Recent advances in Time Series Classification

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1 Distance Shapelet BoW Kernels CCL Recent advances in Time Series Classification Simon Malinowski, LinkMedia Research Team Classification day #3 S. Malinowski Time Series Classification 21/06/17 1 / 55

2 Distance Shapelet BoW Kernels CCL Time Series Classification Time series... A time series x is a set of values x(1), x(2),..., x(l), x(i) R, ordered in time....classification Supervised task : We are given a training set T = {(x k, y k ), 1 k N}, where xk is a time series R L yk is a label associated to x k, y k {1,..., C} Aim : Learn a relationship between the time series in T and their labels to predict unknown labels of testing time series. S. Malinowski Time Series Classification 21/06/17 2 / 55

3 Distance Shapelet BoW Kernels CCL Example of time series classification Normal heartbeat Myocard infarction ECG signal ECG signal Index Index Many other applications: Satellite Image Time Series, gesture recognition, finance, music... S. Malinowski Time Series Classification 21/06/17 3 / 55

4 Distance Shapelet BoW Kernels CCL Main approaches for time series classification 1 Distance-based approaches rely on distance measures between raw time series 2 Shapelet-based approaches rely on shapelets 3 Dictionary-based approaches Bag-of-Words 4 Enhanced Bag-of-Words 5 Ensemble approaches You can find a good recent review about TSC in [Bagnall et al., 2016] Website : timeseriesclassification.com, with source codes and more than 80 datasets S. Malinowski Time Series Classification 21/06/17 4 / 55

5 Distance Shapelet BoW Kernels CCL ED DTW GAK 1 Distance-Based Time Series Classification Euclidean Distance Dynamic Time Warping Global Alignement Kernel 2 Shapelet-Based Time Series Classification 3 Dictionnary-based approaches 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 5 / 55

6 Distance Shapelet BoW Kernels CCL ED DTW GAK 1 Distance-Based Time Series Classification Euclidean Distance Dynamic Time Warping Global Alignement Kernel 2 Shapelet-Based Time Series Classification 3 Dictionnary-based approaches 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 6 / 55

7 Distance Shapelet BoW Kernels CCL ED DTW GAK Euclidean Distance X = x 1,..., x n and Y = y 1,..., y n two time series. d(x, Y ) 2 = n (x i y i ) 2 i= t S. Malinowski Time Series Classification 21/06/17 7 / 55

8 Distance Shapelet BoW Kernels CCL ED DTW GAK Euclidean Distance X = x 1,..., x n and Y = y 1,..., y n two time series. d(x, Y ) 2 = n (x i y i ) 2 i= t Easy to compute Compatible with kernel machines Same lengths Shifts, warpings S. Malinowski Time Series Classification 21/06/17 7 / 55

9 Distance Shapelet BoW Kernels CCL ED DTW GAK 1 Distance-Based Time Series Classification Euclidean Distance Dynamic Time Warping Global Alignement Kernel 2 Shapelet-Based Time Series Classification 3 Dictionnary-based approaches 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 8 / 55

10 Distance Shapelet BoW Kernels CCL ED DTW GAK Dynamic Time Warping [Sakoe and Chiba, 1978] Measure based on the best alignment between two time series t S. Malinowski Time Series Classification 21/06/17 9 / 55

11 Distance Shapelet BoW Kernels CCL ED DTW GAK Dynamic Time Warping x 4 d 4,5 x 3 x 2 d 2,1 x 1 d 1,1 d 1,2 y 1 y 2 y 3 y 4 y 5 d i,j = (x i y j ) 2 S. Malinowski Time Series Classification 21/06/17 10 / 55

12 Distance Shapelet BoW Kernels CCL ED DTW GAK Dynamic Time Warping x 4 d 4,5 x 3 x 2 d 2,1 π 1 x 1 d 1,1 d 1,2 y 1 y 2 y 3 y 4 y 5 S 2 1 = i,j π 1 d i,j S. Malinowski Time Series Classification 21/06/17 10 / 55

13 Distance Shapelet BoW Kernels CCL ED DTW GAK Dynamic Time Warping x 4 d 4,5 x 3 π 2 x 2 d 2,1 π 1 x 1 d 1,1 d 1,2 y 1 y 2 y 3 y 4 y 5 S 1 = i,j π 1 d i,j S 2 2 = i,j π 2 d i,j S. Malinowski Time Series Classification 21/06/17 10 / 55

14 Distance Shapelet BoW Kernels CCL ED DTW GAK Dynamic Time Warping x 4 d 4,5 x 3 π 2 x 2 d 2,1 π 1 x 1 d 1,1 d 1,2 y 1 y 2 y 3 y 4 y 5 S 1 = i,j π 1 d i,j S 2 2 = i,j π 2 d i,j The best alignment is the one leading to the minimum score, this score being the DTW S. Malinowski Time Series Classification 21/06/17 10 / 55

15 Distance Shapelet BoW Kernels CCL ED DTW GAK Dynamic Time Warping x 4 d 4,5 x 3 π 2 x 2 d 2,1 π 1 x 1 d 1,1 d 1,2 y 1 y 2 y 3 y 4 y 5 S 1 = i,j π 1 d i,j S 2 2 = i,j π 2 d i,j The best alignment is the one leading to the minimum score, this score being the DTW Shifts, warpings Complexity Good performance Not a proper distance S. Malinowski Time Series Classification 21/06/17 10 / 55

16 Distance Shapelet BoW Kernels CCL ED DTW GAK Dynamic Time Warping S. Malinowski Time Series Classification 21/06/17 11 / 55

17 Distance Shapelet BoW Kernels CCL ED DTW GAK ED versus DTW 1NN DTW DTW is better here ED is better here Win/Tie/Loose : 50/4/ NN ED S. Malinowski Time Series Classification 21/06/17 12 / 55

18 Distance Shapelet BoW Kernels CCL ED DTW GAK 1 Distance-Based Time Series Classification Euclidean Distance Dynamic Time Warping Global Alignement Kernel 2 Shapelet-Based Time Series Classification 3 Dictionnary-based approaches 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 13 / 55

19 Distance Shapelet BoW Kernels CCL ED DTW GAK Global Alignment Kernel - GAK [Cuturi, 2011] x 4 k 4,5 x 3 x 2 k 2,1 π 1 x 1 k 1,1 k 1,2 y 1 y 2 y 3 y 4 y 5 (xi yj )2 k i,j = e S. Malinowski Time Series Classification 21/06/17 14 / 55

20 Distance Shapelet BoW Kernels CCL ED DTW GAK Global Alignment Kernel - GAK [Cuturi, 2011] x 4 k 4,5 x 3 x 2 k 2,1 π 1 x 1 k 1,1 k 1,2 y 1 y 2 y 3 y 4 y 5 DTW is score of the best path (xi yj )2 k i,j = e S. Malinowski Time Series Classification 21/06/17 14 / 55

21 Distance Shapelet BoW Kernels CCL ED DTW GAK Global Alignment Kernel - GAK [Cuturi, 2011] x 4 k 4,5 x 3 x 2 k 2,1 π 1 x 1 k 1,1 k 1,2 y 1 y 2 y 3 y 4 y 5 DTW is score of the best path GAK considers all possible paths : GAK(X, Y ) = π Π (xi yj )2 k i,j = e (i,j) π k i,j S. Malinowski Time Series Classification 21/06/17 14 / 55

22 Distance Shapelet BoW Kernels CCL ED DTW GAK Global Alignment Kernel - GAK [Cuturi, 2011] x 4 k 4,5 x 3 x 2 k 2,1 π 1 x 1 k 1,1 k 1,2 y 1 y 2 y 3 y 4 y 5 DTW is score of the best path GAK considers all possible paths : GAK(X, Y ) = π Π (xi yj )2 k i,j = e (i,j) π k i,j Shifts, warpings Good performance Can be used in kernel machines Complexity S. Malinowski Time Series Classification 21/06/17 14 / 55

23 Distance Shapelet BoW Kernels CCL Shapelets ST LS 1 Distance-Based Time Series Classification 2 Shapelet-Based Time Series Classification Shapelets Shapelet transform Learning Shapelets 3 Dictionnary-based approaches 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 15 / 55

24 Distance Shapelet BoW Kernels CCL Shapelets ST LS 1 Distance-Based Time Series Classification 2 Shapelet-Based Time Series Classification Shapelets Shapelet transform Learning Shapelets 3 Dictionnary-based approaches 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 16 / 55

25 Distance Shapelet BoW Kernels CCL Shapelets ST LS Shapelets First introduced in 2009 in [Ye and Keogh, 2009] A shapelet is a subsequence (of a time series) that is representative of a class Class 1 Class Index Index S. Malinowski Time Series Classification 21/06/17 17 / 55

26 Distance Shapelet BoW Kernels CCL Shapelets ST LS Shapelets First introduced in 2009 in [Ye and Keogh, 2009] A shapelet is a subsequence (of a time series) that is representative of a class Class 1 Class Index Index S. Malinowski Time Series Classification 21/06/17 17 / 55

27 Distance Shapelet BoW Kernels CCL Shapelets ST LS Shapelets First introduced in 2009 in [Ye and Keogh, 2009] A shapelet is a subsequence (of a time series) that is representative of a class Class 1 Class Index Index Shapelet s 1 is a representative of class 1 if distances between s 1 and time series of class 1 are low distances between s 1 and time series of other classes are high S. Malinowski Time Series Classification 21/06/17 17 / 55

28 Distance Shapelet BoW Kernels CCL Shapelets ST LS Distance between a shapelet and a time series Index S. Malinowski Time Series Classification 21/06/17 18 / 55

29 Distance Shapelet BoW Kernels CCL Shapelets ST LS Distance between a shapelet and a time series Index S. Malinowski Time Series Classification 21/06/17 18 / 55

30 Distance Shapelet BoW Kernels CCL Shapelets ST LS Distance between a shapelet and a time series Index S. Malinowski Time Series Classification 21/06/17 18 / 55

31 Distance Shapelet BoW Kernels CCL Shapelets ST LS Distance between a shapelet and a time series Index S. Malinowski Time Series Classification 21/06/17 18 / 55

32 Distance Shapelet BoW Kernels CCL Shapelets ST LS Distance between a shapelet and a time series Index S. Malinowski Time Series Classification 21/06/17 18 / 55

33 Distance Shapelet BoW Kernels CCL Shapelets ST LS Distance between a shapelet and a time series Index S. Malinowski Time Series Classification 21/06/17 18 / 55

34 Distance Shapelet BoW Kernels CCL Shapelets ST LS Distance between a shapelet and a time series Index S. Malinowski Time Series Classification 21/06/17 18 / 55

35 Distance Shapelet BoW Kernels CCL Shapelets ST LS Distance between a shapelet and a time series This shapelet represents class 1: Index Index Low distance with class 1 time series High distance with class 2 time series S. Malinowski Time Series Classification 21/06/17 18 / 55

36 Distance Shapelet BoW Kernels CCL Shapelets ST LS Bad or good shapelet? A bad shapelet? Distances S. Malinowski Time Series Classification 21/06/17 19 / 55

37 Distance Shapelet BoW Kernels CCL Shapelets ST LS Bad or good shapelet? A bad shapelet? Distances A good shapelet? Distances S. Malinowski Time Series Classification 21/06/17 19 / 55

38 Distance Shapelet BoW Kernels CCL Shapelets ST LS Shapelets Images taken from [Ye and Keogh, 2009] S. Malinowski Time Series Classification 21/06/17 20 / 55

39 Distance Shapelet BoW Kernels CCL Shapelets ST LS Shapelets Images taken from [Ye and Keogh, 2009] S. Malinowski Time Series Classification 21/06/17 20 / 55

40 Distance Shapelet BoW Kernels CCL Shapelets ST LS 1 Distance-Based Time Series Classification 2 Shapelet-Based Time Series Classification Shapelets Shapelet transform Learning Shapelets 3 Dictionnary-based approaches 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 21 / 55

41 Distance Shapelet BoW Kernels CCL Shapelets ST LS Shapelet transform [Hills et al., 2014] This approach is based on 3 steps : 1 Extract the K best shapelets (information gain criterion) 2 Transform each training time series into a K-dimensional vector M = M 1,..., M K, where M i is the distance between the time series and the i th shapelet 3 Train a classifier on the transformed series Picture taken from [Grabocka et al., 2014] S. Malinowski Time Series Classification 21/06/17 22 / 55

42 Distance Shapelet BoW Kernels CCL Shapelets ST LS 1 Distance-Based Time Series Classification 2 Shapelet-Based Time Series Classification Shapelets Shapelet transform Learning Shapelets 3 Dictionnary-based approaches 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 23 / 55

43 Distance Shapelet BoW Kernels CCL Shapelets ST LS Learning shapelets [Grabocka et al., 2014] Based on the shapelet transform principle BUT, shapelets are learned via logistic regression Given a set of weights w 0,..., w K and a set of K shapelets Ŷ i = w 0 + K w k M i,k k=1 L(Y i, Ŷi) = Y i ln(g(ŷi)) (1 Y i )ln(1 g(ŷi)) Objective : find K shapelets and K weights such that this loss is minimized gradient descent S. Malinowski Time Series Classification 21/06/17 24 / 55

44 Distance Shapelet BoW Kernels CCL Shapelets ST LS Comparison between shapelet-based methods Shapelet transform ST is better here Shapelets is better here Win/Tie/Loose : 77/2/6 Shapelet Transform Shapelet Transform is better here Learning Shapelets is better here Win/Tie/Loose : 25/0/ Shapelets Learning Shapelets S. Malinowski Time Series Classification 21/06/17 25 / 55

45 Distance Shapelet BoW Kernels CCL Shapelets ST LS Shapelet transform VS 1NN-DTW Shapelet transform ST is better here 1NN DTW is better here Win/Tie/Loose : 67/4/ NN DTW S. Malinowski Time Series Classification 21/06/17 26 / 55

46 Distance Shapelet BoW Kernels CCL Framework BOTSW 1 Distance-Based Time Series Classification 2 Shapelet-Based Time Series Classification 3 Dictionnary-based approaches Framework Bag-of-Temporal SIFT Words 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 27 / 55

47 Distance Shapelet BoW Kernels CCL Framework BOTSW 1 Distance-Based Time Series Classification 2 Shapelet-Based Time Series Classification 3 Dictionnary-based approaches Framework Bag-of-Temporal SIFT Words 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 28 / 55

48 Distance Shapelet BoW Kernels CCL Framework BOTSW Bag-of-Words framework The BoW framework is the following Time Series [codewords] Selection of Keypoints (or windows) Description of Keypoints (or windows) Bag-of-Words Representation Classifier S. Malinowski Time Series Classification 21/06/17 29 / 55

49 Distance Shapelet BoW Kernels CCL Framework BOTSW Feature extraction over windows Features that have been considered in the literature : Mean, slope, variance, extrema, starting time [Baydogan et al., 2013] SAX symbols (quantized mean) [Lin et al., 2012, Senin and Malinchik, 2013] Fourier Coefficients [Schäfer, 2014] Wavelet coefficients [Wang et al., 2013] Temporal-SIFT descriptors [Bailly et al., 2015] These features are then used in a Bag-of-Word approaches S. Malinowski Time Series Classification 21/06/17 30 / 55

50 Distance Shapelet BoW Kernels CCL Framework BOTSW 1 Distance-Based Time Series Classification 2 Shapelet-Based Time Series Classification 3 Dictionnary-based approaches Framework Bag-of-Temporal SIFT Words 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 31 / 55

51 Distance Shapelet BoW Kernels CCL Framework BOTSW Bag-of-Temporal SIFT Words (BoTSW) Joint work with Adeline Bailly, Romain Tavenard (Rennes 2) and Thomas Guyet (IRISA/AgroCampus)[Bailly et al., 2015] BoTSW can be outlined by the following scheme: Time Series [codewords] Extraction of Keypoints Description of Keypoints Bag-of-Words Representation Classifier S. Malinowski Time Series Classification 21/06/17 32 / 55

52 Distance Shapelet BoW Kernels CCL Framework BOTSW Extraction of Keypoints - Dense Extraction Keypoints are extracted densely in space. S. Malinowski Time Series Classification 21/06/17 33 / 55

53 Distance Shapelet BoW Kernels CCL Framework BOTSW Outline BoTSW can be outlined by the following scheme: Time Series [codewords] Extraction of Keypoints Description of Keypoints Bag-of-Words Representation Classifier S. Malinowski Time Series Classification 21/06/17 34 / 55

54 Distance Shapelet BoW Kernels CCL Framework BOTSW BoTSW - Feature vectors Parameters: n b, the number of blocks (4) and a, the block s size (2). S. Malinowski Time Series Classification 21/06/17 35 / 55

55 Distance Shapelet BoW Kernels CCL Framework BOTSW BoTSW - Feature vectors Parameters: n b, the number of blocks (4) and a, the block s size (2). This description is done for the original time series S(t) and for L(t, σ) = G(t, k s 0 σ) S(t), 0 s s max S. Malinowski Time Series Classification 21/06/17 35 / 55

56 Distance Shapelet BoW Kernels CCL Framework BOTSW Outline BoTSW can be outlined by the following scheme: Time Series [codewords] Extraction of Keypoints Description of Keypoints Bag-of-Words Representation Classifier S. Malinowski Time Series Classification 21/06/17 36 / 55

57 Distance Shapelet BoW Kernels CCL Framework BOTSW Generation of the dictionary k-means to generate the codewords (here k = 6) S. Malinowski Time Series Classification 21/06/17 37 / 55

58 Distance Shapelet BoW Kernels CCL Framework BOTSW BoTSW - Feature vectors assignment S. Malinowski Time Series Classification 21/06/17 38 / 55

59 Distance Shapelet BoW Kernels CCL Framework BOTSW Bag-of-Words Representation Different normalizations can be applied to this frequency vector : Signed-Square-Root (SSR) TF-IDF S. Malinowski Time Series Classification 21/06/17 39 / 55

60 Distance Shapelet BoW Kernels CCL Framework BOTSW BOTSW versus DTW 1NN-DTW NN-DTW is better here BOTSW is better here Win/Tie/Loose : 66/1/ BOTSW (SIFT) S. Malinowski Time Series Classification 21/06/17 40 / 55

61 Distance Shapelet BoW Kernels CCL Framework BOTSW BOTSW versus other BoW approaches BOTSW BOTSW is better here BOSS is better here Win/Tie/Loose : 46/8/31 BOTSW BOTSW is better here TSBF is better here Win/Tie/Loose : 55/2/ BOSS TSBF S. Malinowski Time Series Classification 21/06/17 41 / 55

62 Distance Shapelet BoW Kernels CCL 1 Distance-Based Time Series Classification 2 Shapelet-Based Time Series Classification 3 Dictionnary-based approaches 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 42 / 55

63 Distance Shapelet BoW Kernels CCL From BoW to kernels Joint work with Romain Tavenard, Adeline Bailly (Rennes 2), Laetitia Chapel (IRISA), Benjamin Bustos (Univ. of Chile)[Tavenard et al., 2017] Up to now, feature vectors are extracted from time series these vectors are quantized into words time series are represented as histogram of occurences of words loss of information in the quantization temporal information is lost Design of kernels between sets of feature vectors no quantization of feature vectors integrate temporal information S. Malinowski Time Series Classification 21/06/17 43 / 55

64 Distance Shapelet BoW Kernels CCL Signature Quadratic Form Distance Let X = {x i, x i R d } i=1,...,n be a time series (a set of feature vectors) Let Y = {y i, y i R d } i=1,...,m be a time series (a set of feature vectors) The SQFD between X and Y is defined as : SQFD(X, Y ) 2 = 1 n 2 n n k(x i, x j )+ 1 m 2 i=1 j=1 m m i=1 j=1 k(y i, y j ) 2 n m n i=1 j=1 m k(x i, y j ), where k(.,.) is a local kernel between feature vectors (gaussian kernel for instance) S. Malinowski Time Series Classification 21/06/17 44 / 55

65 Distance Shapelet BoW Kernels CCL Signature Quadratic Form Distance Let X = {x i, x i R d } i=1,...,n be a time series (a set of feature vectors) Let Y = {y i, y i R d } i=1,...,m be a time series (a set of feature vectors) The SQFD between X and Y is defined as : SQFD(X, Y ) 2 = 1 n 2 n n k(x i, x j )+ 1 m 2 i=1 j=1 m m i=1 j=1 k(y i, y j ) 2 n m n i=1 j=1 m k(x i, y j ), where k(.,.) is a local kernel between feature vectors (gaussian kernel for instance) It can be kernelized into K SQFD (X, Y ) = e γ f SQFD(X,Y ) 2. S. Malinowski Time Series Classification 21/06/17 44 / 55

66 Distance Shapelet BoW Kernels CCL Incorporating time in the SQFD kernel The more direct way is to integrate time in the local kernel k(x i, y j ) = e γ l x i x j 2, that now becomes : k t (x i, y j ) = e γt (tj ti )2 k(x i, y j ). S. Malinowski Time Series Classification 21/06/17 45 / 55

67 Distance Shapelet BoW Kernels CCL Classification performance Error rate SQFD-Fourier without time (γ t = 0) SQFD-Fourier with time SQFD-Fourier with time (normalized kernel) BoW Feature map dimension D S. Malinowski Time Series Classification 21/06/17 46 / 55

68 Distance Shapelet BoW Kernels CCL BoW VS Temporal kernel 0.8 SQFD-Fourier (D = 8192) W / T / L = 49 / 8 / 28 p = BoW S. Malinowski Time Series Classification 21/06/17 47 / 55

69 Distance Shapelet BoW Kernels CCL Temporal kernel VS other approaches SQFD-Fourier (D = 8192) W / T / L = 51 / 3 / 31 p = BOSS SQFD-Fourier (D = 8192) W / T / L = 56 / 3 / 26 p < LearningShapelets S. Malinowski Time Series Classification 21/06/17 48 / 55

70 Distance Shapelet BoW Kernels CCL 1 Distance-Based Time Series Classification 2 Shapelet-Based Time Series Classification 3 Dictionnary-based approaches 4 Efficient kernels for time series classification 5 Conclusion S. Malinowski Time Series Classification 21/06/17 49 / 55

71 Distance Shapelet BoW Kernels CCL Conclusion Conclusion Three main familiy of approaches for TSC : Distance-based Shapelet-based Dictionnary-based Shapelet and dictionnary-based are more accurate but there is not A METHOD better than all others Dictionnary-based methods can be improved by temporal kernels S. Malinowski Time Series Classification 21/06/17 50 / 55

72 Distance Shapelet BoW Kernels CCL Bibliography I Bagnall, A., Lines, J., Bostrom, A., Large, J., and Keogh, E. (2016). The great time series classification bake off: a review and experimental evaluation of recent algorithmic advances. Data Mining and Knowledge Discovery, pages Bailly, A., Malinowski, S., Tavenard, R., Guyet, T., and Chapel, L. (2015). Bag-of-Temporal-SIFT-Words for Time Series Classification. In Proceedings of the ECML-PKDD Workshop on Advanced Analytics and Learning on Temporal Data. Baydogan, M. G., Runger, G., and Tuv, E. (2013). A Bag-of-Features Framework to Classify Time Series. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(11): S. Malinowski Time Series Classification 21/06/17 51 / 55

73 Distance Shapelet BoW Kernels CCL Bibliography II Cuturi, M. (2011). Fast global alignment kernels. In Proceedings of the International Conference on Machine Learning, pages Grabocka, J., Schilling, N., Wistuba, M., and Schmidt-Thieme, L. (2014). Learning time-series shapelets. In Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages Hills, J., Lines, J., Baranauskas, E., Mapp, J., and Bagnall, A. (2014). Classification of time series by shapelet transformation. Data Mining and Knowledge Discovery, 28(4): Lin, J., Khade, R., and Li, Y. (2012). Rotation-invariant similarity in time series using bag-of-patterns representation. International Journal of Information Systems, 39: S. Malinowski Time Series Classification 21/06/17 52 / 55

74 Distance Shapelet BoW Kernels CCL Bibliography III Sakoe, H. and Chiba, S. (1978). Dynamic programming algorithm optimization for spoken word recognition. IEEE Transactions on Acoustics, Speech and Signal Processing, 26(1): Schäfer, P. (2014). The BOSS is concerned with time series classification in the presence of noise. Data Mining and Knowledge Discovery, 29(6): Senin, P. and Malinchik, S. (2013). SAX-VSM: Interpretable Time Series Classification Using SAX and Vector Space Model. Proceedings of the IEEE International Conference on Data Mining, pages S. Malinowski Time Series Classification 21/06/17 53 / 55

75 Distance Shapelet BoW Kernels CCL Bibliography IV Tavenard, R., Malinowski, S., Chapel, L., Bailly, A., Sanchez, H., and Bustos, B. (2017). Efficient Temporal Kernels between Feature Sets for Time Series Classification. In Proceedings of ECML-PKDD. Wang, J., Liu, P., F.H. She, M., Nahavandi, S., and Kouzani, A. (2013). Bag-of-Words Representation for Biomedical Time Series Classification. Biomedical Signal Processing and Control, 8(6): Ye, L. and Keogh, E. (2009). Time series shapelets: a new primitive for data mining. In Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages S. Malinowski Time Series Classification 21/06/17 54 / 55

76 Distance Shapelet BoW Kernels CCL Questions? S. Malinowski Time Series Classification 21/06/17 55 / 55

Learning Time-Series Shapelets

Learning Time-Series Shapelets Josif Grabocka, Nicolas Schilling, Martin Wistuba and Lars Schmidt-Thieme Information Systems and Machine Learning Lab (ISMLL) University of Hildesheim, Germany SIGKDD 14,