├── AdjustedRandIndex.m
├── DATASETS
    └── Coffee
    │   ├── Coffee_TEST
    │   └── Coffee_TRAIN
├── DEMO_multivariate.m
├── DEMO_univariate.m
├── LICENSE
├── LoadUAEdataset.m
├── LoadUCRdataset.m
├── MULTIVARIATE_DATASETS
    └── ERing
    │   ├── ERing_DATA.h5
    │   └── ERing_LABEL.h5
├── NCCc_multivariate.m
├── NCCc_univariate.m
├── NormalizedMutualInformation.m
├── README.md
├── RandIndex.m
├── SBD_multivariate.m
├── SBD_univariate.m
├── docs
    └── kShape.png
├── kShape_multivariate.m
└── kShape_univariate.m


/AdjustedRandIndex.m:
--------------------------------------------------------------------------------
 1 | function ari = AdjustedRandIndex(p1, p2)
 2 |     N = length(p1);
 3 |     [~, ~, p1] = unique(p1);
 4 |     N1 = max(p1);
 5 |     [~, ~, p2] = unique(p2);
 6 |     N2 = max(p2);
 7 | 
 8 |     for i=1:1:N1
 9 |         for j=1:1:N2
10 |             G1 = find(p1==i);
11 |             G2 = find(p2==j);
12 |             n(i,j) = length(intersect(G1,G2));
13 |         end
14 |     end
15 | 
16 |     ssm = 0;
17 |     sm1 = 0;
18 |     sm2 = 0;
19 |     for i=1:1:N1
20 |         for j=1:1:N2
21 |             ssm = ssm + nchoosek2(n(i,j),2);
22 |         end
23 |     end
24 |     temp = sum(n,2);
25 |     for i=1:1:N1
26 |         sm1 = sm1 + nchoosek2(temp(i),2);
27 |     end
28 |     temp = sum(n,1);
29 |     for i=1:1:N2
30 |         sm2 = sm2 + nchoosek2(temp(i),2);
31 |     end
32 |     NN = ssm - sm1*sm2/nchoosek2(N,2);
33 |     DD = (sm1 + sm2)/2 - sm1*sm2/nchoosek2(N,2);
34 |     
35 |     if (NN == 0 && DD==0)
36 |        ari = 1;
37 |     else
38 |        ari = NN/DD;
39 |     end
40 | 
41 | 
42 |     function c = nchoosek2(a,b)
43 |         if a>1
44 |             c = nchoosek(a,b);
45 |         else
46 |             c = 0;
47 |         end
48 |     end
49 | end
50 | 


--------------------------------------------------------------------------------
/DATASETS/Coffee/Coffee_TEST:
--------------------------------------------------------------------------------
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29 | 


--------------------------------------------------------------------------------
/DEMO_multivariate.m:
--------------------------------------------------------------------------------
 1 | function DEMO_multivariate(DataSetStartIndex, DataSetEndIndex, thisrun)  
 2 | 
 3 |     Datasets = [];
 4 |     f = dir('MULTIVARIATE_DATASETS');
 5 |     for i = 3:length(f)
 6 |         Datasets = [Datasets; cellstr(f(i).name)];
 7 |     end
 8 | 
 9 |     % Sort Datasets
10 |     [Datasets, DSOrder] = sort(Datasets);    
11 | 
12 |     rand_idxs = zeros(length(Datasets),1);
13 |     timing_idxs = zeros(length(Datasets),1);
14 |     results = zeros(length(Datasets),2);
15 |     
16 |     for i = 1:length(Datasets)
17 |             if (i>=DataSetStartIndex & i<=DataSetEndIndex)
18 |                     display(['Dataset being processed: ', char(Datasets(i))]);
19 |                     DS = LoadUAEdataset(char(Datasets(i)));
20 |                     for rep = 1 : 1
21 | 			[labels centroids] = kShape_multivariate(DS.Data, length(DS.ClassNames));
22 | 			disp(RandIndex(labels, DS.DataClassLabels))
23 | 			disp(AdjustedRandIndex(labels, DS.DataClassLabels))
24 | 			disp(NormalizedMutualInformation(labels, DS.DataClassLabels))
25 | 		    end
26 |             end
27 |     end
28 |     
29 | end
30 | 


--------------------------------------------------------------------------------
/DEMO_univariate.m:
--------------------------------------------------------------------------------
 1 | function DEMO_univariate(DataSetStartIndex, DataSetEndIndex, thisrun)  
 2 |         
 3 |     Datasets = [];
 4 |     f = dir('DATASETS');
 5 |     for i = 3:length(f)
 6 |         Datasets = [Datasets; cellstr(f(i).name)];
 7 |     end
 8 | 
 9 |     % Sort Datasets
10 |     [Datasets, DSOrder] = sort(Datasets);    
11 | 
12 |     rand_idxs = zeros(length(Datasets),1);
13 |     timing_idxs = zeros(length(Datasets),1);
14 |     results = zeros(length(Datasets),2);
15 |     
16 |     for i = 1:length(Datasets)
17 |             if (i>=DataSetStartIndex & i<=DataSetEndIndex)
18 |                     display(['Dataset being processed: ', char(Datasets(i))]);
19 |                     DS = LoadUCRdataset(char(Datasets(i)));
20 |                     for rep = 1 : 1
21 | 			[labels centroids] = kShape_univariate(DS.Data, length(DS.ClassNames));
22 | 			disp(RandIndex(labels, DS.DataClassLabels))
23 | 			disp(AdjustedRandIndex(labels, DS.DataClassLabels))
24 | 			disp(NormalizedMutualInformation(labels, DS.DataClassLabels))
25 | 		    end
26 |             end
27 |     end
28 |     
29 | end
30 | 


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/LICENSE:
--------------------------------------------------------------------------------
 1 | MIT License
 2 | 
 3 | Copyright (c) 2022 The Datum Lab
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 | 


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/LoadUAEdataset.m:
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 1 | function DS = LoadUAEdataset(datasetname)
 2 | 
 3 |     DATA = h5read(['MULTIVARIATE_DATASETS/',datasetname,'/',datasetname,'_DATA.h5'], '/data');
 4 |     DATA = permute(DATA, [3, 2, 1]);
 5 |     LABEL  = h5read(['MULTIVARIATE_DATASETS/',datasetname,'/',datasetname,'_LABEL.h5'], '/data');
 6 |    
 7 |     %DATA = zscore(DATA,[],2);
 8 | 
 9 |     DS.DataClassLabels = [LABEL+1];
10 |     DS.Data = [DATA];
11 |     DS.ClassNames = unique(LABEL);
12 |     DS.DataInstancesCount = length(DS.Data(:,1));
13 | end
14 | 


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/LoadUCRdataset.m:
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 1 | function DS = LoadUCRdataset(datasetname)
 2 |     
 3 |     TRAIN = load(['DATASETS/',datasetname,'/',datasetname,'_TRAIN']);
 4 |     TEST  = load(['DATASETS/',datasetname,'/',datasetname,'_TEST']);
 5 |         
 6 |     TRAIN_labels = TRAIN(:,1);     
 7 |     TRAIN(:,1) = [];                     
 8 |     TEST_labels = TEST(:,1);       
 9 |     TEST(:,1) = [];                     
10 |    
11 |     TRAIN = zscore(TRAIN,[],2);
12 |     TEST = zscore(TEST,[],2);
13 |     
14 |     DS.TrainClassLabels = TRAIN_labels;
15 |     DS.TestClassLabels = TEST_labels;
16 |     DS.DataClassLabels = [TRAIN_labels;TEST_labels];
17 |     
18 |     DS.Train = TRAIN;
19 |     DS.Test = TEST;
20 |     DS.Data = [TRAIN;TEST];
21 |     
22 |     DS.ClassNames = unique(TRAIN_labels);
23 | 
24 |     DS.TrainInstancesCount = length(DS.Train(:,1));
25 |     DS.TestInstancesCount = length(DS.Test(:,1));
26 |     DS.DataInstancesCount = length(DS.Data(:,1));
27 | end
28 | 


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/MULTIVARIATE_DATASETS/ERing/ERing_DATA.h5:
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https://raw.githubusercontent.com/TheDatumOrg/kshape-matlab/95950cbefaf26365b49e4c6f98ddb1882ee35262/MULTIVARIATE_DATASETS/ERing/ERing_DATA.h5


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/MULTIVARIATE_DATASETS/ERing/ERing_LABEL.h5:
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https://raw.githubusercontent.com/TheDatumOrg/kshape-matlab/95950cbefaf26365b49e4c6f98ddb1882ee35262/MULTIVARIATE_DATASETS/ERing/ERing_LABEL.h5


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/NCCc_multivariate.m:
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 1 | function cc_sequence = NCCc_multivariate(x,y)
 2 | 
 3 | if isrow(x)
 4 |     x=x';
 5 | end
 6 | if isrow(y)
 7 |     y=y';
 8 | end
 9 | 
10 | x = squeeze(x);
11 | y = squeeze(y);
12 | 
13 | len = length(x);
14 | 
15 | fftlength = 2^nextpow2(2*len-1);
16 | r = ifft(fft(x,fftlength,1) .* conj(fft(y,fftlength,1)));
17 | r = [r(end-len+2:end, :) ; r(1:len, :)];
18 | 
19 | 
20 | if norm(vecnorm(x,2,2))*norm(vecnorm(y,2,2)) < 1e-9;
21 |    cc_sequence = zeros(1, size(x, 1));
22 |    return;
23 | else
24 |    cc_sequence = sum(r, 2)./(norm(vecnorm(x,2,2))*norm(vecnorm(y,2,2)));
25 | end
26 | 


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/NCCc_univariate.m:
--------------------------------------------------------------------------------
 1 | function cc_sequence = NCCc_univariate(x,y)
 2 | 
 3 | if isrow(x)
 4 |     x=x';
 5 | end
 6 | if isrow(y)
 7 |     y=y';
 8 | end
 9 | 
10 | len = length(x);
11 | 
12 | fftlength = 2^nextpow2(2*len-1);
13 | r = ifft( fft(x,fftlength) .* conj(fft(y,fftlength)) );
14 | 
15 | r = [r(end-len+2:end) ; r(1:len)];
16 | 
17 | cc_sequence = r./(norm(x)*norm(y));
18 | 


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/NormalizedMutualInformation.m:
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 1 | function z = NormalizedMutualInformation(x, y)
 2 | assert(numel(x) == numel(y));
 3 | n = numel(x);
 4 | x = reshape(x,1,n);
 5 | y = reshape(y,1,n);
 6 | 
 7 | l = min(min(x),min(y));
 8 | x = x-l+1;
 9 | y = y-l+1;
10 | k = max(max(x),max(y));
11 | 
12 | idx = 1:n;
13 | Mx = sparse(idx,x,1,n,k,n);
14 | My = sparse(idx,y,1,n,k,n);
15 | 
16 | Pxy = nonzeros(Mx'*My/n);
17 | Hxy = -dot(Pxy,log2(Pxy));
18 | 
19 | Px = nonzeros(mean(Mx,1));
20 | Py = nonzeros(mean(My,1));
21 | Hx = -dot(Px,log2(Px));
22 | Hy = -dot(Py,log2(Py));
23 | 
24 | MI = Hx + Hy - Hxy;
25 | 
26 | z = sqrt((MI/Hx)*(MI/Hy));
27 | z = max(0,z);
28 | 


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/README.md:
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  1 | # *k*-Shape: Efficient and Accurate Clustering of Time Series
  2 | 
  3 | *k*-Shape is a highly accurate and efficient unsupervised method for ***univariate*** and ***multivariate*** time-series clustering. *k*-Shape appeared at the ***ACM SIGMOD 2015*** conference, where it was selected as one of the (2) ***best papers*** and received the inaugural ***2015 ACM SIGMOD Research Highlight Award***. An extended version appeared in the ***ACM TODS 2017*** journal. Since then, *k*-Shape has achieved state-of-the-art performance in both ***univariate*** and ***multivariate*** time-series datasets (i.e., *k*-Shape is among the fastest and most accurate time-series clustering methods, ranked in the top positions of established benchmarks with 100+ datasets). 
  4 | 
  5 | *k*-Shape has been widely adopted across scientific areas (e.g., computer science, social science, space science, engineering, econometrics, biology, neuroscience, and medicine), Fortune 100-500 enterprises (e.g., Exelon, Nokia, and many financial firms), and organizations such as the European Space Agency.
  6 | 
  7 | If you use *k*-Shape in your project or research, cite the following two papers:
  8 | 
  9 | * [ACM SIGMOD 2015](https://www.paparrizos.org/papers/PaparrizosSIGMOD15.pdf)
 10 | * [ACM TODS 2017](https://www.paparrizos.org/papers/PaparrizosTODS17.pdf)
 11 | 
 12 | ## References
 13 | 
 14 | > "k-Shape: Efficient and Accurate Clustering of Time Series"<br/>
 15 | > John Paparrizos and Luis Gravano<br/>
 16 | > 2015 ACM SIGMOD International Conference on Management of Data (**ACM SIGMOD 2015**)<br/>
 17 | 
 18 | ```bibtex
 19 | @inproceedings{paparrizos2015k,
 20 |   title={{k-Shape: Efficient and Accurate Clustering of Time Series}},
 21 |   author={Paparrizos, John and Gravano, Luis},
 22 |   booktitle={Proceedings of the 2015 ACM SIGMOD international conference on management of data},
 23 |   pages={1855--1870},
 24 |   year={2015}
 25 | }
 26 | ```
 27 | 
 28 | > "Fast and Accurate Time-Series Clustering"<br/>
 29 | > John Paparrizos and Luis Gravano<br/>
 30 | > ACM Transactions on Database Systems (**ACM TODS 2017**), volume 42(2), pages 1-49<br/>
 31 | 
 32 | ```bibtex
 33 | @article{paparrizos2017fast,
 34 |   title={{Fast and Accurate Time-Series Clustering}},
 35 |   author={Paparrizos, John and Gravano, Luis},
 36 |   journal={ACM Transactions on Database Systems (ACM TODS)},
 37 |   volume={42},
 38 |   number={2},
 39 |   pages={1--49},
 40 |   year={2017}
 41 | }
 42 | ```
 43 | 
 44 | ## Acknowledgements
 45 | 
 46 | We thank [Teja Bogireddy](https://github.com/bogireddytejareddy) for his valuable help on this repository.
 47 | 
 48 | # *k*-Shape's Matlab Repository
 49 | 
 50 | This repository contains the Matlab implementation for *k*-Shape. For the Python version, check [here](https://github.com/thedatumorg/kshape-python).
 51 | 
 52 | ## Data
 53 | 
 54 | To ease reproducibility, we share our results over two established benchmarks:
 55 | 
 56 | * The UCR Univariate Archive, which contains 128 univariate time-series datasets. 
 57 |   * Download all 128 preprocessed datasets [here](https://www.thedatum.org/datasets/UCR2022_DATASETS.zip).
 58 | * The UAE Multivariate Archive, which contains 28 multivariate time-series datasets. 
 59 |   * Download the first 14 preprocessed datasets [here](https://www.thedatum.org/datasets/UAE2022_DATASETS_1.zip).
 60 |   * Download the remaining 14 preprocessed datasets [here](https://www.thedatum.org/datasets/UAE2022_DATASETS_2.zip).
 61 | 
 62 | For the preprocessing steps check [here](https://github.com/thedatumorg/UCRArchiveFixes).
 63 | 
 64 | 
 65 | ## Usage
 66 | 
 67 | ### Univariate Example
 68 | ```
 69 | $ matlab
 70 | > Datasets = [cellstr('Coffee')]
 71 | > DS = LoadUCRdataset(char(Datasets(i)))
 72 | > [labels centroids] = kShape_univariate(DS.Data, length(DS.ClassNames));
 73 | ```
 74 | ### Multivariate Example
 75 | ```
 76 | $ matlab
 77 | > Datasets = [cellstr('ERing')]
 78 | > DS = LoadUAEdataset(char(Datasets(i)))
 79 | > [labels centroids] = kShape_multivariate(DS.Data, length(DS.ClassNames));
 80 | ```
 81 | 
 82 | Check the [Univariate](https://github.com/thedatumorg/kshape-matlab/blob/main/DEMO_univariate.m) and [Multivariate](https://github.com/thedatumorg/kshape-matlab/blob/main/DEMO_multivariate.m) code examples for benchmarking on the UCR and UAE datasets, respectively.
 83 | 
 84 | 
 85 | ## Results
 86 | 
 87 | The following tables contain the average Rand Index (RI), Adjusted Rand Index (ARI), and Normalized Mutual Information (NMI) accuracy values over 10 runs for *k*-Shape on the univariate and multivariate datasets.
 88 | 
 89 | Note: We collected the results using a single core implementation.
 90 | 
 91 | Server Specifications: Dual Intel(R) Xeon(R) Silver 4116 (24 cores/48 HT), 2.10 GHz, 196GB RAM.
 92 | 
 93 | ### Results on the 128 univariate datasets:
 94 | 
 95 | | Datasets              | RI | ARI | NMI | Runtime (secs) |
 96 | |:-----------------------:|:------------:|:------------:|:------------:|:-----------:|
 97 | | ACSF1 | 0.720130 | 0.133853 | 0.38816 | 16.44156  |
 98 | | Adiac | 0.950243 | 0.245107 | 0.5885544 | 65.73705 |
 99 | | AllGestureWiimoteX | 0.8312724 | 0.097974 | 0.206865 | 44.08482 |
100 | | AllGestureWiimoteY | 0.8322620 | 0.1298562 | 0.2612072 | 41.394241 |
101 | | AllGestureWiimoteZ | 0.8305639 | 0.0805551 | 0.1834998| 36.600462|
102 | | ArrowHead | 0.623006 | 0.17425450 | 0.2533444| 1.3054324 |
103 | | BME | 0.623202 | 0.1905601 | 0.2877219 | 0.4999676 |
104 | | Beef | 0.6586440 | 0.093608 | 0.27548189 | 0.8396471 |
105 | | BeetleFly | 0.52217948 | 0.04438771 | 0.05563189 | 0.536824 |
106 | | BirdChicken | 0.557179 | 0.1147453 | 0.1115865 | 0.3971603 |
107 | | CBF | 0.8754116 | 0.7241217 | 0.76718 | 2.6086939 |
108 | | Car | 0.662184 | 0.135845 | 0.2161395 | 2.8708315 |
109 | | Chinatown | 0.5275538 | 0.043759 | 0.016924 | 0.3752007 |
110 | | ChlorineConcentration | 0.5261843 | -0.0009891 | 0.0007648 | 45.2590362 |
111 | | CinCECGTorso | 0.63144 | 0.0627054 | 0.105833 | 118.6877229 |
112 | | Coffee | 0.7746103 | 0.549642 | 0.5130821 | 0.1543948 |
113 | | Computers | 0.5296809 | 0.05959965 | 0.0573684 | 4.7628411 |
114 | | CricketX | 0.86968 | 0.17770 | 0.358468 | 18.7591078 |
115 | | CricketY | 0.8716223 | 0.202953 | 0.372466 | 20.3061207 |
116 | | CricketZ | 0.8708478 | 0.181479 | 0.366086 | 23.5766044 |
117 | | Crop | 0.922896 | 0.2378824 | 0.4379565 | 2016.38332 |
118 | | DiatomSizeReduction | 0.919138 | 0.8000443 | 0.82079 | 2.0050213 |
119 | | DistalPhalanxOutlineAgeGroup | 0.7089805 | 0.40880 | 0.3327341 | 1.8217814 |
120 | | DistalPhalanxOutlineCorrect | 0.4994557 | -0.0010303 | 2.97467e-05 | 0.9867624 |
121 | | DistalPhalanxTW | 0.861218 | 0.66677209 | 0.5412476 | 2.6783893 |
122 | | DodgerLoopDay | 0.7667177 | 0.2080549 | 0.403120 | 1.537474 |
123 | | DodgerLoopGame | 0.5592195 | 0.118973 | 0.1007804 | 0.4339152 |
124 | | DodgerLoopWeekend | 0.883705 | 0.7639901 | 0.726488 | 0.4244024 |
125 | | ECG200 | 0.615723 | 0.221028 | 0.1355204 | 0.3517059 |
126 | | ECG5000 | 0.794273 | 0.5789588 | 0.551086 | 62.80226 |
127 | | ECGFiveDays | 0.8450622 | 0.69024 | 0.65035860 | 1.9896606 |
128 | | EOGHorizontalSignal | 0.8621825 | 0.22106 | 0.3988588 | 76.3076898 |
129 | | EOGVerticalSignal | 0.8712630 | 0.1987407 | 0.3630311 | 136.628252 |
130 | | Earthquakes | 0.515463 | 0.002441935 | 0.00365934 | 5.8951894 |
131 | | ElectricDevices | 0.699713 | 0.08102712 | 0.1900975 | 798.8596981 |
132 | | EthanolLevel | 0.622721 | 0.0032826 | 0.0076| 63.510865 |
133 | | FaceAll | 0.914647 | 0.446507 | 0.621303 | 77.628496 |
134 | | FaceFour | 0.756274 | 0.37390466 | 0.459848 | 0.666998 |
135 | | FacesUCR | 0.905414 | 0.407250 | 0.602981 | 82.0091669 |
136 | | FiftyWords | 0.951268 | 0.353808 | 0.646822 | 77.2777564 |
137 | | Fish | 0.78469 | 0.1885622 | 0.31931 | 7.698090 |
138 | | FordA | 0.5729417 | 0.14588 | 0.108051 | 392.9051991 |
139 | | FordB | 0.512885 | 0.025769 | 0.0192114 | 338.176240 |
140 | | FreezerRegularTrain | 0.638638 | 0.277277 | 0.211358 | 21.8496562 |
141 | | FreezerSmallTrain | 0.63912 | 0.2782464 | 0.2121770 | 20.948636 |
142 | | Fungi | 0.8383608 | 0.370585 | 0.7441787 | 2.4766722 |
143 | | GestureMidAirD1 | 0.944996 | 0.2924181 | 0.630078 | 20.7455286 |
144 | | GestureMidAirD2 | 0.945983 | 0.32512 | 0.668287 | 17.3725095 |
145 | | GestureMidAirD3 | 0.93191 | 0.1287144 | 0.462995 | 20.0660984 |
146 | | GesturePebbleZ1 | 0.882812| 0.58672 | 0.672185 | 5.3699548 |
147 | | GesturePebbleZ2 | 0.865687 | 0.531216 | 0.627707 | 5.6506422 |
148 | | GunPoint | 0.497487 | -0.005050 | 0.0 | 0.27812729 |
149 | | GunPointAgeSpan | 0.532133 | 0.06442548 | 0.0534333 | 0.8154745 |
150 | | GunPointMaleVersusFemale | 0.7919389 | 0.583864 | 0.574584 | 0.9656176 |
151 | | GunPointOldVersusYoung | 0.518569 | 0.0371419 | 0.02792863 | 0.8558587 |
152 | | Ham | 0.5251766 | 0.050364 | 0.0393745 | 1.4598628 |
153 | | HandOutlines | 0.684268 | 0.36275| 0.2533 | 108.3821474 |
154 | | Haptics | 0.683934 | 0.06481423 | 0.088467| 18.5722705 |
155 | | Herring | 0.5018085 | 0.0038426 | 0.0079538 | 0.5510935 |
156 | | HouseTwenty | 0.518445 | 0.036408 | 0.0294433 | 8.1808792 |
157 | | InlineSkate | 0.7349455 | 0.035525 | 0.1013887 | 60.3541959 |
158 | | InsectEPGRegularTrain | 0.7080033 | 0.3670333 | 0.3815031 | 6.3469509 |
159 | | InsectEPGSmallTrain | 0.706829 | 0.3643330 | 0.381449 | 6.4372878 |
160 | | InsectWingbeatSound | 0.817402 | 0.203979 | 0.417454 | 106.50463 |
161 | | ItalyPowerDemand | 0.632077 | 0.2643881| 0.2290163 | 1.142456 |
162 | | LargeKitchenAppliances | 0.5959861 | 0.1587658 | 0.158297 | 19.1498729 |
163 | | Lightning2 | 0.531735 | 0.057807 | 0.091983 | 1.2679817 |
164 | | Lightning7 | 0.809829 | 0.3245682 | 0.5033405 | 2.9859982 |
165 | | Mallat | 0.9280703 | 0.7319002 | 0.880742 | 63.637825 |
166 | | Meat | 0.81152 | 0.598769 | 0.6618977 | 0.769969 |
167 | | MedicalImages | 0.6758102 | 0.0728651 | 0.2273344 | 21.5877388 |
168 | | MelbournePedestrian | 0.870859 | 0.352634 | 0.475787 | 53.1154542 |
169 | | MiddlePhalanxOutlineAgeGroup | 0.72316083 | 0.4075420 | 0.3944312 | 1.2056471 |
170 | | MiddlePhalanxOutlineCorrect | 0.49977174 | -0.003736340 | 0.0008948 | 1.3280515 |
171 | | MiddlePhalanxTW | 0.824102 | 0.516091 | 0.4439475 | 4.2374399 |
172 | | MixedShapesRegularTrain | 0.813364 | 0.454867 | 0.517074 | 281.8805552 |
173 | | MixedShapesSmallTrain | 0.8043481 | 0.42862725 | 0.4831717 | 132.92262 |
174 | | MoteStrain | 0.803214 | 0.606398 | 0.4989154 | 1.9564175 |
175 | | NonInvasiveFetalECGThorax1 | 0.950663 | 0.3284714 | 0.673888 | 983.400489 |
176 | | NonInvasiveFetalECGThorax2 | 0.966616 | 0.460978 | 0.7620196 | 914.974343 |
177 | | OSULeaf | 0.7845599 | 0.26266825 | 0.36322052 | 5.6948894 |
178 | | OliveOil | 0.84537 | 0.641611 | 0.6482696 | 0.9241004 |
179 | | PLAID | 0.8575927 | 0.2757823 | 0.400212 | 139.861927 |
180 | | PhalangesOutlinesCorrect | 0.50535451 | 0.01068759 | 0.0102117 | 3.467281 |
181 | | Phoneme | 0.9278681 | 0.034855 | 0.21230 | 284.5056299 |
182 | | PickupGestureWiimoteZ | 0.856000 | 0.273205 | 0.520960 | 0.959337 |
183 | | PigAirwayPressure | 0.912801 | 0.02888090 | 0.4359559 | 108.75665 |
184 | | PigArtPressure | 0.957855 | 0.25324 | 0.7065518 | 85.6010015 |
185 | | PigCVP | 0.960429 | 0.185662 | 0.65441 | 95.0936539 |
186 | | Plane | 0.9271633 | 0.73900812 | 0.85989 | 0.5993027 |
187 | | PowerCons | 0.603472 | 0.2073108 | 0.192511 | 1.0429059 |
188 | | ProximalPhalanxOutlineAgeGroup | 0.770749274 | 0.513001 | 0.476826 | 1.5074031 |
189 | | ProximalPhalanxOutlineCorrect | 0.534142 | 0.0669039 | 0.0861243 | 0.5041136 |
190 | | ProximalPhalanxTW | 0.8290153 | 0.5644440 | 0.5501682 | 2.0008952 |
191 | | RefrigerationDevices | 0.557799 | 0.00591210 | 0.007814 | 14.5373435 |
192 | | Rock | 0.703975 | 0.2364493 | 0.34588788 | 14.234106 |
193 | | ScreenType | 0.559913 | 0.01123146 | 0.0121790 | 19.1829763 |
194 | | SemgHandGenderCh2 | 0.5466622 | 0.092221 | 0.058817 | 12.8683178 |
195 | | SemgHandMovementCh2 | 0.7444837 | 0.1319358 | 0.2250277 | 62.862215 |
196 | | SemgHandSubjectCh2 | 0.7296606 | 0.2050891 | 0.2754994 | 49.4141228 |
197 | | ShakeGestureWiimoteZ | 0.901898 | 0.462442 | 0.6747047 | 1.5737051 |
198 | | ShapeletSim | 0.7377881 | 0.4757332 | 0.447908 | 0.9869574 |
199 | | ShapesAll | 0.9780872 | 0.4180266 | 0.740378 | 166.1683117 |
200 | | SmallKitchenAppliances | 0.3737210 | 0.0012730 | 0.0217231 | 4.4734788 |
201 | | SmoothSubspace | 0.627010 | 0.164396 | 0.179225 | 2.1865543 |
202 | | SonyAIBORobotSurface1 | 0.675473 | 0.3505679 | 0.35182660 | 1.6894352 |
203 | | SonyAIBORobotSurface2 | 0.6000775 | 0.1939438 | 0.1365685 | 2.9754101 |
204 | | StarLightCurves | 0.766313 | 0.5122511 | 0.6024638 | 964.46397 |
205 | | Strawberry | 0.504165 | -0.019398 | 0.12339 | 4.6568317 |
206 | | SwedishLeaf | 0.8957285 | 0.32160817 | 0.5586813 | 24.8132561 |
207 | | Symbols | 0.889196 | 0.6500050 | 0.7775430 | 11.0962628 |
208 | | SyntheticControl | 0.88920255 | 0.613962 | 0.710865 | 2.6594387 |
209 | | ToeSegmentation1 | 0.5020124 | 0.00407319 | 0.0050804 | 1.2348743 |
210 | | ToeSegmentation2 | 0.635188 | 0.26236656 | 0.210026 | 0.8832202 |
211 | | Trace | 0.6985025 | 0.4320041 | 0.58108 | 0.748028 |
212 | | TwoLeadECG | 0.5448122 | 0.0896479 | 0.06946036 | 4.2016234 |
213 | | TwoPatterns | 0.687406 | 0.2354546 | 0.3377804 | 67.9150568 |
214 | | UMD | 0.601005 | 0.12067420 | 0.1685033 | 0.6761436 |
215 | | UWaveGestureLibraryAll | 0.91405589 | 0.6146967 | 0.682234 | 306.4056649 |
216 | | UWaveGestureLibraryX | 0.856831 | 0.364044 | 0.4629476 | 164.2872381 |
217 | | UWaveGestureLibraryY | 0.829982 | 0.2456431 | 0.34295234 | 302.7145652 |
218 | | UWaveGestureLibraryZ | 0.8466015 | 0.34710914 | 0.456047 | 186.73311 |
219 | | Wafer | 0.538320 | 0.0138277 | 0.00342959 | 32.045277 |
220 | | Wine | 0.4964785 | -0.0051879 | 0.0010564 | 0.5772297 |
221 | | WordSynonyms | 0.8955053 | 0.226308983 | 0.4521644651 | 45.8095883 |
222 | | Worms | 0.6517901 | 0.0400797 | 0.064035 | 5.9496994 |
223 | | WormsTwoClass | 0.502826 | 0.0054806 | 0.0083700 | 2.8476746 |
224 | | Yoga | 0.4999203 | -0.00026 | 0.00015200 | 151.1891111 |
225 | 
226 | 
227 | ### Results on the 28 multivariate datasets:
228 | 
229 | | Datasets              | RI | ARI | NMI | Runtime (secs) |
230 | |:-----------------------:|:------------:|:------------:|:------------:|:-----------:|
231 | | ArticularyWordRecognition | 0.77671625 | 0.07149355 | 0.3011789 | 1546.01149 |
232 | | AtrialFibrillation | 0.5687356 | 0.011988 | 0.0802680 | 35.360911 |
233 | | BasicMotions | 0.8301898 | 0.5432472 | 0.598455 | 30.48984 |
234 | | CharacterTrajectories | 0.6844712 | 0.1070294 | 0.322181 | 2456.18020 |
235 | | Cricket | 0.8356548 | 0.276009 | 0.5089841 | 1429.36256 |
236 | | DuckDuckGeese | 0.632848 | 0.01925416 | 0.0776541 | 8474.327226 |
237 | | ERing | 0.81792419 | 0.36732625 | 0.455813686 | 163.9078219 |
238 | | Epilepsy | 0.7984578 | 0.4743980 | 0.51779585 | 268.4851809 |
239 | | EthanolConcentration | 0.5652897 | -0.00074536 | 0.003556034 | 611.921332 |
240 | | FaceDetection | 0.5000501 | 0.00010108 | 0.00015046 | 169734.49986 |
241 | | FingerMovements | 0.4999246 | 0.00077181 | 0.00301908 | 146.7177615 |
242 | | HandMovementDirection | 0.564685 | 0.0005354 | 0.015490 | 653.58844 |
243 | | Handwriting | 0.9088080 | 0.0331515 | 0.204900 | 1473.25828 |
244 | | Heartbeat | 0.5034637 | -0.001199 | 0.00083743 | 2197.214505 |
245 | | InsectWingbeat | 0.75276 | 0.00145 | 0.00373 | 868301.6473
246 | | JapaneseVowels | 0.77892996 | 0.0648988 | 0.143400 | 386.25808 |
247 | | LSST | 0.78172231 | 0.05318 | 0.099389 | 2098.3571827 |
248 | | Libras | 0.869726095 | 0.172633 | 0.419726 | 405.35505 |
249 | | MotorImagery | 0.5006273 | 0.0014968 | 0.00320020 | 10928.88054 |
250 | | NATOPS | 0.735945 | 0.0859692 | 0.14600909 | 514.7707 |
251 | | PenDigits | 0.7892067 | 0.163134 | 0.291098 | 1503.162750 |
252 | | PhonemeSpectra | 0.9443979 | 0.0189895 | 0.119970 | 13252.5714916 |
253 | | RacketSports | 0.607855 | 0.0429515 | 0.0708733 | 107.0638691 |
254 | | SelfRegulationSCP1 | 0.542662 | 0.0854783 | 0.072874 | 1256.628221 |
255 | | SelfRegulationSCP2 | 0.499026 | -0.00194560 | 0.000499 | 1021.38219 |
256 | | SpokenArabicDigits | 0.844546 | 0.2130830 | 0.332006 | 6801.11004 |
257 | | StandWalkJump | 0.58490 | 0.11269 | 0.185295 | 623.50776 |
258 | | UWaveGestureLibrary | 0.77915 | 0.1928167 | 0.3521283 | 785.27181 |
259 | 
260 | 
261 | 


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/RandIndex.m:
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 1 | function RI=RandIndex(c1,c2)
 2 |     C=Contingency(c1,c2);
 3 | 
 4 |     n=sum(sum(C));
 5 |     nis=sum(sum(C,2).^2);
 6 |     njs=sum(sum(C,1).^2);
 7 | 
 8 |     t1=nchoosek(n,2);
 9 |     t2=sum(sum(C.^2));
10 |     t3=.5*(nis+njs);
11 | 
12 |     A=t1+t2-t3;
13 | 
14 |     RI=A/t1;
15 | end
16 | 
17 | function Cont=Contingency(Mem1,Mem2)
18 |     Cont=zeros(max(Mem1),max(Mem2));
19 | 
20 |     for i = 1:length(Mem1);
21 |         Cont(Mem1(i),Mem2(i))=Cont(Mem1(i),Mem2(i))+1;
22 |     end
23 | end
24 | 


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/SBD_multivariate.m:
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 1 | function [yshift]= SBD_multivariate(x,y)
 2 | 
 3 | if iscolumn(x)
 4 |     x=x';
 5 | end
 6 | if iscolumn(y)
 7 |     y=y';
 8 | end
 9 | 
10 | X1=NCCc_multivariate(x,y);
11 | [m,d]=max(X1);
12 | 
13 | shift=d-max(length(x),length(y));
14 | 
15 | if shift < 0
16 | 	t = permute(y(1, 1:end, :), [1, 3, 2]);
17 | 	yshift = [t(1, -shift+1:end) zeros(1, -shift)];
18 | else
19 | 	t = permute(y(1, 1:end, :), [1, 3, 2]);
20 | 	yshift = [zeros(1,shift)  t(1, 1:end-shift)];
21 | end
22 | 
23 | yshift = reshape(yshift, 1, size(y, 3), size(y, 2));
24 | yshift = permute(yshift, [1, 3, 2]);
25 | end
26 | 


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/SBD_univariate.m:
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 1 | function [dist shift yshift]= SBD_univariate(x,y)
 2 | 
 3 | if iscolumn(x)
 4 |     x=x';
 5 | end
 6 | if iscolumn(y)
 7 |     y=y';
 8 | end
 9 | 
10 | X1=NCCc_univariate(x,y);
11 | 
12 | [m,d]=max(X1);
13 | 
14 | shift=d-max(length(x),length(y));
15 |  
16 | if shift < 0
17 |         yshift = [y(-shift + 1:end) zeros(1, -shift)];
18 |     else
19 |         yshift = [zeros(1,shift) y(1:end-shift) ];
20 | end
21 | 
22 | dist = 1-m;
23 | 
24 | end
25 | 


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/docs/kShape.png:
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https://raw.githubusercontent.com/TheDatumOrg/kshape-matlab/95950cbefaf26365b49e4c6f98ddb1882ee35262/docs/kShape.png


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/kShape_multivariate.m:
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 1 | function [mem cent] = kShape_multivariate(A, K)
 2 | 
 3 | m=size(A, 1);
 4 | mem = ceil(K*rand(m, 1));
 5 | cent = zeros(K, size(A, 2), size(A, 3));
 6 | 
 7 | for iter = 1:100
 8 |     prev_mem = mem;
 9 |     for k = 1:K
10 | 	u_cent = kshape_centroid(mem, A, k, cent(k,:,:));
11 | 	for p = 1:size(A, 3)
12 | 		cent(k,:,p) = u_cent;
13 | 	end
14 |     end
15 | 
16 |     for i = 1:m
17 |         for k = 1:K
18 |             dist = 1-max(NCCc_multivariate(A(i,:,:), cent(k,:,:)));
19 | 	    D(i,k) = dist;
20 |         end
21 |     end
22 | 
23 |     [val mem] = min(D,[],2);
24 |     if norm(prev_mem-mem) == 0
25 | 	break;
26 |     end
27 | end
28 | end
29 | 
30 | 
31 | function centroid = kshape_centroid(mem, A, k, cur_center)
32 | 
33 | a = [];
34 | for i=1:length(mem)
35 |     if mem(i) == k
36 |         if sum(cur_center) == 0
37 |             opt_a = A(i,:, :);
38 | 	else
39 |             [opt_a] = SBD_multivariate(cur_center, A(i,:,:));
40 |         end
41 |         a = [a; opt_a];
42 |     end
43 | end
44 | 
45 | if size(a,1) == 0;
46 |     centroid = zeros(1, size(A,2)); 
47 |     return;
48 | end;
49 | 
50 | [m, ncolumns, channel]=size(a);
51 | [Y mean2 std2] = zscore(a,[],2);
52 | 
53 | S = Y(:, :, 1)' * Y(:, :, 1);
54 | P = (eye(ncolumns) - 1 / ncolumns * ones(ncolumns));
55 | M = P*S*P;
56 | 
57 | [V D] = eigs(M,1);
58 | centroid = V(:,1);
59 | 
60 | fd1 = [];
61 | fd2 = [];
62 | for p=1:size(a,1)
63 |     ts1 = 0;
64 |     ts2 = 0;
65 |     for q=1:size(a,3)
66 |         s1 = norm(a(p,:,q) - centroid', 'fro') * norm(a(p,:,q) - centroid', 'fro');
67 |         s2 = norm(a(p,:,q) + centroid', 'fro') * norm(a(p,:,q) + centroid', 'fro');
68 |         ts1 = ts1 + s1;
69 |         ts2 = ts2 + s2;
70 |     end
71 |    fd1 = [fd1; sqrt(ts1)];
72 |    fd2 = [fd2; sqrt(ts2)];
73 | end
74 | 
75 | finddistance1 = sum(fd1);
76 | finddistance2 = sum(fd2);
77 | 
78 | if (finddistance1<finddistance2)
79 |     centroid = centroid;
80 | else
81 |     centroid = -centroid;
82 | end
83 | 
84 | centroid = zscore(centroid);
85 | end
86 | 


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/kShape_univariate.m:
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 1 | function [mem cent] = kShape_univariate(A, K)
 2 | 
 3 | m=size(A, 1);
 4 | mem = ceil(K*rand(m, 1));
 5 | cent = zeros(K, size(A, 2));
 6 | 
 7 | for iter = 1:100
 8 |     prev_mem = mem;
 9 |     
10 |     for k = 1:K
11 |         cent(k,:) = kshape_centroid(mem, A, k, cent(k,:));
12 |     end
13 |     
14 |     for i = 1:m
15 |         for k = 1:K
16 |             dist = 1-max(NCCc_univariate(A(i,:), cent(k,:)));
17 | 	    D(i,k) = dist;
18 |         end
19 |     end
20 |     
21 |     [val mem] = min(D,[],2);
22 |     if norm(prev_mem-mem) == 0
23 |         break;
24 |     end
25 | end
26 | 
27 | end
28 | 
29 | function centroid = kshape_centroid(mem, A, k, cur_center)
30 | %Computes centroid
31 | a = [];
32 | for i=1:length(mem)
33 |     if mem(i) == k
34 |         if sum(cur_center) == 0
35 |             opt_a = A(i,:);
36 |         else
37 |              [tmp tmps opt_a] = SBD_univariate(cur_center, A(i,:));
38 |         end
39 |         a = [a; opt_a];
40 |     end
41 | end
42 | 
43 | if size(a,1) == 0;
44 |     centroid = zeros(1, size(A,2)); 
45 |     return;
46 | end;
47 | 
48 | [m, ncolumns]=size(a);
49 | [Y mean2 std2] = zscore(a,[],2);
50 | S = Y' * Y;
51 | P = (eye(ncolumns) - 1 / ncolumns * ones(ncolumns));
52 | M = P*S*P;
53 | 
54 | [V D] = eigs(M,1);
55 | centroid = V(:,1);
56 | 
57 | finddistance1 = sqrt(sum((a(1,:) - centroid').^2));
58 | finddistance2 = sqrt(sum((a(1,:) - (-centroid')).^2));
59 | 
60 | if (finddistance1<finddistance2)
61 |     centroid = centroid;
62 | else
63 |     centroid = -centroid;
64 | end
65 | 
66 | centroid = zscore(centroid);
67 | 
68 | end
69 | 
70 | 


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