├── classification ├── README.md ├── svm.py ├── .gitignore ├── util.py ├── titanic_test.csv └── titanic_train.csv ├── clustering ├── clusters.png ├── README.md ├── tututils.py └── Clustering and Latent Variable Models.ipynb ├── Intro and PCA ├── requirements.txt ├── README.md └── sample-clusters.csv ├── Linear Regression ├── README.md ├── cars_stopping_dist.npz └── LICENSE ├── Dependency checker.ipynb ├── README.md ├── .gitignore └── LICENSE /classification/README.md: -------------------------------------------------------------------------------- 1 | mlss_classification 2 | =================== 3 | -------------------------------------------------------------------------------- /clustering/clusters.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/NICTA/MLSS/HEAD/clustering/clusters.png -------------------------------------------------------------------------------- /Intro and PCA/requirements.txt: -------------------------------------------------------------------------------- 1 | scikit-learn 2 | numpy 3 | matplotlib 4 | scipy 5 | ipython[all] 6 | -------------------------------------------------------------------------------- /Linear Regression/README.md: -------------------------------------------------------------------------------- 1 | # linearRegressionTutorial 2 | Linear Regression Tutorial in iPython Notebook 3 | -------------------------------------------------------------------------------- /Linear Regression/cars_stopping_dist.npz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/NICTA/MLSS/HEAD/Linear Regression/cars_stopping_dist.npz -------------------------------------------------------------------------------- /classification/svm.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | from sklearn import svm 3 | from sklearn.cross_validation import KFold 4 | 5 | import util 6 | 7 | X, Y = util.load_data() 8 | 9 | Xd = X - np.mean(X,axis=0) 10 | Xs = (Xd/np.std(Xd,axis=0)) 11 | Xw = np.dot(Xd, util.whitening_matrix(Xd)) 12 | 13 | # >>> kf = KFold(4, n_folds=2, shuffle=True) 14 | # >>> for train, test in kf: 15 | 16 | # fit the model 17 | clf = svm.NuSVC() 18 | clf.fit(Xw, Y) 19 | 20 | query = util.plot_svm(Xw, Y, clf, 0, 1, (-3,-3), (3,3), (500,500)) 21 | 22 | 23 | -------------------------------------------------------------------------------- /classification/.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | 5 | # C extensions 6 | *.so 7 | 8 | # Distribution / packaging 9 | .Python 10 | env/ 11 | bin/ 12 | build/ 13 | develop-eggs/ 14 | dist/ 15 | eggs/ 16 | lib/ 17 | lib64/ 18 | parts/ 19 | sdist/ 20 | var/ 21 | *.egg-info/ 22 | .installed.cfg 23 | *.egg 24 | 25 | # Installer logs 26 | pip-log.txt 27 | pip-delete-this-directory.txt 28 | 29 | # Unit test / coverage reports 30 | htmlcov/ 31 | .tox/ 32 | .coverage 33 | .cache 34 | nosetests.xml 35 | coverage.xml 36 | 37 | # Translations 38 | *.mo 39 | 40 | # Mr Developer 41 | .mr.developer.cfg 42 | .project 43 | .pydevproject 44 | 45 | # Rope 46 | .ropeproject 47 | 48 | # Django stuff: 49 | *.log 50 | *.pot 51 | 52 | # Sphinx documentation 53 | docs/_build/ 54 | 55 | .ipynb_checkpoints 56 | -------------------------------------------------------------------------------- /clustering/README.md: -------------------------------------------------------------------------------- 1 | #Clustering and Latent Variable Models Tutorial for MLSS 2015 2 | 3 | **Authors**: [Daniel Steinberg](http://www.daniel-steinberg.info/) & [Brian Thorne](http://hardbyte.bitbucket.org/) 4 | 5 | **Institute**: [NICTA](https://www.nicta.com.au/) 6 | 7 | The main tutorial notebook is the file `Clustering and Latent Variable 8 | Models.ipynb`, and the worked solutions can be found in the file `Clustering 9 | and Latent Variable Models - SOLUTIONS.ipynb`. 10 | 11 | You can view the solutions online [here at nbviewer](http://nbviewer.ipython.org/github/NICTA/MLSS/blob/master/clustering/Clustering%20and%20Latent%20Variable%20Models%20-%20SOLUTIONS.ipynb). 12 | 13 | ## File manifest 14 | * `Clustering and Latent Variable Models.ipynb` - the tutorial 15 | * `Clustering and Latent Variable Models - SOLUTIONS.ipynb` - solutions 16 | * `kmeans-image.ipynb` - image compression example 17 | * `tututils.py` - data generation and plotting utilities for the tutorial 18 | 19 | ## Dependencies 20 | * scikit-learn 21 | * numpy 22 | * matplotlib 23 | * scipy 24 | * ipython[all] 25 | * lda (this may also require pbr) 26 | * Pillow 27 | -------------------------------------------------------------------------------- /Dependency checker.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "metadata": { 3 | "name": "", 4 | "signature": "sha256:589fdba333971308108be52102372cc37ac7acc894b57d037e514d0e5c17ec73" 5 | }, 6 | "nbformat": 3, 7 | "nbformat_minor": 0, 8 | "worksheets": [ 9 | { 10 | "cells": [ 11 | { 12 | "cell_type": "markdown", 13 | "metadata": {}, 14 | "source": [ 15 | "# Check your system for the base python packages required for MLSS 2015\n", 16 | "\n", 17 | "Please run the following cell and it will tell you if your python environment can find all of the required packages." 18 | ] 19 | }, 20 | { 21 | "cell_type": "code", 22 | "collapsed": false, 23 | "input": [ 24 | "import imp\n", 25 | "\n", 26 | "packages = ['numpy',\n", 27 | " 'scipy',\n", 28 | " 'matplotlib',\n", 29 | " 'pandas',\n", 30 | " 'sklearn']\n", 31 | "\n", 32 | "for pac in packages:\n", 33 | " try:\n", 34 | " imp.find_module(pac)\n", 35 | " print(\"{}: Ok!\".format(pac))\n", 36 | " except ImportError as e:\n", 37 | " print(\"{}: Error -- {}\".format(pac, e))" 38 | ], 39 | "language": "python", 40 | "metadata": {}, 41 | "outputs": [ 42 | { 43 | "output_type": "stream", 44 | "stream": "stdout", 45 | "text": [ 46 | "numpy: Ok!\n", 47 | "scipy: Ok!\n", 48 | "matplotlib: Ok!\n", 49 | "pandas: Error -- No module named pandas\n", 50 | "sklearn: Ok!\n" 51 | ] 52 | } 53 | ], 54 | "prompt_number": 1 55 | }, 56 | { 57 | "cell_type": "code", 58 | "collapsed": false, 59 | "input": [], 60 | "language": "python", 61 | "metadata": {}, 62 | "outputs": [] 63 | } 64 | ], 65 | "metadata": {} 66 | } 67 | ] 68 | } -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # MLSS 2015 NICTA Labs 2 | A collection of labs for the 2015 Machine Learning Summer School from NICTA 3 | authored by: 4 | 5 | * Finn Lattimore 6 | * Lachlan McCalman 7 | * Simon O'Callaghan 8 | * Alistair Reid 9 | * Daniel Steinberg 10 | * Brian Thorne 11 | * John Vial 12 | 13 | The labs are all self contained in [ipython 14 | notebooks](http://ipython.org/notebook.html) which are python environments that 15 | are locally hosted within a browser. Both the instructions and the code input 16 | cells are in the notebook, and so all you need to do to complete a lab is to 17 | open the corresponding notebook in the directory where you have downloaded the 18 | tutorials, and then work through the exercises in your browser. 19 | 20 | This repository contains the first four labs for MLSS 2015 Syndey: 21 | 22 | 1. [Introduction to Python and PCA](https://github.com/NICTA/MLSS/tree/master/Intro%20and%20PCA) 23 | 2. [Linear Regression](https://github.com/NICTA/MLSS/tree/master/Linear%20Regression) 24 | 3. [Classification](https://github.com/NICTA/MLSS/tree/master/classification) 25 | 4. [Clustering and Latent Variable Models](https://github.com/NICTA/MLSS/tree/master/clustering) 26 | 27 | You can find the general lab instructions [here](http://tinyurl.com/m62udcy), 28 | as well as how to set up your python environment. 29 | 30 | 31 | ## Preview and Solutions 32 | 33 | You can preview all of the lab solutions here: 34 | 35 | 1. [Introduction to Python and PCA](http://nbviewer.ipython.org/github/NICTA/MLSS/blob/master/Intro%20and%20PCA/Intro%20to%20python%20Answers.ipynb) 36 | 2. [Linear Regression](http://nbviewer.ipython.org/github/NICTA/MLSS/blob/master/Linear%20Regression/linearRegressionAnswers.ipynb) 37 | 3. [Classification](http://nbviewer.ipython.org/github/NICTA/MLSS/blob/master/classification/Classification_solutions.ipynb) 38 | 4. [Clustering and Latent Variable Models](http://nbviewer.ipython.org/github/NICTA/MLSS/blob/master/clustering/Clustering%20and%20Latent%20Variable%20Models%20-%20SOLUTIONS.ipynb) 39 | 40 | 41 | ## Dependencies 42 | 43 | General: 44 | * scikit-learn 45 | * numpy 46 | * matplotlib 47 | * scipy 48 | * ipython[all] 49 | 50 | The above can all be checked using the `Dependency checker.ipynb` script in this repo. Optionally for the clustering lab: 51 | * lda (may require you to also pull down pbr) 52 | * Pillow 53 | -------------------------------------------------------------------------------- /clustering/tututils.py: -------------------------------------------------------------------------------- 1 | from pylab import * 2 | import matplotlib.cm as cm 3 | import numpy as np 4 | import scipy.linalg as la 5 | from scipy.stats import chi2 6 | from scipy.spatial import Voronoi, voronoi_plot_2d 7 | from sklearn.datasets import make_blobs 8 | 9 | 10 | def plot_2d_clusters(X, labels, centers): 11 | """ 12 | Given an observation array, a label vector, and the location of the centers 13 | plot the clusters 14 | """ 15 | 16 | clabels = set(labels) 17 | K = len(clabels) 18 | 19 | if len(centers) != K: 20 | raise ValueError("Expecting the number of unique labels and centres to" 21 | " be the same!") 22 | 23 | # Plot the true clusters 24 | figure(figsize=(10, 10)) 25 | ax = gca() 26 | 27 | vor = Voronoi(centers) 28 | 29 | voronoi_plot_2d(vor, ax) 30 | 31 | colors = cm.hsv(np.arange(K)/float(K)) 32 | for k, col in enumerate(colors): 33 | my_members = labels == k 34 | scatter(X[my_members, 0], X[my_members, 1], c=col, marker='o', s=20) 35 | 36 | for k, col in enumerate(colors): 37 | cluster_center = centers[k] 38 | scatter(cluster_center[0], cluster_center[1], c=col, marker='o', s=200) 39 | 40 | axis('tight') 41 | axis('equal') 42 | title('Clusters') 43 | 44 | 45 | def plot_2d_GMMs(X, labels, means, covs, percentcontour=0.66, npoints=30): 46 | """ 47 | Given an observation array, a label vector (integer values), and GMM mean 48 | and covariance parameters, plot the clusters and parameters. 49 | """ 50 | 51 | clabels = set(labels) 52 | K = len(clabels) 53 | 54 | if len(means) != len(covs) != K: 55 | raise ValueError("Expecting the number of unique labels, means and" 56 | "covariances to be the same!") 57 | 58 | phi = np.linspace(-np.pi, np.pi, npoints) 59 | 60 | circle = np.array([np.sin(phi), np.cos(phi)]).T 61 | 62 | figure(figsize=(10, 10)) 63 | gca() 64 | 65 | colors = cm.hsv(np.arange(K)/float(K)) 66 | for k, col in zip(clabels, colors): 67 | 68 | # points 69 | my_members = labels == k 70 | scatter(X[my_members, 0], X[my_members, 1], c=col, marker='o', s=20) 71 | 72 | # means 73 | cluster_center = means[k, :] 74 | scatter(cluster_center[0], cluster_center[1], c=col, marker='o', s=200) 75 | 76 | # covariance 77 | L = la.cholesky(np.array(covs[k]) * chi2.ppf(percentcontour, [3]) 78 | + 1e-5 * np.eye(covs[k].shape[0])) 79 | covpoints = circle.dot(L) + means[k, :] 80 | plot(covpoints[:, 0], covpoints[:, 1], color=col, linewidth=3) 81 | 82 | axis('tight') 83 | axis('equal') 84 | title('Clusters') 85 | 86 | 87 | def load_2d_simple(): 88 | """ 89 | Should be easily clustered with K-Means. 90 | """ 91 | centres = [[1, 1], [-0.5, 0], [1, -1]] 92 | X, labels_true = make_blobs(n_samples=1000, centers=centres, 93 | cluster_std=[[0.3, 0.3]]) 94 | return X 95 | 96 | 97 | def load_2d_hard(): 98 | """ 99 | Returns non-isotropoic data to motivate the use of non-euclidean norms (as 100 | well as the ground truth). 101 | """ 102 | 103 | centres = np.array([[3., -1.], [-2., 1.], [2., 5.]]) 104 | covs = [] 105 | covs.append(np.array([[4., 2.], [2., 1.5]])) 106 | covs.append(np.array([[1, -1.5], [-1.5, 3.]])) 107 | covs.append(np.array([[1., 0.], [0., 1.]])) 108 | 109 | N = [1000, 500, 300] 110 | 111 | X = [np.random.randn(n, 2).dot(la.cholesky(c, lower=True)) + m 112 | for n, m, c in zip(N, centres, covs)] 113 | X = np.vstack(X) 114 | 115 | labels = np.concatenate((np.zeros(N[0]), np.ones(N[1]), 2*np.ones(N[2]))) 116 | 117 | return X, labels 118 | -------------------------------------------------------------------------------- /Intro and PCA/README.md: -------------------------------------------------------------------------------- 1 | # Getting Started 2 | 3 | ## Download Python (2.7 or 3.4) 4 | 5 | Install the Anaconda Python distribution from [continuum.io](http://continuum.io/downloads). 6 | If you want Python 3.4 be sure to click **I WANT PYTHON 3.4**. 7 | 8 | ## Start IPython Notebook 9 | 10 | Find the Anaconda **Launcher** and launch: 11 | 12 | ipython notebook 13 | 14 | Your browser should open up to http://localhost:8888 and show your home directory. 15 | Find your way to the directory where you downloaded and unzipped the MLSS tutorials. 16 | 17 | If you run into trouble, ask one of the friendly tutors. Or start reading the notebook in 18 | readonly mode at [nbviewer.ipython.org](http://nbviewer.ipython.org/github/NICTA/MLSS/blob/master/Intro%20and%20PCA/Intro%20to%20python.ipynb) 19 | 20 | ## Begin the tutorial 21 | 22 | Open the `Intro to python.ipynb` Notebook and start working through the exercises. 23 | 24 | 25 | ## Already have Python? 26 | 27 | Just make sure you have all the requirements installed for this tutorial by running: 28 | 29 | pip install -r requirements.txt 30 | 31 | # Python Quickstart 32 | 33 | # New to Python? 34 | 35 | ## Resources 36 | 37 | - [Learn Python The Hardway](http://learnpythonthehardway.org/book/) 38 | - [Online Python Interactive Debugger](http://people.csail.mit.edu/pgbovine/python/) 39 | - [Dive into Python 3](http://getpython3.com/diveintopython3/) 40 | - [Interactive Python](http://interactivepython.org/courselib/static/thinkcspy/index.html) 41 | 42 | ## Intro to Python Cheatsheet 43 | 44 | Launch the IPython QT console and try run (and understand) these commands: 45 | 46 | ```python 47 | # This is a comment line 48 | # numbers and variables 49 | age = 26 50 | pi = 3.14159 51 | 52 | # strings and methods 53 | s = 'Hugh F Durrant-Whyte' 54 | 55 | # Strings have a method `split` which returns a list of strings split by whitespace 56 | tokens = s.split() 57 | firstName = tokens[0] 58 | middleName = tokens[1] 59 | lastName = tokens[2] 60 | s2 = firstName + ' ' + middleName + ' ' + lastName 61 | 62 | # 'if' statement - indentation matters 63 | if s == s2: 64 | print('yes the strings are equal') 65 | else: 66 | print('no') 67 | 68 | # if statements can also be inline 69 | answer = 'yes' if s == s2 else 'no' 70 | 71 | # list (mutable ordered sequence) 72 | beatles = ['John', 'Paul', 'George'] 73 | beatles.append('Ringo') 74 | print(beatles) 75 | print('Ringo' in beatles) 76 | 77 | 78 | # 'for' loop - indentation matters 79 | # Note that name is defined inside the for loop 80 | for name in beatles: 81 | print('Hello ' + name) 82 | 83 | # Iterating over a range of numbers is easy 84 | # range has the following arguments (start, stop, step) where stop isn't included 85 | for number in range(2, 10, 2): 86 | print(number) 87 | 88 | # tuple (immutable ordered sequence) 89 | ages = (18, 21, 28, 21, 22, 18, 19, 34, 9) 90 | 91 | # Note you can't change the contents of a tuple 92 | 93 | # set (mutable, unordered, no duplicates) 94 | uniqueAges = set(ages) 95 | uniqueAges.add(18) # already in set, no effect 96 | uniqueAges.remove(21) 97 | 98 | 99 | # testing set membership (very fast) 100 | if 18 in uniqueAges: 101 | print('There is an 18-year-old present!') 102 | 103 | # sorting a list 104 | sorted(beatles) # returns a new sorted list 105 | beatles.sort() # in-place - changes beatles list 106 | 107 | # Sorting a set returns a list 108 | orderedUniqueAges = sorted(uniqueAges) 109 | 110 | # There is no guaranteed order when iterating over a set 111 | for thisAge in uniqueAges: 112 | print(thisAge) 113 | 114 | # Instead iterate over the sorted set: 115 | for age in sorted(uniqueAges): 116 | print(age) 117 | 118 | # dict - mapping unique keys to values 119 | netWorth = {} 120 | netWorth['Donald Trump'] = 3000000000 121 | netWorth['Bill Gates'] = 58000000000 122 | netWorth['Tom Cruise'] = 40000000 123 | netWorth['Joe Postdoc'] = 20000 124 | 125 | # Access the value associated with a key 126 | print(netWorth['Donald Trump']) 127 | 128 | # iterating over a dict gives keys 129 | for personName in netWorth: 130 | print(personName + " is worth: ", end='') 131 | print(netWorth[personName]) 132 | 133 | # You can also iterate over key-value pairs: 134 | for (person, worth) in netWorth.items(): 135 | if worth < 1000000: 136 | print('haha ' + person + ' is not a millionaire') 137 | 138 | # testing dict membership is the same as with a set 139 | if 'Tom Cruise' in netWorth: 140 | print('show me the money!') 141 | ``` 142 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | 5 | # C extensions 6 | *.so 7 | 8 | # Distribution / packaging 9 | .Python 10 | env/ 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | lib/ 17 | lib64/ 18 | parts/ 19 | sdist/ 20 | var/ 21 | *.egg-info/ 22 | .installed.cfg 23 | *.egg 24 | 25 | # PyInstaller 26 | # Usually these files are written by a python script from a template 27 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 28 | *.manifest 29 | *.spec 30 | 31 | # Installer logs 32 | pip-log.txt 33 | pip-delete-this-directory.txt 34 | 35 | # Unit test / coverage reports 36 | htmlcov/ 37 | .tox/ 38 | .coverage 39 | .cache 40 | nosetests.xml 41 | coverage.xml 42 | 43 | # Translations 44 | *.mo 45 | *.pot 46 | 47 | # Django stuff: 48 | *.log 49 | 50 | # Sphinx documentation 51 | docs/_build/ 52 | 53 | # PyBuilder 54 | target/ 55 | ======= 56 | ################# 57 | ## Eclipse 58 | ################# 59 | 60 | *.pydevproject 61 | .project 62 | .metadata 63 | bin/ 64 | tmp/ 65 | *.tmp 66 | *.bak 67 | *.swp 68 | *~.nib 69 | local.properties 70 | .classpath 71 | .settings/ 72 | .loadpath 73 | 74 | # External tool builders 75 | .externalToolBuilders/ 76 | 77 | # Locally stored "Eclipse launch configurations" 78 | *.launch 79 | 80 | # CDT-specific 81 | .cproject 82 | 83 | # PDT-specific 84 | .buildpath 85 | 86 | 87 | ################# 88 | ## Visual Studio 89 | ################# 90 | 91 | ## Ignore Visual Studio temporary files, build results, and 92 | ## files generated by popular Visual Studio add-ons. 93 | 94 | # User-specific files 95 | *.suo 96 | *.user 97 | *.sln.docstates 98 | 99 | # Build results 100 | 101 | [Dd]ebug/ 102 | [Rr]elease/ 103 | x64/ 104 | build/ 105 | [Bb]in/ 106 | [Oo]bj/ 107 | 108 | # MSTest test Results 109 | [Tt]est[Rr]esult*/ 110 | [Bb]uild[Ll]og.* 111 | 112 | *_i.c 113 | *_p.c 114 | *.ilk 115 | *.meta 116 | *.obj 117 | *.pch 118 | *.pdb 119 | *.pgc 120 | *.pgd 121 | *.rsp 122 | *.sbr 123 | *.tlb 124 | *.tli 125 | *.tlh 126 | *.tmp 127 | *.tmp_proj 128 | *.log 129 | *.vspscc 130 | *.vssscc 131 | .builds 132 | *.pidb 133 | *.log 134 | *.scc 135 | 136 | # Visual C++ cache files 137 | ipch/ 138 | *.aps 139 | *.ncb 140 | *.opensdf 141 | *.sdf 142 | *.cachefile 143 | 144 | # Visual Studio profiler 145 | *.psess 146 | *.vsp 147 | *.vspx 148 | 149 | # Guidance Automation Toolkit 150 | *.gpState 151 | 152 | # ReSharper is a .NET coding add-in 153 | _ReSharper*/ 154 | *.[Rr]e[Ss]harper 155 | 156 | # TeamCity is a build add-in 157 | _TeamCity* 158 | 159 | # DotCover is a Code Coverage Tool 160 | *.dotCover 161 | 162 | # NCrunch 163 | *.ncrunch* 164 | .*crunch*.local.xml 165 | 166 | # Installshield output folder 167 | [Ee]xpress/ 168 | 169 | # DocProject is a documentation generator add-in 170 | DocProject/buildhelp/ 171 | DocProject/Help/*.HxT 172 | DocProject/Help/*.HxC 173 | DocProject/Help/*.hhc 174 | DocProject/Help/*.hhk 175 | DocProject/Help/*.hhp 176 | DocProject/Help/Html2 177 | DocProject/Help/html 178 | 179 | # Click-Once directory 180 | publish/ 181 | 182 | # Publish Web Output 183 | *.Publish.xml 184 | *.pubxml 185 | *.publishproj 186 | 187 | # NuGet Packages Directory 188 | ## TODO: If you have NuGet Package Restore enabled, uncomment the next line 189 | #packages/ 190 | 191 | # Windows Azure Build Output 192 | csx 193 | *.build.csdef 194 | 195 | # Windows Store app package directory 196 | AppPackages/ 197 | 198 | # Others 199 | sql/ 200 | *.Cache 201 | ClientBin/ 202 | [Ss]tyle[Cc]op.* 203 | ~$* 204 | *~ 205 | *.dbmdl 206 | *.[Pp]ublish.xml 207 | *.pfx 208 | *.publishsettings 209 | 210 | # RIA/Silverlight projects 211 | Generated_Code/ 212 | 213 | # Backup & report files from converting an old project file to a newer 214 | # Visual Studio version. Backup files are not needed, because we have git ;-) 215 | _UpgradeReport_Files/ 216 | Backup*/ 217 | UpgradeLog*.XML 218 | UpgradeLog*.htm 219 | 220 | # SQL Server files 221 | App_Data/*.mdf 222 | App_Data/*.ldf 223 | 224 | ############# 225 | ## Windows detritus 226 | ############# 227 | 228 | # Windows image file caches 229 | Thumbs.db 230 | ehthumbs.db 231 | 232 | # Folder config file 233 | Desktop.ini 234 | 235 | # Recycle Bin used on file shares 236 | $RECYCLE.BIN/ 237 | 238 | # Mac crap 239 | .DS_Store 240 | 241 | 242 | ############# 243 | ## Python 244 | ############# 245 | 246 | *.py[cod] 247 | 248 | # Packages 249 | *.egg 250 | *.egg-info 251 | dist/ 252 | build/ 253 | eggs/ 254 | parts/ 255 | var/ 256 | sdist/ 257 | develop-eggs/ 258 | .installed.cfg 259 | 260 | # Installer logs 261 | pip-log.txt 262 | 263 | # Unit test / coverage reports 264 | .coverage 265 | .tox 266 | 267 | #Translations 268 | *.mo 269 | 270 | #Mr Developer 271 | .mr.developer.cfg 272 | 273 | # Ipython notebook 274 | .ipynb_checkpoints/ 275 | -------------------------------------------------------------------------------- /classification/util.py: -------------------------------------------------------------------------------- 1 | import csv 2 | import numpy as np 3 | import scipy.linalg 4 | import matplotlib.pyplot as pl 5 | from mpl_toolkits.mplot3d import Axes3D 6 | from sklearn import svm 7 | from scipy.stats import multivariate_normal 8 | from scipy.stats import bernoulli 9 | 10 | print("version",1) 11 | 12 | 13 | 14 | class GaussianMixture: 15 | 16 | def __init__(self,mean0,cov0,mean1,cov1): 17 | """ construct a mixture of two gaussians. mean0 is 2x1 vector of means for class 0, cov0 is 2x2 covariance matrix for class 0. 18 | Similarly for class 1""" 19 | self.mean0 = mean0 20 | self.mean1 = mean1 21 | self.cov0 = cov0 22 | self.cov1 = cov1 23 | self.rv0 = multivariate_normal(mean0, cov0) 24 | self.rv1 = multivariate_normal(mean1, cov1) 25 | 26 | def plot(self,data=None): 27 | x1 = np.linspace(-4,4,100) 28 | x2 = np.linspace(-4,4,100) 29 | X1,X2 = np.meshgrid(x1,x2) 30 | pos = np.empty(X1.shape+(2,)) 31 | pos[:,:,0] = X1 32 | pos[:,:,1]= X2 33 | a = self.rv1.pdf(pos)/self.rv0.pdf(pos) 34 | 35 | if data: 36 | nplots = 4 37 | else: 38 | nplots = 3 39 | fig,ax = pl.subplots(1,nplots,figsize = (5*nplots,5)) 40 | [ax[i].spines['left'].set_position('zero') for i in range(0,nplots)] 41 | [ax[i].spines['right'].set_color('none') for i in range(0,nplots)] 42 | [ax[i].spines['bottom'].set_position('zero') for i in range(0,nplots)] 43 | [ax[i].spines['top'].set_color('none') for i in range(0,nplots)] 44 | 45 | ax[0].set_title("p(x1,x2|y = 1") 46 | ax[1].set_title("p(x1,x2|y = 0") 47 | ax[2].set_title("P(y = 1|x1,x2)") 48 | [ax[i].set_xlim([-4,4]) for i in range(0,3)] 49 | [ax[i].set_ylim([-4,4]) for i in range(0,3)] 50 | 51 | cn = ax[0].contourf(x1,x2,self.rv1.pdf(pos)) 52 | cn2 = ax[1].contourf(x1,x2,self.rv0.pdf(pos)) 53 | z = a/(1.0+a) 54 | cn3 = ax[2].contourf(x1,x2,z) 55 | ct = ax[2].contour(cn3,levels=[0.5]) 56 | ax[2].clabel(ct) 57 | 58 | 59 | if data: 60 | X,Y = data 61 | colors = ["blue" if target < 1 else "red" for target in Y] 62 | x = X[:,0] 63 | y = X[:,1] 64 | yis1 = np.where(Y==1)[0] 65 | yis0 = np.where(Y!=1)[0] 66 | ax[3].set_title("Samples colored by class") 67 | ax[3].scatter(x,y,s=30,c=colors,alpha=.5) 68 | ax[0].scatter(x[yis1],y[yis1],s=5,c=colors,alpha=.3) 69 | ax[1].scatter(x[yis0],y[yis0],s=5,c=colors,alpha=.3) 70 | ax[2].scatter(x,y,s=5,c=colors,alpha=.3) 71 | pl.show() 72 | 73 | def sample(self,n_samples,py,plot=False): 74 | """samples Y according to py and corresponding features x1,x2 according to the gaussian for the corresponding class""" 75 | Y = bernoulli.rvs(py,size=n_samples) 76 | X = np.zeros((n_samples,2)) 77 | for i in range(n_samples): 78 | if Y[i] == 1: 79 | X[i,:] = self.rv1.rvs() 80 | else: 81 | X[i,:] = self.rv0.rvs() 82 | if plot: 83 | self.plot(data=(X,Y)) 84 | return X,Y 85 | 86 | 87 | 88 | def load_data_(filename): 89 | with open(filename) as f: 90 | g = (",".join([i[1],i[2],i[4],i[5],i[6],i[7],i[9],i[11]]).encode(encoding='UTF-8') 91 | for i in csv.reader(f,delimiter=",",quotechar='"')) 92 | data = np.genfromtxt(g, delimiter=",",names=True, 93 | dtype=(int,int,np.dtype('a6'),float,int,int,float,np.dtype('a1'))) 94 | embark_dict = {b'S':0, b'C':1, b'Q':2, b'':3} 95 | survived = data['Survived'] 96 | passenger_class = data['Pclass'] 97 | is_female = (data['Sex'] == b'female').astype(int) 98 | age = data['Age'] 99 | sibsp = data['SibSp'] 100 | parch = data['Parch'] 101 | fare = data['Fare'] 102 | embarked = np.array([embark_dict[k] for k in data['Embarked']]) 103 | # skip age for the moment because of the missing data 104 | X = np.vstack((passenger_class, is_female, sibsp, parch, fare, embarked)).T 105 | Y = survived 106 | 107 | return X, Y 108 | 109 | def load_data(): 110 | return load_data_("titanic_train.csv") 111 | 112 | 113 | def load_test_data(): 114 | return load_data_("titanic_test.csv") 115 | 116 | 117 | 118 | def whitening_matrix(X): 119 | """The matrix of Eigenvectors that whitens the input vector X""" 120 | assert (X.ndim == 2) 121 | sigma = np.dot(X.T, X) 122 | e, m = scipy.linalg.eigh(sigma) 123 | return np.dot(m, np.diag(1.0/np.sqrt(e)))*np.sqrt((X.shape[0]-1)) 124 | 125 | 126 | def plot_svm(X, Y, svm_instance, xdim1=0, xdim2=1, minbound=(-3,-3), 127 | maxbound=(3,3), resolution=(100,100)): 128 | """ Plot any two dimensions from an SVM""" 129 | # build the meshgrid for the two dims we care about 130 | d = svm_instance.shape_fit_[1] 131 | n = resolution[0] * resolution[1] 132 | xx, yy = np.meshgrid(np.linspace(minbound[0], maxbound[0], resolution[0]), 133 | np.linspace(minbound[1], maxbound[1], resolution[1])) 134 | query2d = np.c_[xx.ravel(), yy.ravel()] 135 | query = np.zeros((n,d)) 136 | query[:,xdim1] = query2d[:, 0] 137 | query[:,xdim2] = query2d[:, 1] 138 | 139 | Z = svm_instance.decision_function(query) 140 | Z = Z.reshape(xx.shape) 141 | 142 | fig = pl.figure(figsize=(10,10)) 143 | ax = fig.add_subplot(111) 144 | 145 | ax.imshow(Z, interpolation='nearest', 146 | extent=(xx.min(), xx.max(), yy.min(), yy.max()), aspect='auto', 147 | origin='lower', cmap=pl.cm.PuOr_r) 148 | contours = ax.contour(xx, yy, Z, levels=[0], linewidths=2, 149 | linetypes='--') 150 | ax.scatter(X[:, xdim1], X[:, xdim2], s=30, c=Y, cmap=pl.cm.Paired) 151 | # ax.set_xticks(()) 152 | # pl.yticks(()) 153 | ax.set_xlim((minbound[0], maxbound[0])) 154 | ax.set_ylim((minbound[1], maxbound[1])) 155 | pl.show() 156 | 157 | 158 | def illustrate_preprocessing(): 159 | x = np.random.multivariate_normal(np.array([5.0,5.0]), 160 | np.array([[5.0,3.0],[3.0,4.0]]),size=1000) 161 | x_demean = x - np.mean(x, axis=0) 162 | x_unitsd = x_demean/(np.std(x_demean,axis=0)) 163 | x_whiten = np.dot(x_demean, whitening_matrix(x_demean)) 164 | 165 | fig = pl.figure(figsize=(10,10)) 166 | 167 | def mk_subplot(n, data, label): 168 | ax = fig.add_subplot(2,2,n) 169 | ax.scatter(data[:,0], data[:,1]) 170 | ax.set_xlim((-10,10)) 171 | ax.set_ylim((-10,10)) 172 | ax.set_xlabel(label) 173 | 174 | mk_subplot(1, x, "Original") 175 | mk_subplot(2, x_demean, "De-meaned") 176 | mk_subplot(3, x_unitsd, "Unit SD") 177 | mk_subplot(4, x_whiten, "Whitened") 178 | pl.show() 179 | 180 | 181 | def margins_and_hyperplane(): 182 | #gen some data 183 | np.random.seed(0) 184 | n = 20 185 | X = (np.vstack((np.ones((n,2))*np.array([0.5,1]), 186 | np.ones((n,2))*np.array([-0.5,-1]))) + np.random.randn(2*n,2)*0.3) 187 | Y = np.hstack((np.ones(n), np.zeros(n))) 188 | 189 | clf = svm.SVC(kernel='linear') 190 | clf.fit(X, Y) 191 | 192 | # Note the following code comes from a scikit learn example... 193 | # get the separating hyperplane 194 | w = clf.coef_[0] 195 | a = -w[0] / w[1] 196 | xs = np.linspace(-2, 2) 197 | ys = a * xs - (clf.intercept_[0]) / w[1] 198 | 199 | # plot the parallels to the separating hyperplane that pass through the 200 | # support vectors 201 | b = clf.support_vectors_[0] 202 | ys_down = a * xs + (b[1] - a * b[0]) 203 | b = clf.support_vectors_[-1] 204 | ys_up = a * xs + (b[1] - a * b[0]) 205 | 206 | #draw a bad margin 207 | 208 | def line_point_grad(x, grad, p1): 209 | y = grad*(x - p1[0]) + p1[1] 210 | return y 211 | 212 | minp = X[np.argmin(X[:n,0])] 213 | maxp = X[n + np.argmax(X[n:,0])] 214 | yb = line_point_grad(xs, a*20, np.array([0.5*(minp[0]+maxp[0]),0.0])) 215 | yb_down = line_point_grad(xs, a*20, minp) 216 | yb_up = line_point_grad(xs, a*20, maxp) 217 | 218 | # plot the line, the points, and the nearest vectors to the plane 219 | fig = pl.figure(figsize=(10,10)) 220 | ax = fig.add_subplot(111) 221 | ax.plot(xs, ys, 'g-') 222 | ax.plot(xs, yb, 'r-') 223 | ax.plot(xs, yb_down, 'r--') 224 | ax.plot(xs, yb_up, 'r--') 225 | ax.plot(xs, ys_down, 'g--') 226 | ax.plot(xs, ys_up, 'g--') 227 | 228 | ax.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1], 229 | s=80, facecolors='none') 230 | ax.scatter([minp[0],maxp[0]], [minp[1],maxp[1]], 231 | s=80, facecolors='none') 232 | ax.scatter(X[:, 0], X[:, 1], c=Y, cmap=pl.cm.Paired) 233 | ax.set_xlim((-2,2)) 234 | ax.set_ylim((-2,2)) 235 | pl.show() 236 | 237 | 238 | def hard_data(): 239 | #gen some data 240 | np.random.seed(0) 241 | epsilon = 0.05 242 | n = 5000 243 | X1 = np.random.randn(n,2) 244 | X2 = np.random.randn(n,2) 245 | valid1 = X1[:,0]**2 + X1[:,1]**2 < (0.5 - epsilon) 246 | valid2 = np.logical_and((X2[:,0]**2 + X2[:,1]**2 > (0.5 + epsilon)), 247 | (X2[:,0]**2 + X2[:,1]**2 < 1.0)) 248 | 249 | X1 = X1[valid1] 250 | X2 = X2[valid2] 251 | Y1 = np.ones(X1.shape[0]) 252 | Y2 = np.zeros(X2.shape[0]) 253 | X = np.vstack((X1,X2)) 254 | Y = np.hstack((Y1,Y2)) 255 | Z = np.sqrt(2)*X[:,0]*X[:,1] 256 | return X, Y, Z 257 | 258 | def nonlinear_example(): 259 | X, Y, Z = hard_data() 260 | fig = pl.figure(figsize=(10,20)) 261 | ax = fig.add_subplot(211) 262 | ax.scatter(X[:, 0], X[:, 1], c=Y, cmap=pl.cm.Paired) 263 | ax = fig.add_subplot(212, projection='3d') 264 | ax.scatter(X[:,0]**2, X[:,1]**2, Z, c=Y, cmap=pl.cm.Paired) 265 | pl.show() 266 | 267 | def nonlinear_svm(): 268 | X, Y, Z = hard_data() 269 | clf = svm.SVC(kernel='rbf') 270 | clf.fit(X, Y) 271 | plot_svm(X, Y, clf, 0,1, (-1.5,-1.5), (1.5,1.5)) 272 | 273 | 274 | #if __name__ == "__main__": 275 | # 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If you wish to incorporate parts of the Program into other free 251 | programs whose distribution conditions are different, write to the author 252 | to ask for permission. For software which is copyrighted by the Free 253 | Software Foundation, write to the Free Software Foundation; we sometimes 254 | make exceptions for this. Our decision will be guided by the two goals 255 | of preserving the free status of all derivatives of our free software and 256 | of promoting the sharing and reuse of software generally. 257 | 258 | NO WARRANTY 259 | 260 | 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY 261 | FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN 262 | OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES 263 | PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED 264 | OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF 265 | MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS 266 | TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE 267 | PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, 268 | REPAIR OR CORRECTION. 269 | 270 | 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 271 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR 272 | REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, 273 | INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING 274 | OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED 275 | TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY 276 | YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER 277 | PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE 278 | POSSIBILITY OF SUCH DAMAGES. 279 | 280 | END OF TERMS AND CONDITIONS 281 | 282 | How to Apply These Terms to Your New Programs 283 | 284 | If you develop a new program, and you want it to be of the greatest 285 | possible use to the public, the best way to achieve this is to make it 286 | free software which everyone can redistribute and change under these terms. 287 | 288 | To do so, attach the following notices to the program. It is safest 289 | to attach them to the start of each source file to most effectively 290 | convey the exclusion of warranty; and each file should have at least 291 | the "copyright" line and a pointer to where the full notice is found. 292 | 293 | {description} 294 | Copyright (C) {year} {fullname} 295 | 296 | This program is free software; you can redistribute it and/or modify 297 | it under the terms of the GNU General Public License as published by 298 | the Free Software Foundation; either version 2 of the License, or 299 | (at your option) any later version. 300 | 301 | This program is distributed in the hope that it will be useful, 302 | but WITHOUT ANY WARRANTY; without even the implied warranty of 303 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 304 | GNU General Public License for more details. 305 | 306 | You should have received a copy of the GNU General Public License along 307 | with this program; if not, write to the Free Software Foundation, Inc., 308 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. 309 | 310 | Also add information on how to contact you by electronic and paper mail. 311 | 312 | If the program is interactive, make it output a short notice like this 313 | when it starts in an interactive mode: 314 | 315 | Gnomovision version 69, Copyright (C) year name of author 316 | Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 317 | This is free software, and you are welcome to redistribute it 318 | under certain conditions; type `show c' for details. 319 | 320 | The hypothetical commands `show w' and `show c' should show the appropriate 321 | parts of the General Public License. Of course, the commands you use may 322 | be called something other than `show w' and `show c'; they could even be 323 | mouse-clicks or menu items--whatever suits your program. 324 | 325 | You should also get your employer (if you work as a programmer) or your 326 | school, if any, to sign a "copyright disclaimer" for the program, if 327 | necessary. Here is a sample; alter the names: 328 | 329 | Yoyodyne, Inc., hereby disclaims all copyright interest in the program 330 | `Gnomovision' (which makes passes at compilers) written by James Hacker. 331 | 332 | {signature of Ty Coon}, 1 April 1989 333 | Ty Coon, President of Vice 334 | 335 | This General Public License does not permit incorporating your program into 336 | proprietary programs. If your program is a subroutine library, you may 337 | consider it more useful to permit linking proprietary applications with the 338 | library. If this is what you want to do, use the GNU Lesser General 339 | Public License instead of this License. 340 | 341 | -------------------------------------------------------------------------------- /Linear Regression/LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 2, June 1991 3 | 4 | Copyright (C) 1989, 1991 Free Software Foundation, Inc., 5 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 6 | Everyone is permitted to copy and distribute verbatim copies 7 | of this license document, but changing it is not allowed. 8 | 9 | Preamble 10 | 11 | The licenses for most software are designed to take away your 12 | freedom to share and change it. By contrast, the GNU General Public 13 | License is intended to guarantee your freedom to share and change free 14 | software--to make sure the software is free for all its users. This 15 | General Public License applies to most of the Free Software 16 | Foundation's software and to any other program whose authors commit to 17 | using it. (Some other Free Software Foundation software is covered by 18 | the GNU Lesser General Public License instead.) You can apply it to 19 | your programs, too. 20 | 21 | When we speak of free software, we are referring to freedom, not 22 | price. Our General Public Licenses are designed to make sure that you 23 | have the freedom to distribute copies of free software (and charge for 24 | this service if you wish), that you receive source code or can get it 25 | if you want it, that you can change the software or use pieces of it 26 | in new free programs; and that you know you can do these things. 27 | 28 | To protect your rights, we need to make restrictions that forbid 29 | anyone to deny you these rights or to ask you to surrender the rights. 30 | These restrictions translate to certain responsibilities for you if you 31 | distribute copies of the software, or if you modify it. 32 | 33 | For example, if you distribute copies of such a program, whether 34 | gratis or for a fee, you must give the recipients all the rights that 35 | you have. You must make sure that they, too, receive or can get the 36 | source code. And you must show them these terms so they know their 37 | rights. 38 | 39 | We protect your rights with two steps: (1) copyright the software, and 40 | (2) offer you this license which gives you legal permission to copy, 41 | distribute and/or modify the software. 42 | 43 | Also, for each author's protection and ours, we want to make certain 44 | that everyone understands that there is no warranty for this free 45 | software. If the software is modified by someone else and passed on, we 46 | want its recipients to know that what they have is not the original, so 47 | that any problems introduced by others will not reflect on the original 48 | authors' reputations. 49 | 50 | Finally, any free program is threatened constantly by software 51 | patents. We wish to avoid the danger that redistributors of a free 52 | program will individually obtain patent licenses, in effect making the 53 | program proprietary. To prevent this, we have made it clear that any 54 | patent must be licensed for everyone's free use or not licensed at all. 55 | 56 | The precise terms and conditions for copying, distribution and 57 | modification follow. 58 | 59 | GNU GENERAL PUBLIC LICENSE 60 | TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION 61 | 62 | 0. This License applies to any program or other work which contains 63 | a notice placed by the copyright holder saying it may be distributed 64 | under the terms of this General Public License. The "Program", below, 65 | refers to any such program or work, and a "work based on the Program" 66 | means either the Program or any derivative work under copyright law: 67 | that is to say, a work containing the Program or a portion of it, 68 | either verbatim or with modifications and/or translated into another 69 | language. (Hereinafter, translation is included without limitation in 70 | the term "modification".) Each licensee is addressed as "you". 71 | 72 | Activities other than copying, distribution and modification are not 73 | covered by this License; they are outside its scope. The act of 74 | running the Program is not restricted, and the output from the Program 75 | is covered only if its contents constitute a work based on the 76 | Program (independent of having been made by running the Program). 77 | Whether that is true depends on what the Program does. 78 | 79 | 1. You may copy and distribute verbatim copies of the Program's 80 | source code as you receive it, in any medium, provided that you 81 | conspicuously and appropriately publish on each copy an appropriate 82 | copyright notice and disclaimer of warranty; keep intact all the 83 | notices that refer to this License and to the absence of any warranty; 84 | and give any other recipients of the Program a copy of this License 85 | along with the Program. 86 | 87 | You may charge a fee for the physical act of transferring a copy, and 88 | you may at your option offer warranty protection in exchange for a fee. 89 | 90 | 2. You may modify your copy or copies of the Program or any portion 91 | of it, thus forming a work based on the Program, and copy and 92 | distribute such modifications or work under the terms of Section 1 93 | above, provided that you also meet all of these conditions: 94 | 95 | a) You must cause the modified files to carry prominent notices 96 | stating that you changed the files and the date of any change. 97 | 98 | b) You must cause any work that you distribute or publish, that in 99 | whole or in part contains or is derived from the Program or any 100 | part thereof, to be licensed as a whole at no charge to all third 101 | parties under the terms of this License. 102 | 103 | c) If the modified program normally reads commands interactively 104 | when run, you must cause it, when started running for such 105 | interactive use in the most ordinary way, to print or display an 106 | announcement including an appropriate copyright notice and a 107 | notice that there is no warranty (or else, saying that you provide 108 | a warranty) and that users may redistribute the program under 109 | these conditions, and telling the user how to view a copy of this 110 | License. (Exception: if the Program itself is interactive but 111 | does not normally print such an announcement, your work based on 112 | the Program is not required to print an announcement.) 113 | 114 | These requirements apply to the modified work as a whole. If 115 | identifiable sections of that work are not derived from the Program, 116 | and can be reasonably considered independent and separate works in 117 | themselves, then this License, and its terms, do not apply to those 118 | sections when you distribute them as separate works. But when you 119 | distribute the same sections as part of a whole which is a work based 120 | on the Program, the distribution of the whole must be on the terms of 121 | this License, whose permissions for other licensees extend to the 122 | entire whole, and thus to each and every part regardless of who wrote it. 123 | 124 | Thus, it is not the intent of this section to claim rights or contest 125 | your rights to work written entirely by you; rather, the intent is to 126 | exercise the right to control the distribution of derivative or 127 | collective works based on the Program. 128 | 129 | In addition, mere aggregation of another work not based on the Program 130 | with the Program (or with a work based on the Program) on a volume of 131 | a storage or distribution medium does not bring the other work under 132 | the scope of this License. 133 | 134 | 3. You may copy and distribute the Program (or a work based on it, 135 | under Section 2) in object code or executable form under the terms of 136 | Sections 1 and 2 above provided that you also do one of the following: 137 | 138 | a) Accompany it with the complete corresponding machine-readable 139 | source code, which must be distributed under the terms of Sections 140 | 1 and 2 above on a medium customarily used for software interchange; or, 141 | 142 | b) Accompany it with a written offer, valid for at least three 143 | years, to give any third party, for a charge no more than your 144 | cost of physically performing source distribution, a complete 145 | machine-readable copy of the corresponding source code, to be 146 | distributed under the terms of Sections 1 and 2 above on a medium 147 | customarily used for software interchange; or, 148 | 149 | c) Accompany it with the information you received as to the offer 150 | to distribute corresponding source code. (This alternative is 151 | allowed only for noncommercial distribution and only if you 152 | received the program in object code or executable form with such 153 | an offer, in accord with Subsection b above.) 154 | 155 | The source code for a work means the preferred form of the work for 156 | making modifications to it. For an executable work, complete source 157 | code means all the source code for all modules it contains, plus any 158 | associated interface definition files, plus the scripts used to 159 | control compilation and installation of the executable. However, as a 160 | special exception, the source code distributed need not include 161 | anything that is normally distributed (in either source or binary 162 | form) with the major components (compiler, kernel, and so on) of the 163 | operating system on which the executable runs, unless that component 164 | itself accompanies the executable. 165 | 166 | If distribution of executable or object code is made by offering 167 | access to copy from a designated place, then offering equivalent 168 | access to copy the source code from the same place counts as 169 | distribution of the source code, even though third parties are not 170 | compelled to copy the source along with the object code. 171 | 172 | 4. You may not copy, modify, sublicense, or distribute the Program 173 | except as expressly provided under this License. Any attempt 174 | otherwise to copy, modify, sublicense or distribute the Program is 175 | void, and will automatically terminate your rights under this License. 176 | However, parties who have received copies, or rights, from you under 177 | this License will not have their licenses terminated so long as such 178 | parties remain in full compliance. 179 | 180 | 5. You are not required to accept this License, since you have not 181 | signed it. However, nothing else grants you permission to modify or 182 | distribute the Program or its derivative works. These actions are 183 | prohibited by law if you do not accept this License. Therefore, by 184 | modifying or distributing the Program (or any work based on the 185 | Program), you indicate your acceptance of this License to do so, and 186 | all its terms and conditions for copying, distributing or modifying 187 | the Program or works based on it. 188 | 189 | 6. Each time you redistribute the Program (or any work based on the 190 | Program), the recipient automatically receives a license from the 191 | original licensor to copy, distribute or modify the Program subject to 192 | these terms and conditions. You may not impose any further 193 | restrictions on the recipients' exercise of the rights granted herein. 194 | You are not responsible for enforcing compliance by third parties to 195 | this License. 196 | 197 | 7. If, as a consequence of a court judgment or allegation of patent 198 | infringement or for any other reason (not limited to patent issues), 199 | conditions are imposed on you (whether by court order, agreement or 200 | otherwise) that contradict the conditions of this License, they do not 201 | excuse you from the conditions of this License. If you cannot 202 | distribute so as to satisfy simultaneously your obligations under this 203 | License and any other pertinent obligations, then as a consequence you 204 | may not distribute the Program at all. For example, if a patent 205 | license would not permit royalty-free redistribution of the Program by 206 | all those who receive copies directly or indirectly through you, then 207 | the only way you could satisfy both it and this License would be to 208 | refrain entirely from distribution of the Program. 209 | 210 | If any portion of this section is held invalid or unenforceable under 211 | any particular circumstance, the balance of the section is intended to 212 | apply and the section as a whole is intended to apply in other 213 | circumstances. 214 | 215 | It is not the purpose of this section to induce you to infringe any 216 | patents or other property right claims or to contest validity of any 217 | such claims; this section has the sole purpose of protecting the 218 | integrity of the free software distribution system, which is 219 | implemented by public license practices. Many people have made 220 | generous contributions to the wide range of software distributed 221 | through that system in reliance on consistent application of that 222 | system; it is up to the author/donor to decide if he or she is willing 223 | to distribute software through any other system and a licensee cannot 224 | impose that choice. 225 | 226 | This section is intended to make thoroughly clear what is believed to 227 | be a consequence of the rest of this License. 228 | 229 | 8. If the distribution and/or use of the Program is restricted in 230 | certain countries either by patents or by copyrighted interfaces, the 231 | original copyright holder who places the Program under this License 232 | may add an explicit geographical distribution limitation excluding 233 | those countries, so that distribution is permitted only in or among 234 | countries not thus excluded. In such case, this License incorporates 235 | the limitation as if written in the body of this License. 236 | 237 | 9. The Free Software Foundation may publish revised and/or new versions 238 | of the General Public License from time to time. Such new versions will 239 | be similar in spirit to the present version, but may differ in detail to 240 | address new problems or concerns. 241 | 242 | Each version is given a distinguishing version number. If the Program 243 | specifies a version number of this License which applies to it and "any 244 | later version", you have the option of following the terms and conditions 245 | either of that version or of any later version published by the Free 246 | Software Foundation. If the Program does not specify a version number of 247 | this License, you may choose any version ever published by the Free Software 248 | Foundation. 249 | 250 | 10. If you wish to incorporate parts of the Program into other free 251 | programs whose distribution conditions are different, write to the author 252 | to ask for permission. For software which is copyrighted by the Free 253 | Software Foundation, write to the Free Software Foundation; we sometimes 254 | make exceptions for this. Our decision will be guided by the two goals 255 | of preserving the free status of all derivatives of our free software and 256 | of promoting the sharing and reuse of software generally. 257 | 258 | NO WARRANTY 259 | 260 | 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY 261 | FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN 262 | OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES 263 | PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED 264 | OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF 265 | MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS 266 | TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE 267 | PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, 268 | REPAIR OR CORRECTION. 269 | 270 | 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 271 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR 272 | REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, 273 | INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING 274 | OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED 275 | TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY 276 | YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER 277 | PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE 278 | POSSIBILITY OF SUCH DAMAGES. 279 | 280 | END OF TERMS AND CONDITIONS 281 | 282 | How to Apply These Terms to Your New Programs 283 | 284 | If you develop a new program, and you want it to be of the greatest 285 | possible use to the public, the best way to achieve this is to make it 286 | free software which everyone can redistribute and change under these terms. 287 | 288 | To do so, attach the following notices to the program. It is safest 289 | to attach them to the start of each source file to most effectively 290 | convey the exclusion of warranty; and each file should have at least 291 | the "copyright" line and a pointer to where the full notice is found. 292 | 293 | {description} 294 | Copyright (C) {year} {fullname} 295 | 296 | This program is free software; you can redistribute it and/or modify 297 | it under the terms of the GNU General Public License as published by 298 | the Free Software Foundation; either version 2 of the License, or 299 | (at your option) any later version. 300 | 301 | This program is distributed in the hope that it will be useful, 302 | but WITHOUT ANY WARRANTY; without even the implied warranty of 303 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 304 | GNU General Public License for more details. 305 | 306 | You should have received a copy of the GNU General Public License along 307 | with this program; if not, write to the Free Software Foundation, Inc., 308 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. 309 | 310 | Also add information on how to contact you by electronic and paper mail. 311 | 312 | If the program is interactive, make it output a short notice like this 313 | when it starts in an interactive mode: 314 | 315 | Gnomovision version 69, Copyright (C) year name of author 316 | Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 317 | This is free software, and you are welcome to redistribute it 318 | under certain conditions; type `show c' for details. 319 | 320 | The hypothetical commands `show w' and `show c' should show the appropriate 321 | parts of the General Public License. Of course, the commands you use may 322 | be called something other than `show w' and `show c'; they could even be 323 | mouse-clicks or menu items--whatever suits your program. 324 | 325 | You should also get your employer (if you work as a programmer) or your 326 | school, if any, to sign a "copyright disclaimer" for the program, if 327 | necessary. Here is a sample; alter the names: 328 | 329 | Yoyodyne, Inc., hereby disclaims all copyright interest in the program 330 | `Gnomovision' (which makes passes at compilers) written by James Hacker. 331 | 332 | {signature of Ty Coon}, 1 April 1989 333 | Ty Coon, President of Vice 334 | 335 | This General Public License does not permit incorporating your program into 336 | proprietary programs. If your program is a subroutine library, you may 337 | consider it more useful to permit linking proprietary applications with the 338 | library. If this is what you want to do, use the GNU Lesser General 339 | Public License instead of this License. 340 | 341 | -------------------------------------------------------------------------------- /classification/titanic_test.csv: -------------------------------------------------------------------------------- 1 | PassengerId,Survived,Pclass,Name,Sex,Age,SibSp,Parch,Ticket,Fare,Cabin,Embarked 2 | 1,0,3,"Braund, Mr. Owen Harris",male,22,1,0,A/5 21171,7.25,,S 3 | 7,0,1,"McCarthy, Mr. Timothy J",male,54,0,0,17463,51.8625,E46,S 4 | 8,0,3,"Palsson, Master. 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William Thornton II",male,11,1,2,113760,120,B96 B98,S 288 | 810,1,1,"Chambers, Mrs. Norman Campbell (Bertha Griggs)",female,33,1,0,113806,53.1,E8,S 289 | 811,0,3,"Alexander, Mr. William",male,26,0,0,3474,7.8875,,S 290 | 815,0,3,"Tomlin, Mr. Ernest Portage",male,30.5,0,0,364499,8.05,,S 291 | 816,0,1,"Fry, Mr. Richard",male,,0,0,112058,0,B102,S 292 | 819,0,3,"Holm, Mr. John Fredrik Alexander",male,43,0,0,C 7075,6.45,,S 293 | 825,0,3,"Panula, Master. Urho Abraham",male,2,4,1,3101295,39.6875,,S 294 | 827,0,3,"Lam, Mr. Len",male,,0,0,1601,56.4958,,S 295 | 843,1,1,"Serepeca, Miss. Augusta",female,30,0,0,113798,31,,C 296 | 846,0,3,"Abbing, Mr. Anthony",male,42,0,0,C.A. 5547,7.55,,S 297 | 848,0,3,"Markoff, Mr. Marin",male,35,0,0,349213,7.8958,,C 298 | 853,0,3,"Boulos, Miss. Nourelain",female,9,1,1,2678,15.2458,,C 299 | 854,1,1,"Lines, Miss. Mary Conover",female,16,0,1,PC 17592,39.4,D28,S 300 | 856,1,3,"Aks, Mrs. Sam (Leah Rosen)",female,18,0,1,392091,9.35,,S 301 | 857,1,1,"Wick, Mrs. George Dennick (Mary Hitchcock)",female,45,1,1,36928,164.8667,,S 302 | 862,0,2,"Giles, Mr. Frederick Edward",male,21,1,0,28134,11.5,,S 303 | 864,0,3,"Sage, Miss. Dorothy Edith ""Dolly""",female,,8,2,CA. 2343,69.55,,S 304 | 867,1,2,"Duran y More, Miss. Asuncion",female,27,1,0,SC/PARIS 2149,13.8583,,C 305 | 868,0,1,"Roebling, Mr. Washington Augustus II",male,31,0,0,PC 17590,50.4958,A24,S 306 | 870,1,3,"Johnson, Master. Harold Theodor",male,4,1,1,347742,11.1333,,S 307 | 871,0,3,"Balkic, Mr. Cerin",male,26,0,0,349248,7.8958,,S 308 | 878,0,3,"Petroff, Mr. Nedelio",male,19,0,0,349212,7.8958,,S 309 | 879,0,3,"Laleff, Mr. Kristo",male,,0,0,349217,7.8958,,S 310 | 881,1,2,"Shelley, Mrs. William (Imanita Parrish Hall)",female,25,0,1,230433,26,,S 311 | 882,0,3,"Markun, Mr. Johann",male,33,0,0,349257,7.8958,,S 312 | 884,0,2,"Banfield, Mr. Frederick James",male,28,0,0,C.A./SOTON 34068,10.5,,S 313 | 889,0,3,"Johnston, Miss. Catherine Helen ""Carrie""",female,,1,2,W./C. 6607,23.45,,S 314 | -------------------------------------------------------------------------------- /clustering/Clustering and Latent Variable Models.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "metadata": { 3 | "name": "", 4 | "signature": "sha256:36c38689aa3def8a4191cdd49da7dc46982cbae251196e9441d71745753fe356" 5 | }, 6 | "nbformat": 3, 7 | "nbformat_minor": 0, 8 | "worksheets": [ 9 | { 10 | "cells": [ 11 | { 12 | "cell_type": "markdown", 13 | "metadata": {}, 14 | "source": [ 15 | "#Clustering and Latent Variable Models, MLSS 2015\n", 16 | "\n", 17 | "**Authors**: [Daniel Steinberg](http://www.daniel-steinberg.info/) & [Brian Thorne](http://hardbyte.bitbucket.org/)\n", 18 | "\n", 19 | "**Institute**: [NICTA](https://www.nicta.com.au/)" 20 | ] 21 | }, 22 | { 23 | "cell_type": "markdown", 24 | "metadata": {}, 25 | "source": [ 26 | "$$\n", 27 | "\\newcommand{\\brac} [1] {{ \\left( #1 \\right) }}\n", 28 | "\\newcommand{\\sbrac} [1] {{ \\left[ #1 \\right] }}\n", 29 | "\\newcommand{\\cbrac} [1] {{ \\left\\{ #1 \\right\\} }}\n", 30 | "\\newcommand{\\abrac} [1] {{ \\langle #1 \\rangle }}\n", 31 | "\\newcommand{\\real} [1] {{\\mathbb{R}^{#1}}} \n", 32 | "\\newcommand{\\lnorm} [1] {{\\ell_{#1}}} \n", 33 | "\\newcommand{\\norm} [2] {{\\|{#1}\\|_{#2}}} \n", 34 | "\\newcommand{\\abs} [1] {{\\lvert{#1}\\rvert}} \n", 35 | "\\newcommand{\\nullsp} [1] {{\\mathrm{Null}\\!\\brac{#1}}}\n", 36 | "\\newcommand{\\bigo} [1] {{\\mathcal{O}\\!\\brac{#1}}} \n", 37 | "\\newcommand{\\trace} [1] {{\\mathrm{Tr}\\!\\brac{#1}}}\n", 38 | "\\newcommand{\\argmax} [1] {{\\underset{#1}{\\arg\\max~}}}\n", 39 | "\\newcommand{\\argmin} [1] {{\\underset{#1}{\\arg\\min~}}}\n", 40 | "\\newcommand{\\indic} [1] {{{\\mathbf{1}\\!\\sbrac{#1}}}}\n", 41 | "\\newcommand{\\digam} [1] {{\\Psi\\!\\brac{#1}}}\n", 42 | "\\newcommand{\\gamfn} [1] {{\\Gamma\\!\\brac{#1}}}\n", 43 | "\\newcommand{\\gamfnD} [1] {{\\Gamma_D\\!\\brac{#1}}}\n", 44 | "\\newcommand{\\transpose} {{^{\\top}\\!}}\t\t\n", 45 | "\\newcommand{\\deter} [1] {{\\left|{#1}\\right|}}\n", 46 | "\\newcommand{\\prob} [1] {{p\\brac{#1}}} \n", 47 | "\\newcommand{\\probC} [2] {{p\\brac{#1|#2}}}\n", 48 | "\\newcommand{\\qrob} [1] {{q\\!\\brac{#1}}} \n", 49 | "\\newcommand{\\qrobC} [2] {{q\\!\\brac{#1|#2}}} \n", 50 | "\\newcommand{\\gaus} [1] {{\\mathcal{N}\\!\\brac{#1}}}\t\n", 51 | "\\newcommand{\\gausC} [2] {{\\mathcal{N}\\!\\brac{#1|#2}}}\n", 52 | "\\newcommand{\\gam} [1] {{\\mathrm{Gamma}\\!\\brac{#1}}}\t\n", 53 | "\\newcommand{\\gamC} [2] {{\\mathrm{Gamma}\\!\\brac{#1|#2}}}\n", 54 | "\\newcommand{\\betad} [1] {{\\mathrm{Beta}\\!\\brac{#1}}}\n", 55 | "\\newcommand{\\betaC} [2] {{\\mathrm{Beta}({#1}|{#2})}}\n", 56 | "\\newcommand{\\dir} [1] {{\\mathrm{Dir}\\brac{#1}}}\t\n", 57 | "\\newcommand{\\dirC} [2] {{\\mathrm{Dir}\\brac{#1|#2}}}\n", 58 | "\\newcommand{\\DP} [1] {{\\mathrm{DP}\\!\\brac{#1}}}\n", 59 | "\\newcommand{\\SB} [1] {{\\mathrm{SB}\\!\\brac{#1}}}\t\n", 60 | "\\newcommand{\\wish} [1] {{\\mathcal{W}\\!\\brac{#1}}}\t\n", 61 | "\\newcommand{\\wishC} [2] {{\\mathcal{W}\\!\\brac{#1|#2}}}\t\n", 62 | "\\newcommand{\\categ} [1] {{\\mathrm{Categ}\\brac{#1}}}\n", 63 | "\\newcommand{\\categC} [2] {{\\mathrm{Categ}\\brac{#1|#2}}}\n", 64 | "\\newcommand{\\ncons} [1] {{\\mathcal{Z}_{#1}}}\n", 65 | "\\newcommand{\\bigO} [1] {{\\mathcal{O}({#1})}}\n", 66 | "\\newcommand{\\obsall}{\\mathbf{X}}\n", 67 | "\\newcommand{\\obsind}{\\mathbf{x}}\n", 68 | "\\newcommand{\\sobsind}{x}\n", 69 | "\\newcommand{\\iobsall}{\\mathbf{W}}\n", 70 | "\\newcommand{\\iobsind}{\\mathbf{w}}\n", 71 | "\\newcommand{\\obsbar}{\\bar{\\mathbf{x}}}\n", 72 | "\\newcommand{\\obscov}{\\bar{\\mathbf{S}}}\n", 73 | "\\newcommand{\\olaball}{\\mathbf{Z}}\n", 74 | "\\newcommand{\\olabgrp}{\\mathbf{z}}\n", 75 | "\\newcommand{\\olabind}{z}\n", 76 | "\\newcommand{\\ilaball}{\\mathbf{Y}}\n", 77 | "\\newcommand{\\ilabind}{y}\n", 78 | "\\newcommand{\\allparam}{\\boldsymbol\\Theta}\n", 79 | "\\newcommand{\\allhyper}{\\boldsymbol\\Xi}\n", 80 | "\\newcommand{\\mwgtall}{\\mathbf{B}}\n", 81 | "\\newcommand{\\mwgtind}{\\boldsymbol{\\beta}}\n", 82 | "\\newcommand{\\mwgtmix}{\\beta}\n", 83 | "\\newcommand{\\wgtall}{\\boldsymbol\\Pi}\n", 84 | "\\newcommand{\\wgtind}{\\boldsymbol\\pi}\n", 85 | "\\newcommand{\\wgtmix}{\\pi}\n", 86 | "\\newcommand{\\stkall}{\\mathbf{V}}\n", 87 | "\\newcommand{\\stkmix}{v}\n", 88 | "\\newcommand{\\expall}{\\boldsymbol\\Theta}\n", 89 | "\\newcommand{\\expmix}{\\theta}\n", 90 | "\\newcommand{\\hypexn}{\\eta}\n", 91 | "\\newcommand{\\hypexv}{\\boldsymbol\\nu}\n", 92 | "\\newcommand{\\gausmean}{\\boldsymbol\\mu}\n", 93 | "\\newcommand{\\gauscov}{\\boldsymbol\\Sigma}\n", 94 | "\\newcommand{\\hypgausm}{\\mathbf{m}}\n", 95 | "\\newcommand{\\hypgausb}{\\gamma}\n", 96 | "\\newcommand{\\hypgausW}{\\boldsymbol{\\Omega}}\n", 97 | "\\newcommand{\\hypgausp}{\\rho}\n", 98 | "\\newcommand{\\igausmean}{\\boldsymbol\\eta}\n", 99 | "\\newcommand{\\igauscov}{\\boldsymbol\\Psi}\n", 100 | "\\newcommand{\\ihypgausm}{\\mathbf{h}}\n", 101 | "\\newcommand{\\ihypgausb}{\\delta}\n", 102 | "\\newcommand{\\ihypgausW}{\\boldsymbol{\\Phi}}\n", 103 | "\\newcommand{\\ihypgausp}{\\xi}\n", 104 | "\\newcommand{\\dirall}{\\alpha}\n", 105 | "\\newcommand{\\dirmix}{\\alpha}\n", 106 | "\\newcommand{\\dircall}{\\theta}\n", 107 | "\\newcommand{\\dircmix}{\\theta}\n", 108 | "\\newcommand{\\gdaall}{a}\n", 109 | "\\newcommand{\\gdball}{b}\n", 110 | "\\newcommand{\\gdamix}{a}\n", 111 | "\\newcommand{\\gdbmix}{b}\n", 112 | "\\newcommand{\\Cwidthi} {\\ensuremath{C_{w,i}}}\n", 113 | "\\newcommand{\\Cwidths} {\\ensuremath{C_{w,s}}}\n", 114 | "\\newcommand{\\ICAdic} {\\ensuremath{\\mathbf{D}}}\n", 115 | "\\newcommand{\\ICAdicp} {\\ensuremath{\\mathbf{D}^+}}\n", 116 | "\\newcommand{\\ICAresp} {\\ensuremath{\\mathbf{r}}}\n", 117 | "\\newcommand{\\Segment} {\\ensuremath{S_{jin}}}\n", 118 | "\\newcommand{\\dimim} {\\ensuremath{D_\\mathrm{im}}}\n", 119 | "\\newcommand{\\dimseg} {\\ensuremath{D_\\mathrm{seg}}}\n", 120 | "$$" 121 | ] 122 | }, 123 | { 124 | "cell_type": "markdown", 125 | "metadata": {}, 126 | "source": [ 127 | "#Clustering\n", 128 | "Regression and classification are very useful for when we have some targets/labels for training, however, what about situations where we do not have targets/labels? This is where unsupervised methods such as dimensionality reduction and clustering can help us out but trying to infer categories from the data (clustering) or a low dimensional representation from the data (dimensionality reduction). We have already seen a simple dimensionality reduction technique, PCA, in the first tutorial. In this tutorial we will look at some clustering algorithms and a latent variable model that can be both interpreted as clustering and dimensionality reduction.\n", 129 | "\n", 130 | "Clustering is one of the oldest data exploration methods. The objective is for an algorithm to discover sets of *similar* points, or observations, within a larger dataset. These sets are called *clusters*. Similarity is almost always characterised by some distance function between observations, such as Euclidean $\\ell_2$. Some of the more simple algorithms require the number of clusters to be specified in advance, while others can also infer this from the data, usually given other assumptions. K-means was one of the first and still most popular algorithms designed for this task." 131 | ] 132 | }, 133 | { 134 | "cell_type": "markdown", 135 | "metadata": {}, 136 | "source": [ 137 | "##K-means\n", 138 | "\n", 139 | "The objective of K-means clustering is to find $K$ clusters of observations\n", 140 | "within a dataset of $N$ observations, $\\obsall = \\cbrac{\\obsind_n}^N_{n=1}$, where $\\obsind_n \\in \\real{D}$. These clusters are characterised by their means, $\\mathbf{M} =\n", 141 | "\\cbrac{\\gausmean_k}^K_{k=1}$ where $\\gausmean_k \\in \\real{D}$. Each observation\n", 142 | "is assigned to a cluster mean using an integer label $\\olabind_n \\in \\cbrac{1,\\ldots,K}$,\n", 143 | "and $\\olaball = \\cbrac{\\olabind_n}^N_{n=1}$. The objective of K-means is to\n", 144 | "minimise the square loss, or reconstruction error,\n", 145 | "\\begin{equation}\n", 146 | " \\min_{\\mathbf{M},\\olaball} \\sum^N_{n=1} \\sum^K_{k=1} \\indic{\\olabind_n = k}\n", 147 | " \\norm{\\obsind_n - \\gausmean_k}{2}^2.\n", 148 | "\\end{equation}\n", 149 | "Here $\\indic{\\cdot}$ is an indicator function that evaluates to 1 when the\n", 150 | "condition in the brackets is true, and 0 otherwise. $\\norm{\\cdot}{2}$ is an\n", 151 | "$\\ell_2$ norm, or Euclidean distance. This is solved with two simple alternating\n", 152 | "steps. The first is the assignment step;\n", 153 | "\\begin{equation}\n", 154 | " \\olabind_n = \\argmin{k} \\norm{\\obsind_n - \\gausmean_k}{2}^2,\n", 155 | "\\end{equation}\n", 156 | "the next is the update step;\n", 157 | "\\begin{equation}\n", 158 | " \\gausmean_k = \\frac{\\sum_n \\indic{\\olabind_n = k} \\obsind_n}\n", 159 | " {\\sum_n \\indic{\\olabind_n = k}}.\n", 160 | "\\end{equation}\n", 161 | "These two steps are iterated until the square loss in objective has \n", 162 | "converged, and that's it! This is sometimes also referred to as the [Expectation-Maximisation (EM) algorithm](http://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm) because of its relationship to Gausian mixture models - more on this soon.\n", 163 | "\n", 164 | "Unfortunately this is not guaranteed to converge to a global minimum of the objective function, and usually many random initialisations (random choices of $\\obsind_n$ for the initial $\\gausmean_k$) have to be attempted to find the best solution. This algorithm is very fast in practice though. Another disadvantage is that the number of clusters, $K$, has to be specified in advance. Perhaps more of a concern is that clusters are assumed to be essentially spherical in shape because of the Euclidean distance used, which is quite often an over-simplification. It is also useful to have probabilistic assignments, $\\probC{\\olabind_n = k}{\\obsind_n}$ rather than hard assignments. Gaussian mixture models solve these last two problems." 165 | ] 166 | }, 167 | { 168 | "cell_type": "markdown", 169 | "metadata": {}, 170 | "source": [ 171 | "### Exercises\n", 172 | "\n", 173 | "**1)** Have a go at calculating the hard assignments, $\\olabind_n$, for the data, $\\obsind_n$, from the initial means/centres, $\\gausmean_k$, provided. Also try to plot the results using the provided function." 174 | ] 175 | }, 176 | { 177 | "cell_type": "code", 178 | "collapsed": false, 179 | "input": [ 180 | "# Importing some libraries and modules\n", 181 | "%pylab inline\n", 182 | "\n", 183 | "import numpy as np\n", 184 | "import matplotlib.pyplot as plt\n", 185 | "import tututils as tut" 186 | ], 187 | "language": "python", 188 | "metadata": {}, 189 | "outputs": [] 190 | }, 191 | { 192 | "cell_type": "code", 193 | "collapsed": false, 194 | "input": [ 195 | "# Load X from a dataset generation function from tututils\n", 196 | "X = tut.load_2d_simple()\n", 197 | "K = 3 # There are three clusters in this dataset\n", 198 | "N = X.shape[0]\n", 199 | "k_means_cluster_centers = X[np.random.randint(0, N, size=K), :]\n", 200 | "\n", 201 | "# Now calculate Z from X and k_means_cluster_centers.\n", 202 | "# Tip: consider using numpy's argmin()\n", 203 | "\n", 204 | "#TODO: k_means_labels = \n", 205 | "\n", 206 | "# Check your answer by plotting the clusters: \n", 207 | "tut.plot_2d_clusters(X, k_means_labels, k_means_cluster_centers)" 208 | ], 209 | "language": "python", 210 | "metadata": {}, 211 | "outputs": [] 212 | }, 213 | { 214 | "cell_type": "markdown", 215 | "metadata": {}, 216 | "source": [ 217 | "**2)** Now have a go at calculating the cluster means, $\\gausmean_k$, given the cluster assignments, $\\olabind_n$, calculated previously. Again, plot the results using the provided function." 218 | ] 219 | }, 220 | { 221 | "cell_type": "code", 222 | "collapsed": false, 223 | "input": [ 224 | "# Calculate k_means_cluster_centers from X and k_means_labels\n", 225 | "\n", 226 | "#TODO: k_means_cluster_centers = \n", 227 | "\n", 228 | "# Check your answer by plotting the clusters:\n", 229 | "# TIP: You may need to re-do the labels to make the vornoi cells match the labels\n", 230 | "\n", 231 | "#TODO: re-do labels (optional)\n", 232 | "\n", 233 | "tut.plot_2d_clusters(X, k_means_labels, k_means_cluster_centers)" 234 | ], 235 | "language": "python", 236 | "metadata": {}, 237 | "outputs": [] 238 | }, 239 | { 240 | "cell_type": "markdown", 241 | "metadata": {}, 242 | "source": [ 243 | "**3)** Let's tie it all together now, and implement the K-means clustering algorithm in its entirety, you can use the following code as a template, or you can make your own from scratch. Once the algorithm works and converges, plot the final result to see how it differs from the above plots. " 244 | ] 245 | }, 246 | { 247 | "cell_type": "code", 248 | "collapsed": false, 249 | "input": [ 250 | "# Funcion template -- fill in the gaps\n", 251 | "def kmeans(X, K, maxit=100):\n", 252 | " \n", 253 | " # initialise\n", 254 | " N, D = X.shape\n", 255 | " M = X[np.random.randint(0, N, size=K), :]\n", 256 | " obj = np.finfo(float).max\n", 257 | " \n", 258 | " # TODO: Any initialisation code\n", 259 | " \n", 260 | " for i in range(maxit):\n", 261 | " objo = obj\n", 262 | " \n", 263 | " # TODO: E-step, update indicators \n", 264 | " # TODO: M-step, update means\n", 265 | " # TODO: Calculate loss function i.e. obj =\n", 266 | " \n", 267 | " if (objo - obj) / objo < 1e-5:\n", 268 | " break\n", 269 | " \n", 270 | " return Z, M" 271 | ], 272 | "language": "python", 273 | "metadata": {}, 274 | "outputs": [] 275 | }, 276 | { 277 | "cell_type": "code", 278 | "collapsed": false, 279 | "input": [ 280 | "# Call your kmeans function on the data\n", 281 | "\n", 282 | "#TODO: k_means_labels, k_means_cluster_centers = \n", 283 | "\n", 284 | "# plot the final result\n", 285 | "tut.plot_2d_clusters(X, k_means_labels, k_means_cluster_centers)" 286 | ], 287 | "language": "python", 288 | "metadata": {}, 289 | "outputs": [] 290 | }, 291 | { 292 | "cell_type": "markdown", 293 | "metadata": {}, 294 | "source": [ 295 | "**4)** K-means is often used to quantise various datasets, for instance, we can use it to \"compress\" images by clustering the RGB data into fewer colors. Open up the [kmeans-image](http://localhost:8888/notebooks/kmeans-image.ipynb) notebook to run this example (if you are running out of time, feel free to move on)." 296 | ] 297 | }, 298 | { 299 | "cell_type": "markdown", 300 | "metadata": {}, 301 | "source": [ 302 | "##Gaussian Mixture Models\n", 303 | "[Gaussian mixture models](http://en.wikipedia.org/wiki/Mixture_model#Gaussian_mixture_model) (GMMs) can be viewed as a probabilistic generalisation of K-means (i.e. probabilistic cluster assignments) with the added ability to learn ellipsoidal clusters. In a GMM each observation is distributed according to a weighted sum of $K$ multivariate Gaussian distributions;\n", 304 | "\\begin{equation}\n", 305 | " \\obsind_n \\sim \\sum^K_{k=1} \\wgtmix_k \\gausC{\\obsind_n}{\\gausmean_k,\n", 306 | " \\gauscov_k}.\n", 307 | "\\end{equation}\n", 308 | "Here $\\wgtind = [\\wgtmix_1,\\ldots,\\wgtmix_k,\\ldots,\\wgtmix_K]\\transpose$ and $\\wgtmix_k \\in [0,1]$, with $\\sum_k \\wgtmix_k = 1$. $\\gauscov_k$ is a covariance matrix that describes the \"spread\" of uncertainty in the Gaussian distribution, which is usually ellipsoidal in shape. Here is an example of what a GMM may look like in two dimensions (we have plotted the 65% probability mass contours for the Gaussians):\n", 309 | "\n", 310 | "![2D GMM](clusters.png)\n", 311 | "\n", 312 | "The weights of each Gaussian have in this mixture have not been explicitly represented, but they are implicit in the amount of observations (darkness of the voxels) they are modelling.\n", 313 | "\n", 314 | ">The following is a brief explanation of a GMM, it is more complex than K-means, so do not worry if you don't understand it fully - a full grasp of GMMs is not required for the exercises.\n", 315 | "\n", 316 | "We need a way to explicitly assign observations to mixtures or clusters. The same latent variable, $\\olabind_n$, used in K-means is introduced here as an auxiliary variable for this purpose, by inducing the following conditional relationship;\n", 317 | "\\begin{equation}\n", 318 | " \\probC{\\obsind_n}{\\olabind_n} = \\prod^K_{k=1}\n", 319 | " \\gausC{\\obsind_n}{\\gausmean_k, \\gauscov_k}^\\indic{\\olabind_n=k},\n", 320 | "\\end{equation}\n", 321 | "so given a cluster, $\\probC{\\obsind_n}{\\olabind_k=k} = \\gausC{\\obsind_n}\n", 322 | "{\\gausmean_k, \\gauscov_k}$. Now it can be seen that each cluster is\n", 323 | "modelled as a single Gaussian with a full covariance matrix. This auxiliary\n", 324 | "variable is itself distributed according to a Categorical distribution (same as a Multinomial distribution but with only one observation);\n", 325 | "\\begin{equation}\n", 326 | " \\olabind_n \\sim \\categ{\\wgtind} \n", 327 | " = \\prod^K_{k=1} \\wgtmix_k^\\indic{\\olabind_n = k}.\n", 328 | "\\end{equation}\n", 329 | "The joint distribution for this GMM can be written as,\n", 330 | "\\begin{equation}\n", 331 | " \\prob{\\obsall, \\olaball} = \\prod^N_{n=1} \\categC{\\olabind_n}{\\wgtind} \n", 332 | " \\prod^K_{k=1} \n", 333 | " \\gausC{\\obsind_n}{\\gausmean_k, \\gauscov_k}^\\indic{\\olabind_n=k}.\n", 334 | "\\end{equation}\n", 335 | "\n", 336 | "Now we need an algorithm that can learn the labels, $\\olabind_n$, cluster\n", 337 | "parameters, $\\gausmean_k$ and $\\gauscov_k$, and mixture weights, $\\wgtind$. Such an algorithm can be derived by maximising the *log-likelihood* of the data, \n", 338 | "\\begin{equation}\n", 339 | " \\log \\prob{\\obsall} = \\sum_{n=1}^N\n", 340 | " \\log \\sum^K_{k=1} \\wgtmix_k \\gausC{\\obsind_n}{\\gausmean_k,\n", 341 | " \\gauscov_k},\n", 342 | "\\end{equation}\n", 343 | "which is acheived by setting the partial derivative of this equation with respect to each parameter and the labels in turn to zero and solving for the parameters/labels.\n", 344 | "\n", 345 | "Firstly, maximising the log-likelihood with respect to $\\olabind_n$, yields;\n", 346 | "\\begin{equation}\n", 347 | " \\probC{\\olabind_n = k}{\\obsind_n} = \n", 348 | " \\frac{\\wgtmix_k \\gausC{\\obsind_n}{\\gausmean_k, \\gauscov_k}}\n", 349 | " {\\sum_l \\wgtmix_l \\gausC{\\obsind_n}{\\gausmean_l, \\gauscov_l}},\n", 350 | "\\end{equation}\n", 351 | "This is known as the *expectation* step, since the labels are probabilistically assigned their expected value given the observations and cluster parameters. \n", 352 | "\n", 353 | "Next, the parameters can be found by maximising the log-likelihood \n", 354 | "with respect to each parameter; \n", 355 | "\\begin{align}\n", 356 | " \\gausmean_k &= \\frac{\\sum_n \\probC{\\olabind_n=k}{\\obsind_n} \\obsind_n}\n", 357 | " {\\sum_n \\probC{\\olabind_n=k}{\\obsind_n}}, \\\\\n", 358 | " \\gauscov_k &= \\frac{1}{\\sum_n \\probC{\\olabind_n=k}{\\obsind_n}}\n", 359 | " \\sum^N_{n=1} \\probC{\\olabind_n = k}{\\obsind_n} (\\obsind_n -\n", 360 | " \\gausmean_k)(\\obsind_n - \\gausmean_k)\\transpose, \\\\\n", 361 | " \\wgtmix_k &= \\sum^N_{n=1} \\frac{\\probC{\\olabind_n = k}{\\obsind_n}}\n", 362 | " {\\sum_k \\probC{\\olabind_n = k}{\\obsind_n}}.\n", 363 | "\\end{align}\n", 364 | "This is called the *maximisation* step, because the value of the\n", 365 | "log-likelihood is maximised with respect to the parameters given the estimated latent variables. These two steps are iterated until the log-likelihood converges. This is known as the *expectation-maximisation* EM algorithm. For all intents and purposes it is the same algorithm used to learn K-means. \n", 366 | "\n", 367 | "Unfortunately this algorithm has a few drawbacks. Like K-means, it is only\n", 368 | "guaranteed to converge to a local maximum of the likelihood function. Also, the Gaussian cluster updates require a full $D \\times D$ covariance matrix inversion, which has an $\\bigO{D^3}$ computational cost. This can be circumvented by using diagonal covariance Gaussian clusters, or other distributions such as Multinomial, that have only $\\bigO{D}$ computational cost. Though some expressive power is lost since inter-dimensional correlation is not modelled.\n", 369 | "\n", 370 | "Another drawback is that this algorithm still cannot choose $K$. One way to\n", 371 | "allow the EM algorithm to choose $K$ is to include a penalty, or\n", 372 | "regulariser, for having too many parameters. In this way the maximum-likelihood fitting objective can be traded off against a model complexity penalty. Some popular penalties are the [Akaike information criterion](http://en.wikipedia.org/wiki/Akaike_information_criterion) and the [Bayesian information criterion](http://en.wikipedia.org/wiki/Bayesian_information_criterion). These criterion tend to under-penalise model complexity, and are sometimes computationally costly to calculate. Another way to choose $K$ is to use a fully Bayesian treatment, where we place prior distributions on the parameters (e.g. mean, covariance and weights), and then optimise the [log *marginal* likelihood](http://en.wikipedia.org/wiki/Marginal_likelihood) of the model, which also naturally incorporates a penalty for complexity. In the case of mixture models, the Bayesian learning algorithms can have very little additional computational cost compared to EM. For more information on EM algorithms for mixture models, see (Bishop, 2006) Chapters 9 and 10.\n", 373 | "\n" 374 | ] 375 | }, 376 | { 377 | "cell_type": "markdown", 378 | "metadata": {}, 379 | "source": [ 380 | "### Exercises\n", 381 | "\n", 382 | "**5)** Run K-means on the following dataset with 3 clusters and visualise the results" 383 | ] 384 | }, 385 | { 386 | "cell_type": "code", 387 | "collapsed": false, 388 | "input": [ 389 | "# Load X from a dataset generation function from tututils\n", 390 | "X, truth = tut.load_2d_hard()\n", 391 | "\n", 392 | "#TODO: run K-means\n", 393 | "\n", 394 | "tut.plot_2d_clusters(X, labels, centres)" 395 | ], 396 | "language": "python", 397 | "metadata": {}, 398 | "outputs": [] 399 | }, 400 | { 401 | "cell_type": "markdown", 402 | "metadata": {}, 403 | "source": [ 404 | "**6)** Now cluster the same data with a GMM, why do you think these results are so different?" 405 | ] 406 | }, 407 | { 408 | "cell_type": "code", 409 | "collapsed": false, 410 | "input": [ 411 | "from sklearn.mixture import GMM\n", 412 | "\n", 413 | "# Hint, use covariance_type='full' option\n", 414 | "\n", 415 | "#TODO: run GMM\n", 416 | "\n", 417 | "# Plot\n", 418 | "tut.plot_2d_GMMs(X, labels, means, covs)" 419 | ], 420 | "language": "python", 421 | "metadata": {}, 422 | "outputs": [] 423 | }, 424 | { 425 | "cell_type": "markdown", 426 | "metadata": {}, 427 | "source": [ 428 | "**7)** Ok, now try K-means and GMMs with 6 clusters and plot the results, what happens?" 429 | ] 430 | }, 431 | { 432 | "cell_type": "code", 433 | "collapsed": false, 434 | "input": [ 435 | "# Kmeans clustering\n", 436 | "\n", 437 | "#TODO: run K-means\n", 438 | "\n", 439 | "tut.plot_2d_clusters(X, labels_k, centres)\n", 440 | "\n", 441 | "# GMM clustering\n", 442 | "\n", 443 | "#TODO: run GMM\n", 444 | "\n", 445 | "# Plot\n", 446 | "tut.plot_2d_GMMs(X, labels_g, means, covs)" 447 | ], 448 | "language": "python", 449 | "metadata": {}, 450 | "outputs": [] 451 | }, 452 | { 453 | "cell_type": "markdown", 454 | "metadata": {}, 455 | "source": [ 456 | "As you can see, if we don't have a reasonable idea of the number of clusters before we begin, we may not get great results. As mentioned before, there are clustering methods that can also infer the number of clusters, some of which include:\n", 457 | "* variational Bayes Gaussian mixture models (VBGMM) ([Attias, 1999](http://arxiv.org/pdf/1301.6676.pdf); Bishop, 2006)\n", 458 | "* Dirichlet process or infinite Gaussian mixture models ([Rasmussen, 1999](http://www.gatsby.ucl.ac.uk/~edward/pub/inf.mix.nips.99.pdf))\n", 459 | "* Spectral clustering ([von Luxburg, 2007](http://www.informatik.uni-hamburg.de/ML/contents/people/luxburg/publications/Luxburg07_tutorial.pdf))\n", 460 | "* [DBSCAN](http://scikit-learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html)\n", 461 | "\n", 462 | "The scikit learn [clustering](http://scikit-learn.org/stable/modules/clustering.html) documentation also has a nice summary of the capabilites of many popular clustering algorithms, including a demonstration of the types of cluster shapes that can be modelled:\n", 463 | "\n", 464 | "Scikit learn cluster demo\n", 465 | "\n", 466 | "**8)** If we have some kind of ground truth labels (as we do in the `truth` variable from ex. 5) we can get a measure of a clustering solutions validity from various measures. One of the more popular and robust measure is [Normalised Mutual Information](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.normalized_mutual_info_score.html) (NMI). What is nice about this measure is that the *number of cluster labels do not have to match the number of ground truth labels* unlike many classification metrics. \n", 467 | "\n", 468 | "Run both K-means and the GMM for varying number of clusters (1 to 6), and plot their NMI vs. number of clusters. " 469 | ] 470 | }, 471 | { 472 | "cell_type": "code", 473 | "collapsed": false, 474 | "input": [ 475 | "from sklearn.metrics import normalized_mutual_info_score\n", 476 | "\n", 477 | "Ks = range(1, 7)\n", 478 | "NMI_k = []\n", 479 | "NMI_g = []\n", 480 | "\n", 481 | "for k in Ks:\n", 482 | " \n", 483 | " # Kmeans clustering\n", 484 | " \n", 485 | " #TODO: run K-means\n", 486 | " #TODO: get NMI\n", 487 | " #TODO: append NMI, i.e. NMI_k.append(TODO)\n", 488 | " \n", 489 | " # GMM clustering\n", 490 | " \n", 491 | " #TODO: run GMM\n", 492 | " #TODO: get NMI\n", 493 | " #TODO: append NMI, i.e. NMI_g.append(TODO)\n", 494 | "\n", 495 | "#TODO: Plot both K-means NMI and GMM NMI vs. number of clusters" 496 | ], 497 | "language": "python", 498 | "metadata": {}, 499 | "outputs": [] 500 | }, 501 | { 502 | "cell_type": "markdown", 503 | "metadata": {}, 504 | "source": [ 505 | "In reality, if we had all, or even some, of the labels like this it would more prudent to use a supervised classification method and the corresponding supervised classification performance metrics (like percent classification error, F-measure, etc). However clustering is still useful as a data exploration strategy, as well as a feature creation method for classification -- it is quite common to see kmeans with (very) large K being used to cluster inputs to a linear classifier to improve classification performance, among other strategies.\n", 506 | "\n", 507 | "As a final note, I would recommend against using the implementation of [Variational Bayes GMMs](http://scikit-learn.org/stable/modules/generated/sklearn.mixture.VBGMM.html) and [Dirichlet Process GMMs](http://scikit-learn.org/stable/modules/generated/sklearn.mixture.DPGMM.html) in scikit learn for now, I have never had much luck with them, and could not even get them to fit the above datasets. If you would like to test out these algorithms, I have a much more robust implementation in [libcluster](https://github.com/dsteinberg/libcluster). " 508 | ] 509 | }, 510 | { 511 | "cell_type": "markdown", 512 | "metadata": {}, 513 | "source": [ 514 | "# Topic Models\n", 515 | "The purpose of topic modelling is to generally learn some low-dimensional representation of a large collection of textual documents, called a *corpus*. The representation can be used to summarize a corpus, or for retrieval of documents that are similar to a query document.\n", 516 | "\n", 517 | "Typically topic models are learned by analysing the distribution of words within a corpus, in particular how they cluster together within documents that have similar subjects. These clusters of words are referred to as \"topics\", and documents may comprise several topics in different amounts. These topics are essentially the low-dimensional representation of documents learned by topic models. \n", 518 | "\n", 519 | "## Latent Dirichlet Allocation\n", 520 | "One of the most well known topic models is [latent Dirichlet allocation](http://en.wikipedia.org/wiki/Latent_Dirichlet_allocation) (LDA) (Blei, 2003), also known as multinomial PCA (Buntine, 2002). \n", 521 | "\n", 522 | "Typically a corpus is broken down as follows:\n", 523 | "* There are $J$ documents in a corpus,\n", 524 | "* there are $N_j$ words in each document, $j$,\n", 525 | "* a word, $\\sobsind_{nj}$, is represented as an *index* into a vocabulary, i.e. $\\sobsind_{jn} \\in \\cbrac{1,\\ldots,D}$ where $D$ is the size of the vocabulary.\n", 526 | "\n", 527 | "So we can think of our whole dataset (corpus) being made up of sub-datasets (documents), $\\obsall = \\cbrac{\\obsall_j}^J_{j=1}$, which are collections of words in each document, $\\obsall_j = \\cbrac{\\sobsind_{jn}}^{N_j}_{n=1}$. This is called a *bag of words* model, because order of the words is assumed unimportant. This simplifying assumption is known as the exchangeability assumption. \n", 528 | "\n", 529 | "LDA goes on to model a corpus as follows:\n", 530 | "* Each document, $j$, is represented as a *low-dimensional* proportion of $K$ topics $$\\wgtind_j \\sim \\dir{\\dirall},$$ where $\\wgtind_j = \\cbrac{\\wgtmix_{j1}, \\ldots, \\wgtmix_{jK}}$ and $\\sum_k \\wgtmix_k = 1$.\n", 531 | "* Each word, $\\sobsind_{jn}$, is drawn from a *per-topic vocabulary*, represented as a categorical distribution, in proportion to the *per-document topic mixture* $$\\sobsind_{jn} \\sim \\sum^K_{k=1} \\wgtmix_{jk} \\categC{\\sobsind_{jn}}{\\mwgtind_k},$$ where $\\mwgtind_k$ are the parameters of the topic categorical distribution (which are also vector of weights that sum to one).\n", 532 | "\n", 533 | "This is very similar to the GMM we saw before, the differences being that we now have Categorical clusters as opposed to Gaussian clusters, and that we have mixture weights, $\\wgtmix_{jk}$, *specific to each document*. What is nice is that the clusters/topics are *shared* over all documents. This enables us to view these topic/cluster weights, $\\wgtind_j$ as a low-dimensional description of the original document, i.e. a mixture of topics!\n", 534 | "\n", 535 | "This is a Bayesian model and sometimes has a prior also placed on $\\mwgtind_k \\sim \\dir{\\dircall}$, which is called smoothed LDA.\n", 536 | "\n", 537 | "LDA can use fast sampling techniques, such as Gibbs sampling, or approximate marginal likelihood techniques, such as variational Bayes, for learning the model latent variables and hyper-parameters. Limitations have also been found with LDA. For example, it is not effective in choosing the number of topics ($K$), and the symmetric Dirichlet prior over topic weights, has been found to be too restrictive. Hierarchical Dirichlet processes (Teh, 2006) have been developed to overcome both of these issues (but is beyond the scope of this tutorial)." 538 | ] 539 | }, 540 | { 541 | "cell_type": "markdown", 542 | "metadata": {}, 543 | "source": [ 544 | "**9)** For this exercise we will run LDA on a fairly standard dataset comprising news articles from Reuters.\n", 545 | "\n", 546 | "For this exercise you'll need [this](https://pypi.python.org/pypi/lda) python LDA package. It can be installed via pip easily:\n", 547 | " \n", 548 | " $ sudo pip install lda # you may need to use your distribution's version of pip (pip3, pip-python3, conda etc)\n", 549 | "\n", 550 | "Also, this *may* require you to also manually install the `pbr` python package (also through pip). \n", 551 | "Now, essentially follow the getting started tutorial in the [documentation](http://pythonhosted.org//lda/getting_started.html). It is worth noting that this dataset has undergone quite a bit of pre-processing, such as removing certain [\"stop\" words](http://en.wikipedia.org/wiki/Stop_words) so the resultant topics are not inundated with common and uninformative words likes \"and\"." 552 | ] 553 | }, 554 | { 555 | "cell_type": "code", 556 | "collapsed": false, 557 | "input": [ 558 | "import lda\n", 559 | "import lda.datasets\n", 560 | "\n", 561 | "# Load the data\n", 562 | "X = lda.datasets.load_reuters()\n", 563 | "vocab = lda.datasets.load_reuters_vocab()\n", 564 | "\n", 565 | "# TODO: create the LDA object with 20 topics\n", 566 | "#model = \n", 567 | "\n", 568 | "# TODO: fit the LDA object to data\n", 569 | "\n", 570 | "# Print out a selection of topics\n", 571 | "topic_word = model.topic_word_ # model.components_ also works\n", 572 | "n_top_words = 8\n", 573 | "for i, topic_dist in enumerate(topic_word):\n", 574 | " topic_words = np.array(vocab)[np.argsort(topic_dist)][:-n_top_words:-1]\n", 575 | " print('Topic {}: {}'.format(i, ' '.join(topic_words)))" 576 | ], 577 | "language": "python", 578 | "metadata": {}, 579 | "outputs": [] 580 | }, 581 | { 582 | "cell_type": "markdown", 583 | "metadata": {}, 584 | "source": [ 585 | "**10)** Try setting the number of topics found to different numbers, and see what impact there is on the results." 586 | ] 587 | }, 588 | { 589 | "cell_type": "code", 590 | "collapsed": false, 591 | "input": [ 592 | "# TODO, repeat above, but with a different number of topics" 593 | ], 594 | "language": "python", 595 | "metadata": {}, 596 | "outputs": [] 597 | }, 598 | { 599 | "cell_type": "markdown", 600 | "metadata": {}, 601 | "source": [ 602 | "# Bibliography\n", 603 | "\n", 604 | "* (Bishop, 2006) C. M. Bishop. Pattern Recognition and Machine Learning. Springer Science+Business Media, Cambridge, UK, 2006.\n", 605 | "\n", 606 | "* (Blei, 2003) D. M. Blei and M. I. Jordan. Modeling annotated data. In Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval, SIGIR \u201903, pages 127\u2013134, New York, NY, USA, 2003. ACM. ISBN 1-58113-646-3.\n", 607 | "\n", 608 | "* (Buntine, 2002) W. Buntine. Variational extensions to EM and multinomial PCA. Machine Learning: ECML 2002, pages 23\u201334, 2002.\n", 609 | "\n", 610 | "* (Teh, 2006) Y. W. Teh, M. I. Jordan, M. J. Beal, and D. M. Blei. Hierarchical Dirichlet processes. Journal of the American Statistical Association, 101(476):1566\u20131581, 2006.\n", 611 | "\n" 612 | ] 613 | } 614 | ], 615 | "metadata": {} 616 | } 617 | ] 618 | } -------------------------------------------------------------------------------- /classification/titanic_train.csv: -------------------------------------------------------------------------------- 1 | PassengerId,Survived,Pclass,Name,Sex,Age,SibSp,Parch,Ticket,Fare,Cabin,Embarked 2 | 2,1,1,"Cumings, Mrs. John Bradley (Florence Briggs Thayer)",female,38,1,0,PC 17599,71.2833,C85,C 3 | 3,1,3,"Heikkinen, Miss. Laina",female,26,0,0,STON/O2. 3101282,7.925,,S 4 | 4,1,1,"Futrelle, Mrs. Jacques Heath (Lily May Peel)",female,35,1,0,113803,53.1,C123,S 5 | 5,0,3,"Allen, Mr. William Henry",male,35,0,0,373450,8.05,,S 6 | 6,0,3,"Moran, Mr. James",male,,0,0,330877,8.4583,,Q 7 | 9,1,3,"Johnson, Mrs. Oscar W (Elisabeth Vilhelmina Berg)",female,27,0,2,347742,11.1333,,S 8 | 11,1,3,"Sandstrom, Miss. 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