB}{58,181,75}
9 | \definecolor{light_blue}{RGB}{0,153,228}
10 |
11 | \setbeamertemplate{frametitle}[default][center]
12 | \setbeamertemplate{navigation symbols}{}
13 | \setbeamerfont{footline}{series=\bfseries}
14 | \setbeamertemplate{footline}[page number]
15 |
16 | \usepackage{tikz}
17 | \newcommand{\topline}{%
18 | \tikz[remember picture, overlay] {%
19 | \draw[gray, thick] ([xshift = 1cm, yshift = -1.2cm]current page.north west) -- ([xshift = -1cm, yshift = -1.2cm, xshift = \paperwidth]current page.north west);}}
20 |
21 | \begin{document}
22 |
23 | \begin{frame}
24 | \frametitle{\color{light_red}\textbf{Background}}
25 | \topline
26 |
27 | \resizebox{11cm}{!}{
28 | \begin{tikzpicture}
29 |
30 | %%% B. F. Skinner %%%
31 | \pgfdeclareimage[height = 4cm]{skinner}{images/Skinner.jpg}
32 | \draw (0, 2.5) node {\color{light_red}\textbf{\large{Verbal Behavior}}};
33 | \node (skinner) at (0, 0) {\pgfuseimage{skinner}};
34 | \draw (0, -2.5) node {\large\textbf{B. F. Skinner}};
35 |
36 | \node [circle, line width = 1mm, draw = light_blue, fill = white, minimum size = 0.4cm] (node1) at (0, 3.2) {};
37 | \draw (0, 4) node {\Large\textbf{1940s}};
38 |
39 | %%% Social Learning book 1 %%%
40 | \node [circle, line width = 1mm, draw = light_blue, fill = white, minimum size = 0.4cm] (node2) at (5, 3.2) {};
41 | \draw (5, 4) node {\Large\textbf{1941}};
42 | \draw (5, 2.7) node {\color{light_red}\textbf{\large{Social Learning}}};
43 | \draw (5, 2.3) node {\color{light_red}\textbf{\large{Theory}}};
44 | \draw (5, 1.3) node {\large\textbf{Neil Miller}};
45 | \draw (5, 0.8) node {\large\textbf{John Dollard}};
46 |
47 | %%% Path between Skinner and Social Learning book 1 %%%
48 | \path [line width = 1mm, draw = light_blue, -] (node1) edge (node2);
49 |
50 | %%% Social Learning book 2 %%%
51 | \node [circle, line width = 1mm, draw = light_blue, fill = white, minimum size = 0.4cm] (node3) at (10, 3.2) {};
52 | \draw (10, 4) node {\Large\textbf{1954}};
53 | \draw (10, 2.7) node {\color{light_red}\textbf{\large{Social Learning}}};
54 | \draw (10, 2.3) node {\color{light_red}\textbf{\large{and Clinical Psychology}}};
55 | \draw (10, 1.3) node {\large\textbf{Julian B. Rotter}};
56 |
57 | %%% Path between book 1 and book 2 %%%
58 | \draw [line width = 1mm, draw = light_blue] (5.2, 3.2) -- (7.5, 3.2) -- (7.6, 3.5) -- (7.8, 2.9) -- (7.9, 3.2) -- (9.8, 3.2);
59 |
60 | %%% Noam Chomsky %%%
61 | \pgfdeclareimage[height = 4cm]{chomsky}{images/Chomsky.png}
62 | \node (chomsky) at (15, 0) {\pgfuseimage{chomsky}};
63 | \node [circle, line width = 1mm, draw = light_blue, fill = white, minimum size = 0.4cm] (node4) at (15, 3.2) {};
64 | \draw (15, 4) node {\Large\textbf{1959}};
65 | \draw (15, 2.7) node {\color{light_red}\textbf{\large{Criticism of}}};
66 | \draw (15, 2.3) node {\color{light_red}\textbf{\large{Verbal Behavior}}};
67 | \draw (15, -2.5) node {\large\textbf{Noam Chomsky}};
68 |
69 | %%% Path between book 2 and Chomsky %%%
70 | \draw [line width = 1mm, draw = light_blue] (5.2 + 5, 3.2) -- (7.5 + 5, 3.2) -- (7.6 + 5, 3.5) -- (7.8 + 5, 2.9) -- (7.9 + 5, 3.2) -- (9.8 + 5, 3.2);
71 |
72 | %%% Albert Bandura %%%
73 | \pgfdeclareimage[height = 4cm]{bandura}{images/Bandura.jpg}
74 | \node (bandura) at (20, 0) {\pgfuseimage{bandura}};
75 | \node [circle, line width = 1mm, draw = light_green, fill = white, minimum size = 0.4cm] (node5) at (20, 3.2) {};
76 | \draw (20, 4) node {\Large\textbf{1963}};
77 | \draw (20, 2.7) node {\color{light_red}\textbf{\large{Social Learning}}};
78 | \draw (20, 2.3) node {\color{light_red}\textbf{\large{Theory}}};
79 | \draw (20, -2.5) node {\large\textbf{Albert Bandura}};
80 |
81 | %%% Path between Chomsky and Bandura %%%
82 | \draw [line width = 1mm, draw = light_blue] (5.2 + 10, 3.2) -- (7.5 + 10, 3.2) -- (7.6 + 10, 3.5) -- (7.8 + 10, 2.9) -- (7.9 + 10, 3.2) -- (9.8 + 10, 3.2);
83 |
84 | %%% Path between Chomsky and Bandura %%%
85 | \draw [line width = 1mm, draw = light_green] (5.2 + 15, 3.2) -- (6.5 + 15, 3.2) -- (6.6 + 15, 3.5) -- (6.8 + 15, 2.9) -- (6.9 + 15, 3.2) -- (7.8 + 15, 3.2);
86 |
87 | \end{tikzpicture}
88 | }
89 |
90 | \noindent\rule[0ex]{\linewidth}{0.2pt}
91 |
92 | \vspace{0.8em}
93 |
94 | \small
95 |
96 | Contribution of Bandura's Theory:
97 |
98 | \vspace{0.5em}
99 |
100 | \centering
101 |
102 | \begin{tikzpicture}
103 | \draw (0, 0) node {\footnotesize\textbf{Social Learning = \fbox{Observational learning} + \fbox{Behavior learning}}};
104 | \draw (0, 1) node {\scriptsize{\textbf{\color{gray}Elements: \color{light_red}attention, retention, reproduction, motivation}}};
105 | \draw [very thick, draw = light_blue, ->] (0, 0.25) -- (0.5, 0.8);
106 |
107 | \draw (3, -1) node {\scriptsize{\textbf{\color{gray}Responses to \color{light_red}environmental stimuli}}};
108 | \draw [very thick, draw = light_blue, ->] (3, -0.25) -- (3.5, -0.8);
109 |
110 | \end{tikzpicture}
111 |
112 | \end{frame}
113 |
114 |
115 | \begin{frame}
116 | \frametitle{\color{light_red}\textbf{Bobo Doll Experiments}}
117 | \topline
118 |
119 | \begin{columns}
120 | \begin{column}{0.3\textwidth}
121 | \centering
122 | \includegraphics[scale = 0.2]{images/bobo_doll.png}
123 |
124 | \end{column}
125 | \begin{column}{0.7\textwidth}
126 | \centering
127 | \includegraphics[scale = 0.45]{images/bobo_doll_experiment.jpg}
128 | \end{column}
129 | \end{columns}
130 |
131 | \noindent\rule[0ex]{\linewidth}{0.2pt}
132 |
133 | \vspace{0.8em}
134 |
135 | \small
136 |
137 | Contribution of Bandura's Theory:
138 |
139 | \vspace{0.5em}
140 |
141 | \centering
142 |
143 | \begin{tikzpicture}
144 | \draw (0, 0) node {\footnotesize\textbf{Social Learning = \fbox{Observational learning} + \fbox{\color{gray}Behavior learning}}};
145 | \draw (0, 1) node {\scriptsize{\textbf{\color{gray}Elements: \color{light_red}attention, retention, reproduction, motivation}}};
146 | \draw [very thick, draw = light_blue, ->] (0, 0.25) -- (0.5, 0.8);
147 |
148 | \draw (3, -1) node {\scriptsize{\textbf{\color{gray}Responses to environmental stimuli}}};
149 | \draw [very thick, draw = gray, ->] (3, -0.25) -- (3.5, -0.8);
150 |
151 | \end{tikzpicture}
152 |
153 | \end{frame}
154 |
155 | \end{document}
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/example/tensor-factorization/slides.tex:
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1 | \documentclass{beamer}
2 |
3 | \usepackage[utf8]{inputenc}
4 | \usefonttheme{professionalfonts}
5 | \usepackage{tikz}
6 | \usetikzlibrary{bayesnet}
7 | \newcommand{\topline}{
8 | \tikz[remember picture, overlay] {
9 | \draw[gray, thick] ([xshift = 1cm, yshift = -1.2cm]current page.north west)
10 | -- ([xshift = -1cm, yshift = -1.2cm, xshift = \paperwidth]current page.north west);}}
11 |
12 | \setbeamertemplate{frametitle}[default][center]
13 | \setbeamertemplate{navigation symbols}{}
14 | \setbeamerfont{footline}{series = \bfseries}
15 | \setbeamertemplate{footline}[page number]
16 |
17 | \begin{document}
18 |
19 | \begin{frame}
20 | \frametitle{\color{black}\textbf{Tensor Factorization}}
21 | \topline
22 | \footnotesize
23 | {Bayesian treatment}\footnote{\scriptsize$\mathcal{N}(\cdot)$: Gaussian/Normal distribution; $\text{Gamma}(\cdot)$: Gamma distribution.}:
24 | \vspace{-2em}
25 | \begin{columns}
26 | \begin{column}{0.6\textwidth}
27 | \vspace{-15em}
28 |
29 | \uncover<1->{\scriptsize{Suppose that \emph{the observation follows Gaussian distribution}:
30 | \begin{equation*}
31 | y_{ijt}\sim\mathcal{N}\left(\sum_{r=1}^{R}u_{ir}v_{jr}x_{tr},\tau^{-1}\right),(i,j,t)\in\Omega.
32 | \end{equation*}
33 | }
34 | \uncover<2->{In the Bayesian setting, we place \emph{conjugate priors} on model parameters, i.e.,
35 | \begin{equation*}
36 | \begin{aligned}
37 | \boldsymbol{u}_{i}&\sim\mathcal{N}\left(\boldsymbol{\mu}_{u},\Lambda_{u}^{-1}\right),i=1,2,\ldots,M, \\
38 | \boldsymbol{v}_{j}&\sim\mathcal{N}\left(\boldsymbol{\mu}_{v},\Lambda_{v}^{-1}\right),j=1,2,\ldots,N, \\
39 | \boldsymbol{x}_{t}&\sim\mathcal{N}\left(\boldsymbol{\mu}_{x},\Lambda_{x}^{-1}\right),t=1,2,\ldots,T, \\
40 | \tau&\sim\text{Gamma}(\alpha,\beta). \\
41 | \end{aligned}
42 | \end{equation*}
43 | }
44 | }
45 | \end{column}
46 | \begin{column}[t]{0.35\textwidth}
47 | \begin{tikzpicture}
48 | \uncover<1->{\node[circle,draw=black,fill=gray!20,inner sep=0pt,minimum size=0.8cm] (obs) at (2,-1) {\small{$y_{ijt}$}};
49 | \node[circle,draw=black,fill=green!10] (ui) at (0.8,0) {\small{$\boldsymbol{u}_{i}$}};
50 | \node[circle,draw=black,fill=green!10] (vj) at (2,1) {\small{$\boldsymbol{v}_{j}$}};
51 | \node[circle,draw=black,fill=green!10] (xt) at (3.2,0) {\small{$\boldsymbol{x}_{t}$}};
52 | \node[circle,draw=black,fill=green!10] (tau) at (4.2,-1) {\small{$\tau$}};
53 | \path[draw=black,->] (ui) edge (obs);
54 | \path[draw=black,->] (vj) edge (obs);
55 | \path[draw=black,->] (xt) edge (obs);
56 | \path[draw=black,->] (tau) edge (obs);
57 | \node [text width=0.8cm] (m) at (1,-1.2) {\small{$M$}};
58 | \plate[] {plate1} {(obs)(ui)(m)} { };
59 | \node [text width=0.9cm] (n) at (2,-2.3) {\small{$N$}};
60 | \plate[] {plate2} {(obs)(vj)(n)} { };
61 | \node [text width=0.2cm] (f) at (3.2,-1.3) {\small{$T$}};
62 | \plate[] {plate3} {(obs)(xt)(f)} { };
63 | }
64 | \uncover<2->{\node[circle,draw=black,fill=red!10,inner sep=0pt,minimum size=0.7cm] (muv) at (1.3,2.2) {\small{$\boldsymbol{\mu}_{v}$}};
65 | \node[circle,draw=black,fill=red!10,inner sep=0pt,minimum size=0.7cm] (lambdav) at (2.7,2.2) {\small{$\Lambda_{v}$}};
66 | \node[text width=0.6cm] (gamma) at (4.2,0) {\small{$\alpha,\beta$}};
67 | \node[text width=0.4cm] (mu0) at (1.3,3.2) {\small{$\boldsymbol{\mu}_{0}$}};
68 | \node[text width=0.9cm] (wnu0) at (2.7,3.2) {\small{$W_{0},\nu_{0}$}};
69 | \node[text width=0.6cm] (cdots1) at (0.8,0.8) {\LARGE\color{red!50}{$\cdots$}};
70 | \node[text width=0.6cm] (cdots2) at (3.2,0.8) {\LARGE\color{red!50}{$\cdots$}};
71 | \path[draw=black,->] (muv) edge (vj);
72 | \path[draw=black,->] (lambdav) edge (vj);
73 | \path[draw=black,->] (lambdav) edge (muv);
74 | \path[draw=black,->] (mu0) edge (muv);
75 | \path[draw=black,->] (wnu0) edge (lambdav);
76 | \path[draw=black,->] (gamma) edge (tau);
77 | }
78 | \end{tikzpicture}
79 |
80 | \end{column}
81 | \end{columns}
82 |
83 | \end{frame}
84 |
85 | \end{document}
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/reading-notes/NYC_transportation/main.tex:
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1 | \documentclass{beamer}
2 |
3 | \usepackage[utf8]{inputenc}
4 | \usepackage{amsmath,amsthm}
5 | \usepackage{amssymb}
6 | \usepackage{bbm}
7 | \usepackage{amsfonts}
8 | \usepackage{wasysym}
9 |
10 | \usepackage{xcolor}
11 | \definecolor{lightred}{RGB}{209,105,81}
12 | \definecolor{lightgreen}{RGB}{58,181,75}
13 | \definecolor{thickblue}{RGB}{5,43,108}
14 | \definecolor{lightblue}{RGB}{0,153,228}
15 |
16 | \usepackage{graphicx}
17 | \graphicspath{ {./graphics/} }
18 |
19 | \usepackage{enumitem}
20 | \usepackage{pifont}
21 |
22 |
23 | \setbeamertemplate{frametitle}[default][center]
24 | \setbeamertemplate{navigation symbols}{}
25 | \setbeamerfont{footline}{series=\bfseries}
26 | \setbeamertemplate{footline}[page number]
27 |
28 | \usepackage{tikz}
29 | \newcommand{\topline}{%
30 | \tikz[remember picture,overlay] {%
31 | \draw[gray, thick] ([xshift=1cm,yshift=-1.2cm]current page.north west)
32 | -- ([xshift=-1cm,yshift=-1.2cm,xshift=\paperwidth]current page.north west);}}
33 |
34 |
35 | %Information to be included in the title page:
36 | \title{\color{lightred}\textbf{Transportation of New York}}
37 | \author{Xinyu Chen}
38 |
39 | \vspace{-10em}
40 | % \institute{Overleaf}
41 | \date{ }
42 |
43 |
44 |
45 | \begin{document}
46 |
47 | \begin{frame}
48 |
49 | \begin{center}
50 | {\color{lightred}\Large\textbf{Transportation of New York}}
51 |
52 | \vspace{2em}
53 |
54 | \textbf{\color{thickblue}Xinyu Chen}
55 | \end{center}
56 |
57 | % \titlepage
58 | \vspace{2em}
59 |
60 | \centering
61 |
62 | \includegraphics[scale=0.2]{graphics/citibike_travel.png}
63 | \includegraphics[scale=0.165]{graphics/nyc_bus.png}
64 |
65 | \end{frame}
66 |
67 |
68 | \begin{frame}
69 | \frametitle{\color{lightred}\textbf{Outline}}
70 | \topline
71 | {\color{black}
72 | \begin{itemize}[label=\ding{212}]
73 | \item Introduction
74 | \item Modal share
75 | \item Transportation systems
76 | \begin{itemize}[label=\ding{48}]
77 | \item {\small{Transit system}}
78 | \item {\small{Shared mobility}}
79 | % \item Private car
80 | % \item Pedestrian infrastructure
81 | \end{itemize}
82 | \item GHG emissions
83 | \item Traffic safety
84 | % \item Comparing New York to Montreal
85 | \item Travel behavior trend
86 | \item Uniqueness of transport
87 | \item Reference
88 | % \item A research article
89 | \end{itemize}
90 | }
91 | \end{frame}
92 |
93 |
94 | \begin{frame}
95 |
96 | \frametitle{\color{lightred}\textbf{Introduction}}
97 | \topline
98 |
99 | \begin{columns}
100 | \begin{column}{0.45\textwidth}
101 | \includegraphics[scale=0.3]{graphics/lady_liberty.jpg}
102 |
103 | \vspace{0.5em}
104 |
105 | \includegraphics[scale=0.48]{graphics/Midtown_Manhattan.jpg}
106 |
107 | \end{column}
108 | \begin{column}{0.55\textwidth}
109 |
110 | \textbf{\color{thickblue}New York City}
111 |
112 | \footnotesize
113 |
114 | - The \textbf{\color{lightred}most populous city} in the US
115 |
116 | - The \textbf{\color{lightred}most densely populated major city} in the US
117 |
118 | \centering
119 | \includegraphics[scale=0.28]{graphics/Empire_State_Building.jpg}
120 |
121 | \end{column}
122 | \end{columns}
123 |
124 | \end{frame}
125 |
126 |
127 | \begin{frame}
128 | \frametitle{\color{lightred}\textbf{Introduction}}
129 | \topline
130 |
131 | \textbf{\color{thickblue}New York City}
132 |
133 | {\footnotesize
134 |
135 | - \textbf{\color{black}784 $\text{km}^{2}$} \hspace{1em} - Population: \textbf{8.34 million} (2019)
136 | }
137 |
138 | \vspace{1em}
139 | {\centering\includegraphics[scale=0.2]{graphics/nyc_map.png}
140 | }
141 |
142 | \vspace{1em}
143 |
144 | \textbf{\color{thickblue}Montreal}
145 |
146 | {\footnotesize
147 |
148 | - \textbf{\color{black}432 $\text{km}^{2}$} \hspace{1em} - Population: \textbf{4.20} (2019)
149 | }
150 |
151 |
152 | \end{frame}
153 |
154 |
155 | \begin{frame}
156 | \frametitle{\color{lightred}\textbf{Introduction}}
157 | \topline
158 |
159 | \begin{columns}
160 | % \hspace{-2em}
161 | \begin{column}{0.8\textwidth}
162 | \includegraphics[scale=0.27]{graphics/nyc_mobility_stat1.png}\hspace{-0.4em}
163 | \includegraphics[scale=0.27]{graphics/nyc_mobility_stat2.png}
164 | \end{column}
165 |
166 | \hspace{-5em}
167 | \vspace{-15em}
168 | \begin{column}{0.4\textwidth}
169 |
170 | % \textbf{\color{thickblue}New York City}
171 |
172 | \textbf{\color{lightgreen}Growth in 1980-2010:}
173 | \begin{itemize}[label=\ding{212}]\footnotesize
174 | \item Population: \textbf{16\%}
175 | \item Employment: \textbf{12\%}
176 | \item Tourism: \textbf{187\%}
177 | \item Subway rideship: \textbf{59\%}
178 | \end{itemize}
179 | \end{column}
180 | \end{columns}
181 |
182 | \end{frame}
183 |
184 |
185 | \begin{frame}
186 | \frametitle{\textbf{\color{lightred}Modal share of NYC residents}}
187 | \topline
188 |
189 | \begin{columns}
190 | \begin{column}{0.5\textwidth}
191 |
192 | \includegraphics[scale=0.25]{graphics/modal_share.png}
193 |
194 | \end{column}
195 | \begin{column}{0.5\textwidth}
196 | \textbf{\color{thickblue}Findings}
197 |
198 | \vspace{1em}
199 | \footnotesize
200 |
201 | \begin{itemize}[label=\ding{48}]
202 | \item Subway/Railroad/Ferry is the largest mode among workers commuting outside of their borough of residence, except on Staten Island.
203 | \item In Queens and Staten Island, the plurality of workers use cars for commuting.
204 | \end{itemize}
205 | \end{column}
206 | \end{columns}
207 |
208 | \end{frame}
209 |
210 |
211 |
212 | \begin{frame}
213 |
214 | \frametitle{\color{lightred}\textbf{Transit system}}
215 | \topline
216 |
217 | \begin{columns}
218 | \begin{column}{0.4\textwidth}
219 | \textbf{\color{thickblue}Subway in NYC}
220 |
221 | {\footnotesize
222 |
223 | \begin{itemize}[label=\ding{212}]
224 | \item {\color{lightblue}6,600 subway cars}
225 | \item {\color{lightblue}472 subway stations}
226 | \item Daily rideship: $\approx$ {\color{lightblue}5.5 million}
227 | \item Annual rideship:
228 | \begin{itemize}[label=\ding{48}]
229 | \item {\color{lightblue}1.76 billion} (2015)
230 | \item {\color{lightblue}1.70 billion} (2019)
231 | \end{itemize}
232 | \end{itemize}
233 | }
234 |
235 | \textbf{\color{thickblue}Subway in Montreal}
236 |
237 | {\footnotesize
238 |
239 | \begin{itemize}[label=\ding{212}]
240 | \item {\color{lightblue}68 subway stations}
241 | \item Daily rideship: $\approx$ {\color{lightblue}1.4 million} (Q4 2018)
242 | \item Annual rideship: {\color{lightblue}0.35 billion} (2016)
243 | \end{itemize}
244 | }
245 |
246 | \end{column}
247 |
248 | \hspace{-3em}
249 |
250 | \begin{column}{0.6\textwidth}
251 | \includegraphics[scale=0.3]{graphics/subway_map.png}
252 | \end{column}
253 |
254 | \end{columns}
255 |
256 | \end{frame}
257 |
258 |
259 | \begin{frame}
260 |
261 | \frametitle{\color{lightred}\textbf{Transit system}}
262 | \topline
263 | \begin{columns}
264 | \begin{column}{0.45\textwidth}
265 | \textbf{\color{thickblue}Bus in NYC}
266 | {\footnotesize
267 | \begin{itemize}[label=\ding{48}]
268 | \item {\color{lightblue}5,927 vehicles} in the bus fleet
269 | \item All 100\% accessible to riders with disabilities
270 | \item {\color{lightblue}234 local bus routes}
271 | \item {\color{lightblue}20 Select Bus Service routes}
272 | \item {\color{lightblue}73 express routes}
273 | \item Annual rideship:
274 | \begin{itemize}[label=\ding{48}]
275 | \item {\color{lightblue}651 million} (2015)
276 | \item {\color{lightblue}557 million} (2019)
277 | \end{itemize}
278 |
279 | \end{itemize}
280 | }
281 |
282 | \textbf{\color{thickblue}Bus in Montreal}
283 | {\footnotesize
284 | \begin{itemize}[label=\ding{48}]
285 | \item {\color{lightblue}1,449 vehicles} in the bus fleet
286 | \item {\color{lightblue}220 bus lines}
287 | \item Annual rideship:
288 | \begin{itemize}[label=\ding{48}]
289 | \item {\color{lightblue}234 million} (2015)
290 | \item {\color{lightblue}223 million} (2017)
291 | \end{itemize}
292 |
293 | \end{itemize}
294 | }
295 |
296 | % \includegraphics[scale=0.5]{x}
297 | \end{column}
298 |
299 | \hspace{-4em}
300 |
301 | \begin{column}{0.55\textwidth}
302 | \begin{columns}
303 | \begin{column}{0.27\textwidth}
304 | \includegraphics[scale=0.25]{graphics/manhattan_bus_map.png}
305 | \end{column}
306 |
307 | \hspace{-3em}
308 |
309 | \begin{column}{0.27\textwidth}
310 | \includegraphics[scale=0.18]{graphics/bronx_bus_map.png}
311 | \includegraphics[scale=0.18]{graphics/brooklyn_bus_map.png}
312 | \end{column}
313 | \end{columns}
314 | \end{column}
315 |
316 | \end{columns}
317 |
318 | \end{frame}
319 |
320 |
321 |
322 |
323 | \begin{frame}
324 |
325 | \frametitle{\color{lightred}\textbf{Shared mobility}}
326 | \topline
327 |
328 | \centering
329 | \includegraphics[scale=0.34]{graphics/shared_mobility.png}
330 |
331 |
332 | \end{frame}
333 |
334 |
335 | \begin{frame}
336 |
337 | \frametitle{\color{lightred}\textbf{Shared mobility}}
338 | \topline
339 |
340 | \textbf{\color{thickblue}Ride-hailing}
341 |
342 | \vspace{1em}
343 |
344 | \includegraphics[scale=0.2]{graphics/taxi_pickup1.png}
345 | \includegraphics[scale=0.2]{graphics/taxi_pickup2.png}
346 |
347 | \vspace{1em}
348 |
349 | \footnotesize
350 |
351 | Over the past 4 years,
352 |
353 | - {\color{lightblue}ride-hailing apps have grown from 0 to 15 million trips per month}
354 |
355 | - {\color{lightblue}taxi usage has only declined by around 5 million trips per month}
356 |
357 | \end{frame}
358 |
359 |
360 |
361 | \begin{frame}
362 | \frametitle{\color{lightred}\textbf{Shared mobility}}
363 | \topline
364 |
365 | \textbf{\color{thickblue}Citi Bike}
366 |
367 | \vspace{1em}
368 |
369 | \begin{columns}
370 | \begin{column}{0.65\textwidth}
371 | \includegraphics[scale=0.14]{graphics/find_a_bike.png}
372 |
373 | \vspace{1em}
374 |
375 | \includegraphics[scale=0.22]{graphics/citibike.png}\hspace{1em}
376 | \includegraphics[scale=0.41]{graphics/citibike2.png}
377 | \end{column}
378 |
379 | \hspace{-5em}
380 |
381 | \begin{column}{0.45\textwidth}
382 | {\footnotesize
383 | \begin{itemize}[label=\ding{212}]
384 | \item The {\color{lightblue}nation's largest bike share} program.
385 | \item {\color{lightblue}15,000 bikes}
386 | \item {\color{lightblue}1,000+ stations}
387 | \end{itemize}
388 | }
389 |
390 | \vspace{1em}
391 |
392 | \textbf{\color{thickblue}Bikes in Montreal}
393 | {\footnotesize
394 | \begin{itemize}[label=\ding{212}]
395 | \item {\color{lightblue}540+ stations}
396 | \end{itemize}
397 | }
398 | \end{column}
399 | \end{columns}
400 |
401 |
402 | \end{frame}
403 |
404 |
405 | \begin{frame}
406 | \frametitle{\color{lightred}\textbf{Shared mobility}}
407 | \topline
408 |
409 | \textbf{\color{thickblue}Citi Bike}
410 |
411 | \vspace{1em}
412 |
413 | \begin{columns}
414 | \begin{column}{0.5\textwidth}
415 | \includegraphics[scale=0.25]{graphics/citibike_popular_road.png}
416 |
417 | \end{column}
418 |
419 | \hspace{-5em}
420 |
421 | \begin{column}{0.5\textwidth}
422 |
423 | \includegraphics[scale=0.25]{graphics/citibike_monthly_trips.png}
424 |
425 | \vspace{1em}
426 |
427 | \footnotesize
428 | \begin{itemize}[label=\ding{212}]
429 | \item {\color{lightblue}dramatically fewer rides during the cold winter months}
430 | \item {\color{lightblue}1,000,000+ rides in some months}
431 | % \item {\color{lightblue}The August 2015 increase in rides corresponds to the system’s first major expansion}
432 | \end{itemize}
433 | \end{column}
434 | \end{columns}
435 |
436 | \end{frame}
437 |
438 |
439 | \begin{frame}
440 | \frametitle{\color{lightred}\textbf{GHG emissions}}
441 | \topline
442 |
443 | \begin{columns}
444 | \begin{column}{0.7\textwidth}
445 | \centering
446 | \includegraphics[scale=0.24]{graphics/nyc_ghg.png}
447 |
448 | \hspace{1em}
449 |
450 | \includegraphics[scale=0.24]{graphics/nyc_ghg_transport.png}
451 |
452 | \end{column}
453 | \begin{column}{0.3\textwidth}
454 | \textbf{\color{thickblue}Findings}
455 |
456 | \footnotesize
457 | \vspace{1em}
458 |
459 | - {\color{lightblue}GHG emissions have reduced 15\%}
460 |
461 | - {\color{lightblue}On-road transport is the most remarkable factor for GHG emission in transportation}
462 |
463 | \end{column}
464 | \end{columns}
465 |
466 |
467 | \end{frame}
468 |
469 |
470 | \begin{frame}
471 | \frametitle{\color{lightred}\textbf{Traffic safety}}
472 | \topline
473 |
474 | \textbf{\color{lightred}Crash summary (severity)}
475 |
476 | \vspace{1em}
477 |
478 | {\centering{
479 | \footnotesize
480 | \begin{tabular}{l|rr|rr} \hline
481 | & \multicolumn{2}{c|}{New York State} & \multicolumn{2}{c}{New York City} \\
482 | & 2015 & 2019 & 2015 & 2019 \\ \hline
483 | Total & 251,142 & 418,687 & 41,632 & 121,091 \\
484 | Fatal & 1,045 & 881 & 232 & 205 \\
485 | Serious & 9,097 & 10,043 & 2,213 & 3,147 \\
486 | Moderate & 15,229 & 16,219 & 4,108 & 5,899 \\
487 | Minor & 75,084 & 85,527 & 24,184 & 35,982 \\
488 | Unk severity & 3,576 & 2,854 & 2,326 & 1,655 \\
489 | Property damage & 147,111 & 303,163 & 8,569 & 74,203 \\
490 | \hline
491 | \end{tabular}
492 | }}
493 |
494 |
495 | % {\centering{
496 | % \footnotesize
497 | % \begin{tabular}{l|ccccc} \hline
498 | % & Total & Fatal & Serious & Moderate & Minor & Unk \\ \hline
499 | % New York State (2015) & 294,556 & 1,045 & 113,396 & 180,115 \\
500 | % New York State (2019) & 447,021 & 881 & 121,068 & 325,072 \\
501 | % New York City (2015) & \\
502 | % \hline
503 | % \end{tabular}
504 | % }}
505 |
506 |
507 | \end{frame}
508 |
509 |
510 |
511 |
512 | \begin{frame}
513 |
514 | \frametitle{\color{lightred}\textbf{Travel behavior trend}}
515 | \topline
516 |
517 | % \textbf{\color{lightgreen}Drivers of travel}
518 |
519 | \begin{columns}
520 | % \hspace{-2em}
521 | \begin{column}{0.5\textwidth}
522 | \includegraphics[scale=0.27]{graphics/mobility1.png}\hspace{-0.1em}
523 | \includegraphics[scale=0.27]{graphics/mobility2.png}
524 | \end{column}
525 |
526 | % \hspace{-5em}
527 | \vspace{-15em}
528 | \begin{column}{0.5\textwidth}
529 |
530 | % \textbf{\color{thickblue}New York City}
531 |
532 | \textbf{\color{lightgreen}Trend}
533 | \begin{itemize}[label=\ding{212}]\footnotesize
534 | \item \textbf{\color{lightred}Subway ridership} {\color{lightblue}has grown an average of 2\% since 2010}.
535 | \item \textbf{\color{lightred}Bus rideship} {\color{lightblue}dropped 46 million passengers between 2010 and 2015}.
536 | \item \textbf{\color{lightred}Cycling} {\color{lightblue}increased by 80\% between 2010 and 2015 as bike infrastructure continued to expand on city streets}.
537 | \item \textbf{\color{lightred}Ferry ridership} {\color{lightblue}has fluctuated in recent years}.
538 | \end{itemize}
539 | \end{column}
540 | \end{columns}
541 |
542 |
543 |
544 |
545 |
546 | \end{frame}
547 |
548 |
549 | \begin{frame}
550 |
551 | \frametitle{\color{lightred}\textbf{Uniqueness of transport}}
552 | \topline
553 |
554 | \includegraphics[scale=0.27]{graphics/cv_technology.png}
555 |
556 | \vspace{1em}
557 |
558 | \footnotesize{New tool to help city {{\color{lightblue}eliminate traffic related deaths}} and {{\color{lightblue}reduce crash related injuries and damage to both the vehicles and infrastructure}}.}
559 |
560 |
561 | \end{frame}
562 |
563 |
564 |
565 |
566 | \begin{frame}
567 | \frametitle{\color{lightred}\textbf{Reference}}
568 | \topline
569 |
570 | Data and images are taken from:
571 |
572 | \footnotesize
573 |
574 | \begin{itemize}[label=\ding{48}]
575 | \item \url{https://www1.nyc.gov/assets/planning/download/pdf/plans/transportation/peripheral_travel_02e.pdf}
576 | \item \url{https://new.mta.info/agency/new-york-city-transit/subway-bus-ridership-2019}
577 | \item NYMTC: \url{https://www.nymtc.org/ABOUT-US/annual-reports}
578 | \item Citi Bike website: \url{https://www.citibikenyc.com/}
579 | \item Todd W. Schneider (2016). A tale of twenty-two million Citi Bike rides: Analyzing the NYC bike share system. [Blog post]
580 | \item NYC Connected Vehicle Project: \url{https://www.cvp.nyc/}
581 | \item ITSMR website: \url{https://www.itsmr.org/sas-guest-portal/}
582 | \item NYC Taxi \& Limousine Commission (TLC) website: \url{https://www1.nyc.gov/site/tlc/index.page}
583 | \item Todd W. Schneider (2015). Analyzing 1.1 billion NYC taxi and Uber trips with a vengeance. [Blog post]
584 | \item GHG emissions: \url{https://nyc-ghg-inventory.cusp.nyu.edu/}
585 | \item \url{http://tram.mcgill.ca/Teaching/srp/documents/NickC.pdf}
586 | \end{itemize}
587 |
588 | \end{frame}
589 |
590 |
591 | \begin{frame}
592 | % \frametitle{\color{black}\textbf{Summary}}
593 | % \topline
594 |
595 |
596 | \vspace{2em}
597 |
598 | \centering\Large {\textbf{\color{lightred}Thanks for your attention!}}
599 | \end{frame}
600 |
601 |
602 |
603 | \end{document}
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/reading-notes/deblurring-images-slides/main.tex:
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1 | \documentclass{beamer}
2 | \usepackage[utf8]{inputenc}
3 | \usefonttheme{professionalfonts}
4 | \usepackage{xcolor}
5 | \usepackage{graphicx}
6 | \usepackage{amsmath, amsthm, amssymb, amsfonts}
7 | \usepackage{bbm}
8 |
9 | \usepackage{tikz}
10 | \usepackage{pgfplots}
11 |
12 | \newcommand{\topline}{%
13 | \tikz[remember picture,overlay] {%
14 | \draw[gray, thick] ([xshift=1cm,yshift=-1.2cm]current page.north west)
15 | -- ([xshift=-1cm,yshift=-1.2cm,xshift=\paperwidth]current page.north west);}}
16 |
17 | \usepackage{caption}
18 | \usepackage{tabularx, booktabs}
19 | \usepackage{multirow}
20 | \usepackage{multicol}
21 |
22 | \definecolor{light_red}{RGB}{209,105,81}
23 | \definecolor{fair_red}{RGB}{237,27,47}
24 | \definecolor{light_green}{RGB}{58,181,75}
25 | \definecolor{thick_blue}{RGB}{5,43,108}
26 | \definecolor{fair_blue}{RGB}{0,112,192}
27 | \definecolor{light_blue}{RGB}{0,153,228}
28 | \definecolor{light_brown}{RGB}{132, 60, 11}
29 |
30 | \setbeamertemplate{frametitle}[default][center]
31 | \setbeamertemplate{navigation symbols}{}
32 | \setbeamerfont{footline}{series=\bfseries}
33 | \setbeamertemplate{footline}[page number]
34 |
35 | \setbeamertemplate{itemize items}[circle]
36 | \setbeamercolor{itemize item}{fg=black}
37 |
38 | \setbeamercolor{block title}{fg = black, bg = light_blue!40}
39 | \setbeamercolor{block body}{fg = black, bg = white}
40 | \setbeamertemplate{blocks}[rounded][shadow]
41 | \setbeamercolor{block title example}{fg = black, bg = orange!40}
42 | \setbeamercolor{block body example}{fg = black, bg = white}
43 |
44 | \setbeamercolor{block title alerted}{fg = black, bg = light_red!40}
45 | \setbeamercolor{section number projected}{bg=gray}
46 | \setbeamercolor{section number projected}{bg=gray}
47 | \setbeamercolor{subsection number projected}{bg=gray}
48 |
49 | \setbeamertemplate{footline}[frame number]{}
50 |
51 |
52 | \begin{document}
53 |
54 | \begin{frame}[plain]
55 |
56 | \begin{columns}
57 | \begin{column}{0.5\textwidth}
58 |
59 | \begin{center}
60 | {\color{black!80}\Large\textbf{Deblurring Images}
61 |
62 | \vspace{0.2em}
63 |
64 | \large\textbf{Matrices, Spectra, and Filtering}}
65 |
66 | \small
67 |
68 | \vspace{2em}
69 |
70 | \textbf{Xinyu Chen} ({\color{fair_blue}\url{https://xinychen.github.io}})
71 |
72 | \vspace{0.8em}
73 |
74 | {October 11, 2022}
75 |
76 | \end{center}
77 |
78 | \end{column}
79 |
80 | \begin{column}{0.5\textwidth}
81 |
82 | \begin{center}
83 | \includegraphics[scale=0.12]{graphics/book-cover.png}
84 | \end{center}
85 |
86 | \end{column}
87 | \end{columns}
88 |
89 | \end{frame}
90 |
91 | \begin{frame}[plain]
92 |
93 | \large
94 | \begin{itemize}
95 | \item[\color{black}$\circ$] \textbf{Chapter 1: The Image Deblurring Problem}
96 | \color{gray}
97 | \item[\color{gray}$\circ$] \textbf{Chapter 4: Structured Matrix Computations}
98 | \end{itemize}
99 |
100 | \end{frame}
101 |
102 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
103 | \topline
104 |
105 | About the image deblurring\footnote{The images and Matlab functions discussed in the book are available at {\color{fair_blue}\url{https://archive.siam.org/books/fa03/}}.}:
106 | \begin{itemize}\small
107 | \item \textbf{[Significance]} Image deblurring is fundamental in making pictures sharp and useful.
108 | \item \textbf{[General idea]} Recovering the original and sharp image by using a mathematical model of blurring process.
109 | \item \textbf{[Fact]} No hope to recover the original image exactly!
110 | \item \textbf{[Technical goal]} Develop efficient and reliable algorithms for recovering as much information as possible from the given data.
111 | \item \textbf{[Representation]} A digital image is a two- or three-dimensional array of numbers representing intensities on a grayscale or color scale.
112 | \end{itemize}
113 |
114 | \end{frame}
115 |
116 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
117 | \topline
118 |
119 | A blurred picture and simple linear model.
120 | \small
121 | \begin{itemize}
122 | \item \textbf{Sharp image} vs. \textbf{blurred image}
123 | \begin{center}
124 | \includegraphics[width=0.75\textwidth]{graphics/sharp-vs-blurred-images.png}
125 | \end{center}
126 | \item Notation: $\boldsymbol{X}\in\mathbb{R}^{m\times n}$ (desired \textbf{sharp} image) vs. $\boldsymbol{B}\in\mathbb{R}^{m\times n}$ (recorded \textbf{blurred} image)
127 | \item A simple linear model:
128 | \begin{itemize}\footnotesize
129 | \item[\color{black}$\circ$] Suppose the blurring of the columns in the image is independent of the blurring of the rows.
130 | \item[\color{black}$\circ$] \textbf{Bilinear relationship}: $\boxed{\boldsymbol{A}_{c}\boldsymbol{X}\boldsymbol{A}_{r}^\top=\boldsymbol{B}}$
131 | \end{itemize}
132 | \end{itemize}
133 |
134 | \end{frame}
135 |
136 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
137 | \topline
138 |
139 | A first attempt at deblurring.
140 | \small
141 | \begin{itemize}
142 | \item Recall that the simple linear model:
143 | \begin{equation}
144 | \boldsymbol{A}_{c}\boldsymbol{X}\boldsymbol{A}_{r}^\top=\boldsymbol{B}\quad\Longrightarrow\quad\boldsymbol{X}_{\text{naive}}=\boldsymbol{A}_{c}^{-1}\boldsymbol{B}(\boldsymbol{A}_{r}^{\top})^{-1}
145 | \end{equation}
146 | ignores several types of errors.
147 | \item Let
148 | \begin{equation}
149 | \boldsymbol{B}_{\text{exact}}=\boldsymbol{A}_{c}\boldsymbol{X}\boldsymbol{A}_{r}^\top
150 | \end{equation}
151 | be the ideal (noise-free) blurred image, ignoring all kinds of errors.
152 | \item Consider small random errors (noise) in the recorded blurred image:
153 | \begin{equation}
154 | \boldsymbol{B}=\boldsymbol{B}_{\text{exact}}+\boldsymbol{E}=\boldsymbol{A}_{c}\boldsymbol{X}\boldsymbol{A}_{r}^\top+\boldsymbol{E}
155 | \end{equation}
156 | where $\boldsymbol{E}\in\mathbb{R}^{m\times n}$ is the \textbf{noise image}.
157 | \end{itemize}
158 |
159 | \end{frame}
160 |
161 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
162 | \topline
163 |
164 | A first attempt at deblurring.
165 | \small
166 |
167 | \begin{exampleblock}{\footnotesize\textbf{The naive reconstruction}}
168 | Recall that
169 | \begin{equation}
170 | \begin{cases}
171 | \boldsymbol{X}_{\text{naive}}=\boldsymbol{A}_{c}^{-1}\boldsymbol{B}(\boldsymbol{A}_{r}^\top)^{-1} \\
172 | \boldsymbol{B}=\boldsymbol{B}_{\text{exact}}+\boldsymbol{E}=\boldsymbol{A}_{c}\boldsymbol{X}\boldsymbol{A}_{r}^\top+\boldsymbol{E}
173 | \end{cases}
174 | \end{equation}
175 | we therefore have the naive reconstruction:
176 | \begin{equation}
177 | \begin{aligned}
178 | \boldsymbol{X}_{\text{naive}}=&\boldsymbol{A}_{c}^{-1}\boldsymbol{B}(\boldsymbol{A}_{r}^{\top})^{-1} \\
179 | =&\boldsymbol{A}_{c}^{-1}\boldsymbol{B}_{\text{exact}}(\boldsymbol{A}_{r}^{\top})^{-1}+\boldsymbol{A}_{c}^{-1}\boldsymbol{E}(\boldsymbol{A}_{r}^{\top})^{-1} \\
180 | =&\boldsymbol{X}+\boldsymbol{A}_{c}^{-1}\boldsymbol{E}(\boldsymbol{A}_{r}^{\top})^{-1}
181 | \end{aligned}
182 | \end{equation}
183 |
184 | \end{exampleblock}
185 |
186 | \begin{itemize}
187 | \item The blurred image consists of two components: the first component is the \textbf{exact image}, and the second component is the \textbf{inverted noise}.
188 | \end{itemize}
189 |
190 | \end{frame}
191 |
192 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
193 | \topline
194 |
195 | A first attempt at deblurring.
196 | \small
197 | \begin{itemize}
198 | \item A simple test: \textbf{Exact image} $\boldsymbol{X}\in\mathbb{R}^{m\times n}$ vs. \textbf{blurred image} $\boldsymbol{B}\in\mathbb{R}^{m\times n}$
199 | \begin{center}
200 | \includegraphics[width=0.75\textwidth]{graphics/exact-vs-blurred-images.png}
201 | \end{center}
202 | \end{itemize}
203 |
204 | \end{frame}
205 |
206 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
207 | \topline
208 | \small
209 | \begin{alertblock}{\footnotesize\textbf{Lemma}}
210 | For the simple model $\boldsymbol{B}=\boldsymbol{A}_{c}\boldsymbol{X}\boldsymbol{A}_{r}^\top+\boldsymbol{E}$, the relative error in the naive reconstruction $\boldsymbol{X}_{\text{naive}}=\boldsymbol{A}_{c}^{-1}\boldsymbol{B}(\boldsymbol{A}_{r}^\top)^{-1}$ satisfies
211 | \begin{equation}
212 | \frac{\|\boldsymbol{X}_{\text{naive}}-\boldsymbol{X}\|_{F}}{\|\boldsymbol{X}\|_{F}}\leq \text{cond}(\boldsymbol{A}_{c})\cdot\text{cond}(\boldsymbol{A}_{r})\cdot\frac{\|\boldsymbol{E}\|_{F}}{\|\boldsymbol{B}\|_{F}}
213 | \end{equation}
214 | where $\|\cdot\|_{F}$ denotes the Frobenius norm\footnote{For any $\boldsymbol{X}\in\mathbb{R}^{m\times n}$, we have $\|\boldsymbol{X}\|_{F}=\sqrt{\sum_{i=1}^{m}\sum_{j=1}^{n}x_{ij}^2}$.}, and $\text{cond}(\cdot)$ denotes the conditional number\footnote{For any $\boldsymbol{A}\in\mathbb{R}^{N\times N}$ whose singular values are strictly positive, namely, $\sigma_1\geq\cdots\geq\sigma_N>0$, we have $\text{cond}(\boldsymbol{A})=\sigma_1/\sigma_N$.}.
215 | \end{alertblock}
216 |
217 | \end{frame}
218 |
219 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
220 | \topline
221 |
222 | Deblurring using a general linear model.
223 | \begin{itemize}\small
224 | \item In most situations, the blur is indeed \textbf{linear}, or at least well approximated by a linear model.
225 | \item A general linear model via \textbf{vectorization}.
226 | \begin{itemize}\footnotesize
227 | \item[\color{black}$\circ$] Given sharp image $\boldsymbol{X}\in\mathbb{R}^{m\times n}$ and blurred image $\boldsymbol{B}\in\mathbb{R}^{m\times n}$, since the blurring is assumed to be a linear operation, there must exist a large \textbf{blurring matrix} $\boldsymbol{A}\in\mathbb{R}^{N\times N}$ ($N=mn$) such that
228 | \begin{equation}
229 | \boldsymbol{A}\boldsymbol{x}=\boldsymbol{b}
230 | \end{equation}
231 | with
232 | \begin{equation}
233 | \boldsymbol{x}=\text{vec}(\boldsymbol{X})=\begin{bmatrix} \boldsymbol{x}_{1} \\ \vdots \\ \boldsymbol{x}_{n} \end{bmatrix}\in\mathbb{R}^{N},\quad\boldsymbol{b}=\text{vec}(\boldsymbol{B})=\begin{bmatrix}
234 | \boldsymbol{b}_{1} \\ \vdots \\ \boldsymbol{b}_{n} \end{bmatrix}\in\mathbb{R}^{N}
235 | \end{equation}
236 | \item[\color{black}$\circ$] The naive approach to image deblurring is simply to solve this linear algebraic system.
237 | \end{itemize}
238 | \end{itemize}
239 |
240 | \end{frame}
241 |
242 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
243 | \topline
244 |
245 | Deblurring using a general linear model.
246 | \small
247 | \begin{exampleblock}{\footnotesize\textbf{The naive reconstruction (matrix-form)}}
248 | Recall that
249 | \begin{equation}
250 | \begin{cases}
251 | \boldsymbol{X}_{\text{naive}}=\boldsymbol{A}_{c}^{-1}\boldsymbol{B}(\boldsymbol{A}_{r}^\top)^{-1} \\
252 | \boldsymbol{B}=\boldsymbol{B}_{\text{exact}}+\boldsymbol{E}=\boldsymbol{A}_{c}\boldsymbol{X}\boldsymbol{A}_{r}^\top+\boldsymbol{E}
253 | \end{cases}
254 | \end{equation}
255 | we therefore have the naive reconstruction:
256 | \begin{equation}
257 | \begin{aligned}
258 | \boldsymbol{X}_{\text{naive}}=&\boldsymbol{A}_{c}^{-1}\boldsymbol{B}(\boldsymbol{A}_{r}^{\top})^{-1} \\
259 | =&\boldsymbol{A}_{c}^{-1}\boldsymbol{B}_{\text{exact}}(\boldsymbol{A}_{r}^{\top})^{-1}+\boldsymbol{A}_{c}^{-1}\boldsymbol{E}(\boldsymbol{A}_{r}^{\top})^{-1} \\
260 | =&\boldsymbol{X}+\boldsymbol{A}_{c}^{-1}\boldsymbol{E}(\boldsymbol{A}_{r}^{\top})^{-1}
261 | \end{aligned}
262 | \end{equation}
263 |
264 | \end{exampleblock}
265 |
266 | \begin{exampleblock}{\footnotesize\textbf{The naive reconstruction (vector-form)}}
267 | Vectorize blurred image $\boldsymbol{B}$ and noise image $\boldsymbol{E}$ as $\boldsymbol{b}_{\text{exact}}=\text{vec}(\boldsymbol{B}_{\text{exact}})=\boldsymbol{A}\boldsymbol{x}$ and $\boldsymbol{e}=\text{vec}(\boldsymbol{E})$, respectively, then we have
268 | \begin{equation}
269 | \boldsymbol{x}_{\text{naive}}=\boldsymbol{A}^{-1}\boldsymbol{b}=\boldsymbol{A}^{-1}\boldsymbol{b}_{\text{exact}}+\boldsymbol{A}^{-1}\boldsymbol{e}=\boldsymbol{x}+\boldsymbol{A}^{-1}\boldsymbol{e}
270 | \end{equation}
271 | \end{exampleblock}
272 |
273 | \end{frame}
274 |
275 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
276 | \topline
277 |
278 | Deblurring using a general linear model.
279 |
280 | \small
281 | \begin{itemize}
282 | \item Relationship between matrix- and vector-form reconstruction:
283 | \begin{equation}
284 | \begin{aligned}
285 | \boldsymbol{X}_{\text{naive}}&=\boldsymbol{A}_{c}^{-1}\boldsymbol{B}(\boldsymbol{A}_{r}^{\top})^{-1} \\
286 | \Longrightarrow~\boldsymbol{x}_{\text{naive}}&=(\boldsymbol{A}_{r}^{-1}\otimes\boldsymbol{A}_{c}^{-1})\boldsymbol{b} \\
287 | &=(\boldsymbol{A}_{r}\otimes\boldsymbol{A}_{c})^{-1}\boldsymbol{b}
288 | \end{aligned}
289 | \end{equation}
290 | it therefore demonstrates that $\boldsymbol{A}\triangleq\boldsymbol{A}_{r}\otimes\boldsymbol{A}_{c}$.
291 | \item Property of Kronecker product $\otimes$:
292 | \begin{alertblock}{\footnotesize\textbf{Proposition}}
293 | Let $\boldsymbol{A}\in\mathbb{R}^{m\times m}$, $\boldsymbol{X}\in\mathbb{R}^{m\times n}$, and $\boldsymbol{B}\in\mathbb{R}^{n\times n}$ be three matrices commensurate from multiplication in that order, then it holds that
294 | \begin{equation}
295 | \text{vec}(\boldsymbol{A}\boldsymbol{X}\boldsymbol{B})=(\boldsymbol{B}^\top\otimes\boldsymbol{A})\text{vec}(\boldsymbol{X})
296 | \end{equation}
297 | \end{alertblock}
298 |
299 | \end{itemize}
300 |
301 | \end{frame}
302 |
303 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
304 | \topline
305 |
306 | Deblurring using a general linear model.
307 |
308 | \small
309 | \begin{alertblock}{\footnotesize\textbf{Singular value decomposition (SVD)}}
310 | For any $\boldsymbol{A}\in\mathbb{R}^{N\times N}$ whose singular values are strictly positive, we have
311 | \begin{equation}
312 | \boldsymbol{A}=\boldsymbol{U}\boldsymbol{\Sigma}\boldsymbol{V}^\top=\sum_{i=1}^{N}\sigma_{i}\boldsymbol{u}_{i}\boldsymbol{v}_{i}^\top\quad\Longrightarrow\quad\boldsymbol{A}^{-1}=\sum_{i=1}^{N}\frac{1}{\sigma_{i}}\boldsymbol{u}_{i}\boldsymbol{v}_{i}^\top
313 | \end{equation}
314 | \end{alertblock}
315 |
316 | \begin{exampleblock}{\footnotesize\textbf{The naive reconstruction with SVD}}
317 | The naive reconstruction can be written as follows,
318 | \begin{equation}
319 | \boldsymbol{x}_{\text{naive}}=\boldsymbol{A}^{-1}\boldsymbol{b}=\boldsymbol{V}\boldsymbol{\Sigma}^{-1}\boldsymbol{U}^\top\boldsymbol{b}=\sum_{i=1}^{N}\frac{\boldsymbol{u}_{i}^\top\boldsymbol{b}}{\sigma_i}\boldsymbol{v}_{i}
320 | \end{equation}
321 | in which the inverted noise is
322 | \begin{equation}
323 | \boldsymbol{A}^{-1}\boldsymbol{e}=\boldsymbol{V}\boldsymbol{\Sigma}^{-1}\boldsymbol{U}^\top\boldsymbol{e}=\sum_{i=1}^{N}\frac{\boldsymbol{u}_{i}^\top\boldsymbol{e}}{\sigma_i}\boldsymbol{v}_{i}
324 | \end{equation}
325 | \end{exampleblock}
326 |
327 | \end{frame}
328 |
329 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
330 | \topline
331 |
332 | Deblurring using a general linear model.
333 |
334 | \small
335 |
336 | \begin{itemize}
337 | \item Recall that the inverted noise is
338 | \begin{equation*}
339 | \boldsymbol{A}^{-1}\boldsymbol{e}=\boldsymbol{V}\boldsymbol{\Sigma}^{-1}\boldsymbol{U}^\top\boldsymbol{e}=\sum_{i=1}^{N}\frac{\boldsymbol{u}_{i}^\top\boldsymbol{e}}{\sigma_i}\boldsymbol{v}_{i}
340 | \end{equation*}
341 | \item Properties for image deblurring problems:
342 | \begin{itemize}\footnotesize
343 | \item[\color{black}$\circ$] The error components $|\boldsymbol{u}_{i}^\top\boldsymbol{e}|$ are small and typically of roughly the same order of magnitude for all $i$.
344 | \item[\color{black}$\circ$] The singular values decay to a value very close to zero. As a consequence, the condition number $\text{cond}(\boldsymbol{A})=\sigma_1/\sigma_N$ is very large, indicating that \textbf{the solution is very sensitive to perturbation and rounding errors}.
345 | \item[\color{black}$\circ$] \textbf{The singular vectors corresponding to the smaller singular values typically represent high-frequency information}. That is, as $i$ increases, the vectors $\boldsymbol{u}_{i}$ and $\boldsymbol{v}_{i}$ tend to have more sign changes.
346 | \end{itemize}
347 | \end{itemize}
348 |
349 | \end{frame}
350 |
351 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
352 | \topline
353 |
354 | Deblurring using a general linear model.
355 |
356 | \small
357 |
358 | \begin{itemize}
359 | \item Recall that the inverted noise is
360 | \begin{equation*}
361 | \boldsymbol{A}^{-1}\boldsymbol{e}=\boldsymbol{V}\boldsymbol{\Sigma}^{-1}\boldsymbol{U}^\top\boldsymbol{e}=\sum_{i=1}^{N}\frac{\boldsymbol{u}_{i}^\top\boldsymbol{e}}{\sigma_i}\boldsymbol{v}_{i}
362 | \end{equation*}
363 | \end{itemize}
364 |
365 | \begin{exampleblock}{\footnotesize\textbf{Remark}}
366 | For $\boldsymbol{A}^{-1}\boldsymbol{e}$, the quantities $\boldsymbol{u}_{i}^\top\boldsymbol{e}/\sigma_i$ are the expansion coefficients for the basis vectors $\boldsymbol{v}_{i}$. When these quantities are small in magnitude, the solution has very little contribution from $\boldsymbol{v}_{i}$, but when we divide by a small singular values such as $\sigma_N$, we greatly magnify the corresponding error component $\boldsymbol{u}_{N}^\top\boldsymbol{e}$ which in turn contributes a large multiple of the high-frequency information contained in $\boldsymbol{v}_{N}$ to the reconstruction solution.
367 | \end{exampleblock}
368 |
369 | \begin{itemize}
370 | \item Thus, we can remove the high-frequency components that are dominated by error.
371 | \end{itemize}
372 | \end{frame}
373 |
374 | \begin{frame}{\color{black}\textbf{The Image Deblurring Problem}}
375 | \topline
376 |
377 | Deblurring using a general linear model.
378 | \small
379 | \begin{itemize}
380 | \item The naive reconstruction with SVD:
381 | \begin{equation}
382 | \boldsymbol{x}_{\text{naive}}=\sum_{i=1}^{N}\frac{\boldsymbol{u}_{i}^\top\boldsymbol{b}}{\sigma_i}\boldsymbol{v}_{i}
383 | \end{equation}
384 | \item The truncated expansion with $k] (0, 0.25) -- (0.5, 0.8);
179 |
180 | \draw (3, -1) node {\scriptsize{\textbf{\color{gray}Responses to \color{light_red}environmental stimuli}}};
181 | \draw [very thick, draw = light_blue, ->] (3, -0.25) -- (3.5, -0.8);
182 |
183 | \end{tikzpicture}
184 |
185 | \end{frame}
186 |
187 |
188 | \begin{frame}
189 | \frametitle{\color{light_red}\textbf{Bobo Doll Experiments}}
190 | \topline
191 |
192 | \begin{columns}
193 | \begin{column}{0.3\textwidth}
194 | \centering
195 | \includegraphics[scale = 0.2]{graphics/bobo_doll.png}
196 |
197 | \end{column}
198 | \begin{column}{0.7\textwidth}
199 | \centering
200 | \includegraphics[scale = 0.45]{graphics/bobo_doll_experiment.jpg}
201 | \end{column}
202 | \end{columns}
203 |
204 | \noindent\rule[0ex]{\linewidth}{0.2pt}
205 |
206 | \vspace{0.8em}
207 |
208 | \small
209 |
210 | \pause
211 |
212 | {\color{black}Contribution of Bandura's Theory:}
213 |
214 | \vspace{0.5em}
215 |
216 | \centering
217 |
218 | \begin{tikzpicture}
219 | \draw (0, 0) node {\footnotesize\textbf{Social Learning = \fbox{Observational learning} + \fbox{\color{gray}Behavior learning}}};
220 | \draw (0, 1) node {\scriptsize{\textbf{\color{gray}Elements: \color{light_red}attention, retention, reproduction, motivation}}};
221 | \draw [very thick, draw = light_blue, ->] (0, 0.25) -- (0.5, 0.8);
222 |
223 | \draw (3, -1) node {\scriptsize{\textbf{\color{gray}Responses to environmental stimuli}}};
224 | \draw [very thick, draw = gray, ->] (3, -0.25) -- (3.5, -0.8);
225 |
226 | \end{tikzpicture}
227 |
228 | \end{frame}
229 |
230 |
231 | \begin{frame}
232 | \frametitle{\color{light_red}\textbf{People Can Learn Through Observation}}
233 | \topline
234 |
235 | % \centering
236 | \begin{center}
237 | \includegraphics[width = 0.85\textwidth]{graphics/use_chopsticks.png}
238 | \end{center}
239 |
240 | \vspace{0.5em}
241 |
242 | \pause
243 |
244 | \footnotesize
245 | \textbf{\color{gray}Elements of social learning:}
246 | \scriptsize
247 | \begin{itemize}
248 | \item[\ding{212}] \textbf{\color{light_red}Attention:} {\color{light_blue}\scriptsize{Dedicate attention to learning.}}
249 | \item[\ding{212}] \textbf{\color{light_red}Retention:} {\color{light_blue}\scriptsize{Ability to store information.}}
250 | \item[\ding{212}] \textbf{\color{light_red}Reproduction:} {\color{light_blue}\scriptsize{Perform the behavior you observed.}}
251 | \item[\ding{212}] \textbf{\color{light_red}Motivation:} {\color{light_blue}\scriptsize{Be motivated to imitate the behavior that has been modeled.}}
252 | \end{itemize}
253 |
254 | \end{frame}
255 |
256 |
257 | \begin{frame}
258 |
259 | \frametitle{\color{light_red}\textbf{- Sustainable Transport Innovations}}
260 | \topline
261 |
262 | {\footnotesize\color{thick_blue}\textbf{- Sustainable transport projects} (Netherlands)\footnote{\scriptsize{\color{black!75}J.C.J.M. van den Bergh et al., Social learning by doing in sustainable transport innovations: Ex-post analysis of common factors behind successes and failures. Research Policy, 2007, 36: 247-259.}}:}
263 |
264 | \vspace{0.5em}
265 |
266 | \resizebox{10.5cm}{!}{
267 | \begin{tikzpicture}
268 | \draw (0, 0.75) node {\small\textbf{\color{thick_blue}-}};
269 | \draw (0, 0) node {\scriptsize\textbf{\color{light_blue}Public transport travel info.}};
270 | \draw (0, -0.5) node {\scriptsize\textbf{\color{light_blue}Traintaxi}};
271 | \draw (0, -1.0) node {\scriptsize\textbf{\color{light_blue}Catalytic converter}};
272 | \draw [very thick, draw = gray, dashed] (2.5, 0.5) -- (2.5, -1.0);
273 |
274 | \draw (5, 0.75) node {\small\textbf{\color{thick_blue}-}};
275 | \draw (5, 0) node {\scriptsize\textbf{\color{light_red}Autodate}};
276 | \draw (5, -0.5) node {\scriptsize\textbf{\color{light_red}Leiden park \& ride}};
277 | \draw (5, -1.0) node {\scriptsize\textbf{\color{light_red}Public transport pass for students}};
278 | \draw [very thick, draw = gray, dashed] (7.5, 0.5) -- (7.5, -1.0);
279 |
280 | \draw (10, 0.75) node {\small\textbf{\color{thick_blue}-}};
281 | \draw (10, -0.25) node {\scriptsize\textbf{\color{gray}Electronic road pricing}};
282 | \draw (10, -0.75) node {\scriptsize\textbf{\color{gray}Alternating carpool lane}};
283 |
284 | \end{tikzpicture}
285 | }
286 |
287 | \vspace{-0.2em}
288 |
289 | \noindent\rule[0ex]{\linewidth}{0.2pt}
290 |
291 | \vspace{0.5em}
292 |
293 | {\footnotesize\color{thick_blue}\textbf{- How to do?}}
294 |
295 | \begin{itemize}\footnotesize
296 | \item[\ding{212}] {\color{fair_blue}Identify sustainable transport innovation projects}
297 | \item[\ding{212}] {\color{fair_blue}Define factors} {\scriptsize\color{gray}(e.g., technological, administrative, political, economic)}
298 | \item[\ding{212}] {\color{fair_blue}Collect data from interviewees}
299 | \item[\ding{212}] {\color{fair_blue}Apply social learning mechanism}
300 | \end{itemize}
301 |
302 | \end{frame}
303 |
304 |
305 | \begin{frame}
306 |
307 | \frametitle{\color{light_red}\textbf{- Sustainable Transport Innovations}}
308 | \topline
309 |
310 | {\footnotesize\color{thick_blue}\textbf{- Sustainable transport projects} (Netherlands)\footnote{\scriptsize{\color{black!75}J.C.J.M. van den Bergh et al., Social learning by doing in sustainable transport innovations: Ex-post analysis of common factors behind successes and failures. Research Policy, 2007, 36: 247-259.}}:}
311 |
312 | \vspace{0.5em}
313 |
314 | \resizebox{11cm}{!}{
315 | \begin{tikzpicture}
316 | \draw (0, 0.75) node {\small\textbf{\color{thick_blue}Success}};
317 | \draw (0, 0) node {\scriptsize\textbf{\color{light_blue}Public transport travel info.}};
318 | \draw (0, -0.5) node {\scriptsize\textbf{\color{light_blue}Traintaxi}};
319 | \draw (0, -1.0) node {\scriptsize\textbf{\color{light_blue}Catalytic converter}};
320 | \draw [very thick, draw = gray, dashed] (2.5, 0.5) -- (2.5, -1.0);
321 |
322 | \draw (5, 0.75) node {\small\textbf{\color{thick_blue}Ambiguous}};
323 | \draw (5, 0) node {\scriptsize\textbf{\color{light_red}Autodate}};
324 | \draw (5, -0.5) node {\scriptsize\textbf{\color{light_red}Leiden park \& ride}};
325 | \draw (5, -1.0) node {\scriptsize\textbf{\color{light_red}Public transport pass for students}};
326 | \draw [very thick, draw = gray, dashed] (7.5, 0.5) -- (7.5, -1.0);
327 |
328 | \draw (10, 0.75) node {\small\textbf{\color{thick_blue}Failure}};
329 | \draw (10, -0.25) node {\scriptsize\textbf{\color{gray}Electronic road pricing}};
330 | \draw (10, -0.75) node {\scriptsize\textbf{\color{gray}Alternating carpool lane}};
331 |
332 | \end{tikzpicture}
333 | }
334 |
335 | \vspace{-0.2em}
336 |
337 | \noindent\rule[0ex]{\linewidth}{0.2pt}
338 |
339 | \vspace{0.5em}
340 |
341 | {\footnotesize\color{thick_blue}\textbf{- Findings by using social learning:}}
342 |
343 | \begin{itemize}\footnotesize
344 | \item[\ding{212}] {\color{fair_blue}Predominant factors:{\color{gray}\scriptsize Political, process-related, socio-cultural, and psychological factors}}
345 | \item[\ding{212}]{\color{fair_blue}Less important factors:{\color{gray}\scriptsize Technical and economic factors}}
346 | \item[\ding{212}] {\color{fair_blue}Communication is an important element of social learning to foster innovations.}
347 | \end{itemize}
348 |
349 | \end{frame}
350 |
351 |
352 | % \begin{frame}
353 |
354 | % \frametitle{\color{light_red}\textbf{Modeling Travellers' Change of Behaviour}}
355 | % \topline
356 |
357 | % Incorporating social interaction and social learning in modeling ...
358 |
359 | % Social interaction is a medium for social learning to happen.
360 |
361 | % - 1st level: an interdependent situation where travellers are in a similar transport system with other travellers.
362 |
363 | % - 2nd level: happen through observation by a traveller of other travellers' choices without involving processes of communications.
364 |
365 | % Social learning: Individuals learn from others' experiences or observed behaviours.
366 |
367 | % Uncertainty:
368 |
369 | % - Effects of natural events (e.g., rain, snow)
370 |
371 | % - Effects of human-made events (e.g., accidents, roadworks)
372 |
373 | % - Travellers' choices
374 |
375 | % Uncertainties contribute to the complex and dynamic process of travel behavioural change
376 |
377 | % \end{frame}
378 |
379 |
380 | % \begin{frame}
381 | % \frametitle{\color{light_red}\textbf{Modeling Travellers' Change of Behavior}}
382 | % \topline
383 |
384 | % \textbf{\color{light_green}Laboratory experiment:}
385 |
386 | % \begin{itemize}\footnotesize
387 | % \item[\ding{212}] Computer interface based on Z-tree
388 | % \item[\ding{212}] Simulates a repeated decision-making environments.
389 | % \item[\ding{212}] Whether or not contribute to an employer-based demand management initiative to reduce employees' car-use.
390 | % \item[\ding{212}] Two schemes of social information about other participants' behaviour.
391 | % \end{itemize}
392 |
393 | % \textbf{\color{light_green}Simulation experiment:}
394 |
395 | % \begin{itemize}\footnotesize
396 | % \item[\ding{212}] A larger system with more individuals
397 | % \item[\ding{212}] Individual layer + interaction layer
398 | % \end{itemize}
399 |
400 |
401 | % \end{frame}
402 |
403 |
404 | \begin{frame}
405 | \frametitle{\textbf{\color{light_red}A Potential Research Idea}}
406 | \topline
407 |
408 | \begin{columns}
409 | \begin{column}{0.3\textwidth}
410 | \centering
411 | \includegraphics[scale = 0.2]{graphics/wechat.png}
412 | \end{column}
413 | \begin{column}{0.6\textwidth}
414 | \centering
415 | \includegraphics[scale = 0.28]{graphics/congested_taxi.jpeg}
416 | \end{column}
417 | \end{columns}
418 |
419 | \vspace{0.5em}
420 |
421 | \noindent\rule[0ex]{\linewidth}{0.2pt}
422 |
423 | \vspace{0.2em}
424 |
425 | \begin{block}{\color{black}\footnotesize[Idea] {\color{light_red}\textbf{Social learning and social network of taxi drivers}}\footnote{\scriptsize{\color{black!75}Y. Sunitiyoso, et al., On the potential for recognising of social interaction and social learning in modelling travellers’ change of behaviour under uncertainty. Transportmetrica, 2011, 7(1): 5-30.}}}
426 | \vspace{0.5em}
427 | \color{light_blue}
428 | \beamergotobutton{Idea from} \footnotesize In China, it is very common that taxi drivers have some certain Wechat teams for \textbf{communication}. They share and discuss \textbf{travel demands} and \textbf{traffic conditions} with other taxi drivers on Wechat.
429 | \end{block}
430 |
431 | \vspace{0.3em}
432 |
433 | \footnotesize[Question] {\color{light_red}Can social learning and social network help \textbf{improve the income of taxi drivers}?}
434 |
435 | \end{frame}
436 |
437 |
438 | \begin{frame}
439 | \frametitle{\color{lightred}\textbf{Reference}}
440 | \topline
441 |
442 | \footnotesize
443 | \begin{enumerate}
444 | \item Social learning on wikipedia. [\href{https://en.wikipedia.org/wiki/Social_learning_theory}{\color{blue!80!black}website}]
445 | \item Bobo doll experiment on wikipedia. [\href{https://en.wikipedia.org/wiki/Bobo_doll_experiment}{\color{blue!80!black}website}]
446 | \item How social learning theory works. [\href{https://www.verywellmind.com/social-learning-theory-2795074}{\color{blue!80!black}post}]
447 | \item How observational learning affects behavior. [\href{https://www.verywellmind.com/what-is-observational-learning-2795402}{\color{blue!80!black}post}]
448 | \item J.C.J.M. van den Bergh et al., Social learning by doing in sustainable transport innovations: Ex-post analysis of common factors behind successes and failures. Research Policy, 2007, 36: 247-259.
449 | \item Y. Sunitiyoso, et al., On the potential for recognising of social interaction and social learning in modelling travellers’ change of behaviour under uncertainty. Transportmetrica, 2011, 7(1): 5-30.
450 | \end{enumerate}
451 |
452 | \end{frame}
453 |
454 |
455 | \begin{frame}
456 |
457 | \vspace{2em}
458 |
459 | \centering\Large {\textbf{\color{lightred}Thanks for your attention!}}
460 |
461 | % \vspace{0.5em}
462 |
463 | % \footnotesize
464 | % {\color{gray}LaTeX codes for creating these slides are publicly available at:}
465 |
466 | \end{frame}
467 |
468 |
469 |
470 | \end{document}
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