GENDIS: Genetic Discovery of Shapelets
<p>A schematic overview of shapelet discovery.</p> "> Figure 2
<p>A conceptual overview of GENetic DIscovery of Shapelets (<span class="html-small-caps"><tt>gendis</tt></span>).</p> "> Figure 3
<p>An example of a one-point crossover operation on two shapelet sets.</p> "> Figure 4
<p>An example of one- and two-point crossover applied on individual shapelets.</p> "> Figure 5
<p>An example of the shapelet merging crossover operation.</p> "> Figure 6
<p>The fitness as a function of the number of generations, for six datasets, using three different configurations of initialization operations.</p> "> Figure 7
<p>The fitness as a function of the number of generations, for six datasets, using four different configurations of crossover operations.</p> "> Figure 8
<p>The fitness as a function of the number of generations, for six datasets, using four different configurations of mutation operations.</p> "> Figure 9
<p>The generated training and test set for the artificial classification problem.</p> "> Figure 10
<p>The obtained feature representations using a dependent and independent approach.</p> "> Figure 11
<p>A two-class problem with two time series per class and the extracted shapelets with corresponding distances on an ordered line by a brute-force approach versus <span class="html-small-caps"><tt>gendis</tt></span>.</p> "> Figure 12
<p>A pairwise distance matrix between discovered shapelet sets of two different runs.</p> "> Figure 13
<p>The evaluation setup used to compare <span class="html-small-caps"><tt>gendis</tt></span> to other shapelet techniques.</p> "> Figure 14
<p>A critical difference diagram of the four evaluated shapelet discovery algorithms with a significance level of <math display="inline"><semantics> <mrow> <mn>0.1</mn> </mrow> </semantics></math>.</p> ">
Abstract
:1. Introduction
1.1. Background
1.2. Related Work
1.3. Our Contribution
2. Materials and Methods
2.1. Time Series Matrix and Label Vector
2.2. Shapelets and Shapelet Sets
2.3. Distance Matrix Calculation
2.4. Shapelet Set Discovery
2.5. Genetic Discovery of Interpretable Shapelets
2.5.1. Conceptual Overview
2.5.2. Initialization
2.5.3. Fitness
2.5.4. Crossover
2.5.5. Mutations
2.5.6. Selection, Elitism, and Early Stopping
2.5.7. List of All Hyper-Parameters
- Maximum shapelets per candidate (W): the maximum number of shapelets in a newly generated individual during initialization (default: ).
- Population size (P): the total number of candidates that are evaluated and evolved in every iteration (default: 100).
- Maximum number of generations (G): the maximum number of iterations the algorithm runs (default: 100).
- Early stopping patience (): the algorithm preemptively stops evolving when no better individual has been found for iterations (default: 10).
- Mutation probability (): the probability that a mutation operator gets applied to an individual in each iteration (default: ).
- Crossover probability (): the probability that a crossover operator is applied on a pair of individuals in each iteration (default: ).
- Maximum shapelet length (): the maximum length of the shapelets in each shapelet set (individual) (default: M).
- The operations used during the initialization, crossover, and mutation phases are configurable as well (default: all mentioned operations).
3. Results and Discussion
3.1. Efficiency of Genetic Operators
3.1.1. Datasets
3.1.2. Initialization Operators
- Initializing the individuals with K-means (Initialization 1)
- Randomly initializing the shapelet sets (Initialization 2)
- Using both initialization operations
3.1.3. Crossover Operators
- Using solely point crossovers on the shapelet sets (Crossover 1)
- Using solely point crossovers on individual shapelets (Crossover 2)
- Using solely merge crossovers (Crossover 3)
- Using all three crossover operations
3.1.4. Mutation Operators
- Masking a random part of a shapelet (Mutation 1)
- Removing a random shapelet from the set (Mutation 2)
- Adding a shapelet, randomly sampled from the data, to the set (Mutation 3)
- Using all three mutation operations
3.2. Evaluating Sets of Candidates Versus Single Candidates
3.3. Discovering Shapelets Outside the Data
3.4. Stability
3.5. Comparing gendis to fs, st, and lts
4. Conclusions and Future Work
- evolutionary algorithms are gradient-free, allowing for an easy configuration of the optimization objective, which does not need to be differentiable
- only the maximum length of all shapelets has to be tuned, as opposed to the number of shapelets and the length of each shapelet, due to the fact that gendis evaluates entire sets of shapelets
- easy control over the runtime of the algorithm
- the possibility of discovering shapelets that do not need to be a subsequence of the input time series
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Dataset | #Cls | TS_len | #Train | #Test |
---|---|---|---|---|
ItalyPowerDemand | 2 | 24 | 67 | 1029 |
SonyAIBORobotSurface2 | 2 | 65 | 27 | 953 |
FaceAll | 14 | 131 | 560 | 1690 |
Wine | 2 | 234 | 57 | 54 |
PhalangesOutlinesCorrect | 2 | 80 | 1800 | 858 |
Herring | 2 | 512 | 64 | 64 |
Dataset | #Cls | TS_len | #Train | #Test | GENDIS | ST | LTS | FS | #Shapes | |
---|---|---|---|---|---|---|---|---|---|---|
Ens | LR | |||||||||
Adiac | 37 | 176 | 390 | 391 | 66.2 | 69.8 | 76.8 | 42.9 | 55.5 | 39 |
ArrowHead | 3 | 251 | 36 | 175 | 79.4 | 82.0 | 85.1 | 84.1 | 67.5 | 39 |
Beef | 5 | 470 | 30 | 30 | 51.5 | 58.8 | 73.6 | 69.8 | 50.2 | 41 |
BeetleFly | 2 | 512 | 20 | 20 | 90.6 | 87.5 | 87.5 | 86.2 | 79.6 | 42 |
BirdChicken | 2 | 512 | 20 | 20 | 90.0 | 90.5 | 92.7 | 86.4 | 86.2 | 45 |
CBF | 3 | 128 | 30 | 900 | 99.1 | 97.6 | 98.6 | 97.7 | 92.4 | 43 |
Car | 4 | 577 | 60 | 60 | 82.5 | 83.0 | 90.2 | 85.6 | 73.6 | 48 |
ChlorineConcentration | 3 | 166 | 467 | 3840 | 60.9 | 57.5 | 68.2 | 58.6 | 56.6 | 30 |
CinCECGTorso | 4 | 1639 | 40 | 1380 | 92.1 | 91.5 | 91.8 | 85.5 | 74.1 | 57 |
Coffee | 2 | 286 | 28 | 28 | 98.9 | 98.6 | 99.5 | 99.5 | 91.7 | 44 |
Computers | 2 | 720 | 250 | 250 | 75.4 | 72.7 | 78.5 | 65.4 | 50.0 | 38 |
CricketX | 12 | 300 | 390 | 390 | 73.1 | 66.6 | 77.7 | 74.4 | 47.9 | 41 |
CricketY | 12 | 300 | 390 | 390 | 69.8 | 64.3 | 76.2 | 72.6 | 50.9 | 41 |
CricketZ | 12 | 300 | 390 | 390 | 72.6 | 65.9 | 79.8 | 75.4 | 46.6 | 40 |
DiatomSizeReduction | 4 | 345 | 16 | 306 | 97.4 | 96.5 | 91.1 | 92.7 | 87.3 | 45 |
DistalPhalanxOutlineAgeGroup | 3 | 80 | 400 | 139 | 84.4 | 83.2 | 81.9 | 81.0 | 74.5 | 32 |
DistalPhalanxOutlineCorrect | 2 | 80 | 600 | 276 | 82.4 | 81.5 | 82.9 | 82.2 | 78.0 | 32 |
DistalPhalanxTW | 6 | 80 | 400 | 139 | 76.7 | 76.0 | 69.0 | 65.9 | 62.3 | 33 |
ECG200 | 2 | 96 | 100 | 100 | 86.3 | 86.5 | 84.0 | 87.1 | 80.6 | 30 |
ECG5000 | 5 | 140 | 500 | 4500 | 94.0 | 93.8 | 94.3 | 94.0 | 92.2 | 34 |
ECGFiveDays | 2 | 136 | 23 | 861 | 99.9 | 100.0 | 95.5 | 98.5 | 98.6 | 33 |
Earthquakes | 2 | 512 | 322 | 139 | 78.4 | 73.7 | 73.7 | 74.2 | 74.7 | 44 |
ElectricDevices | 7 | 96 | 8926 | 7711 | 83.7 | 77.6 | 89.5 | 70.9 | 26.2 | 31 |
FaceAll | 14 | 131 | 560 | 1690 | 94.5 | 92.6 | 96.8 | 92.6 | 77.2 | 38 |
FaceFour | 4 | 350 | 24 | 88 | 93.2 | 94.1 | 79.4 | 95.7 | 86.9 | 41 |
FacesUCR | 14 | 131 | 200 | 2050 | 90.1 | 89.0 | 90.9 | 93.9 | 70.1 | 39 |
FiftyWords | 50 | 270 | 450 | 455 | 72.9 | 71.8 | 71.3 | 69.4 | 51.2 | 39 |
Fish | 7 | 463 | 175 | 175 | 87.0 | 90.5 | 97.4 | 94.0 | 74.2 | 50 |
FordA | 2 | 500 | 3601 | 1320 | 90.8 | 90.7 | 96.5 | 89.5 | 78.5 | 37 |
FordB | 2 | 500 | 3636 | 810 | 89.5 | 89.8 | 91.5 | 89.0 | 78.3 | 38 |
GunPoint | 2 | 150 | 50 | 150 | 96.9 | 95.7 | 99.9 | 98.3 | 93.0 | 39 |
Ham | 2 | 431 | 109 | 105 | 72.9 | 77.2 | 80.8 | 83.2 | 67.7 | 37 |
HandOutlines | 2 | 2709 | 1000 | 370 | 89.7 | 91.0 | 92.4 | 83.7 | 84.1 | 41 |
Haptics | 5 | 1092 | 155 | 308 | 45.2 | 43.9 | 51.2 | 47.8 | 35.6 | 55 |
Herring | 2 | 512 | 64 | 64 | 59.6 | 61.8 | 65.3 | 62.8 | 55.8 | 42 |
InlineSkate | 7 | 1882 | 100 | 550 | 43.8 | 39.3 | 39.3 | 29.9 | 25.7 | 58 |
InsectWingbeatSound | 11 | 256 | 220 | 1980 | 57.3 | 57.5 | 61.7 | 55.0 | 48.8 | 36 |
ItalyPowerDemand | 2 | 24 | 67 | 1029 | 95.6 | 96.0 | 95.3 | 95.2 | 90.9 | 31 |
LargeKitchenAppliances | 3 | 720 | 375 | 375 | 91.0 | 90.4 | 93.3 | 76.5 | 41.9 | 33 |
Lightning2 | 2 | 637 | 60 | 61 | 80.9 | 79.1 | 65.9 | 75.9 | 48.0 | 39 |
Lightning7 | 7 | 319 | 70 | 73 | 78.2 | 76.3 | 72.4 | 76.5 | 10.1 | 39 |
Mallat | 8 | 1024 | 55 | 2345 | 98.2 | 97.3 | 97.2 | 95.1 | 89.3 | 58 |
Dataset | #Cls | TS_len | #Train | #Test | GENDIS | ST | LTS | FS | #Shapes | |
---|---|---|---|---|---|---|---|---|---|---|
Ens | LR | |||||||||
Meat | 3 | 448 | 60 | 60 | 98.7 | 98.8 | 96.6 | 81.4 | 92.4 | 48 |
MedicalImages | 10 | 99 | 381 | 760 | 72.4 | 68.6 | 69.1 | 70.4 | 60.9 | 37 |
MiddlePhalanxOutlineAgeGroup | 3 | 80 | 400 | 154 | 74.4 | 73.2 | 69.4 | 67.9 | 61.3 | 30 |
MiddlePhalanxOutlineCorrect | 2 | 80 | 600 | 291 | 80.7 | 79.6 | 81.5 | 82.2 | 71.6 | 30 |
MiddlePhalanxTW | 6 | 80 | 399 | 154 | 62.2 | 63.1 | 57.9 | 54.0 | 51.9 | 37 |
MoteStrain | 2 | 84 | 20 | 1252 | 86.3 | 86.6 | 88.2 | 87.6 | 79.3 | 36 |
NonInvasiveFatalECGThorax1 | 42 | 750 | 1800 | 1965 | 84.7 | 89.4 | 94.7 | 60.0 | 71.0 | 41 |
NonInvasiveFatalECGThorax2 | 42 | 750 | 1800 | 1965 | 87.1 | 92.3 | 95.4 | 73.9 | 75.8 | 37 |
OSULeaf | 6 | 427 | 200 | 242 | 76.2 | 75.8 | 93.4 | 77.1 | 67.9 | 45 |
OliveOil | 4 | 570 | 30 | 30 | 86.1 | 88.8 | 88.1 | 17.2 | 76.5 | 53 |
PhalangesOutlinesCorrect | 2 | 80 | 1800 | 858 | 80.8 | 78.7 | 79.4 | 78.3 | 73.0 | 30 |
Plane | 7 | 144 | 105 | 105 | 99.2 | 99.3 | 100.0 | 99.5 | 97.0 | 34 |
ProximalPhalanxOutlineAgeGroup | 3 | 80 | 400 | 205 | 84.1 | 83.9 | 84.1 | 83.2 | 79.7 | 32 |
ProximalPhalanxOutlineCorrect | 2 | 80 | 600 | 291 | 86.2 | 85.7 | 88.1 | 79.3 | 79.7 | 30 |
ProximalPhalanxTW | 6 | 80 | 400 | 205 | 81.7 | 80.2 | 80.3 | 79.4 | 71.6 | 31 |
RefrigerationDevices | 3 | 720 | 375 | 375 | 68.6 | 62.4 | 76.1 | 64.2 | 57.4 | 34 |
ScreenType | 3 | 720 | 375 | 375 | 52.8 | 52.8 | 67.6 | 44.5 | 36.5 | 37 |
ShapeletSim | 2 | 500 | 20 | 180 | 100.0 | 100.0 | 93.4 | 93.3 | 100.0 | 34 |
ShapesAll | 60 | 512 | 600 | 600 | 79.6 | 79.3 | 85.4 | 76.0 | 59.8 | 44 |
SmallKitchenAppliances | 3 | 720 | 375 | 375 | 74.3 | 74.2 | 80.2 | 66.3 | 33.3 | 37 |
SonyAIBORobotSurface1 | 2 | 70 | 20 | 601 | 96.0 | 95.6 | 88.8 | 90.6 | 91.8 | 34 |
SonyAIBORobotSurface2 | 2 | 65 | 27 | 953 | 88.6 | 87.0 | 92.4 | 90.0 | 84.9 | 34 |
StarLightCurves | 3 | 1024 | 1000 | 8236 | 95.9 | 95.3 | 97.7 | 88.8 | 90.8 | 30 |
Strawberry | 2 | 235 | 613 | 370 | 95.2 | 95.1 | 96.8 | 92.5 | 91.7 | 34 |
SwedishLeaf | 15 | 128 | 500 | 625 | 88.7 | 87.7 | 93.9 | 89.9 | 75.8 | 37 |
Symbols | 6 | 398 | 25 | 995 | 93.4 | 92.5 | 86.2 | 91.9 | 90.8 | 43 |
SyntheticControl | 6 | 60 | 300 | 300 | 98.8 | 98.7 | 98.7 | 99.5 | 92.0 | 39 |
ToeSegmentation1 | 2 | 277 | 40 | 228 | 92.0 | 90.7 | 95.4 | 93.4 | 90.4 | 40 |
ToeSegmentation2 | 2 | 343 | 36 | 130 | 93.1 | 90.6 | 94.7 | 94.3 | 87.3 | 36 |
Trace | 4 | 275 | 100 | 100 | 100.0 | 99.9 | 100.0 | 99.6 | 99.8 | 25 |
TwoLeadECG | 2 | 82 | 23 | 1139 | 95.8 | 96.6 | 98.4 | 99.4 | 92.0 | 36 |
TwoPatterns | 4 | 128 | 1000 | 4000 | 95.8 | 93.1 | 95.2 | 99.4 | 69.6 | 33 |
UWaveGestureLibraryAll | 8 | 945 | 896 | 3582 | 94.9 | 94.8 | 94.2 | 68.0 | 76.6 | 44 |
UWaveGestureLibraryX | 8 | 315 | 896 | 3582 | 80.2 | 77.9 | 80.6 | 80.4 | 69.4 | 42 |
UWaveGestureLibraryY | 8 | 315 | 896 | 3582 | 71.5 | 69.5 | 73.7 | 71.8 | 59.1 | 40 |
UWaveGestureLibraryZ | 8 | 315 | 896 | 3582 | 74.4 | 72.2 | 74.7 | 73.7 | 63.8 | 42 |
Wafer | 2 | 152 | 1000 | 6164 | 99.4 | 99.3 | 100.0 | 99.6 | 98.1 | 24 |
Wine | 2 | 234 | 57 | 54 | 86.5 | 86.4 | 92.6 | 52.4 | 79.4 | 39 |
WordSynonyms | 25 | 270 | 267 | 638 | 68.4 | 62.8 | 58.2 | 58.1 | 46.1 | 42 |
Worms | 5 | 900 | 181 | 77 | 65.6 | 59.9 | 71.9 | 64.2 | 62.2 | 47 |
WormsTwoClass | 2 | 900 | 181 | 77 | 74.1 | 69.1 | 77.9 | 73.6 | 70.6 | 50 |
Yoga | 2 | 426 | 300 | 3000 | 83.3 | 80.2 | 82.3 | 83.3 | 72.1 | 40 |
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Vandewiele, G.; Ongenae, F.; De Turck, F. GENDIS: Genetic Discovery of Shapelets. Sensors 2021, 21, 1059. https://doi.org/10.3390/s21041059
Vandewiele G, Ongenae F, De Turck F. GENDIS: Genetic Discovery of Shapelets. Sensors. 2021; 21(4):1059. https://doi.org/10.3390/s21041059
Chicago/Turabian StyleVandewiele, Gilles, Femke Ongenae, and Filip De Turck. 2021. "GENDIS: Genetic Discovery of Shapelets" Sensors 21, no. 4: 1059. https://doi.org/10.3390/s21041059