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Time Series Data Mining Challenges Time Series Data Mining Challenges Jose A. Lozano Basque Center for Applied Mathematics (BCAM) University of the Basque Country UPV/EHU MACsPro, Vienna, March 21-23, 2019

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Time Series Data Mining Challenges Basque Country

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Time Series Data Mining Challenges Donostia-San Sebastián

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Time Series Data Mining Challenges Bilbao

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Time Series Data Mining Challenges Outline of the presentation 1 Time Series Data Mining Activities 2 Clustering 3 (Early) Supervised Classification 4 Outlier/Anomaly Detection 5 Conclusions and Future Work

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Time Series Data Mining Challenges Time Series Data Mining Activities Outline of the presentation 1 Time Series Data Mining Activities 2 Clustering 3 (Early) Supervised Classification 4 Outlier/Anomaly Detection 5 Conclusions and Future Work

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Time Series Data Mining Challenges Time Series Data Mining Activities Time series all around Temporal correlation High dimen- sionality Noisy Industry 4.0 Bio Signals Weather Forecasting Shapes

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Time Series Data Mining Challenges Time Series Data Mining Activities Time series forecasting

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Time Series Data Mining Challenges Time Series Data Mining Activities Time series data Base: our object of study A set of time series (usually big) Different lengths Multidimensional

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Time Series Data Mining Challenges Time Series Data Mining Activities Clustering Clustering Algorithm

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Time Series Data Mining Challenges Time Series Data Mining Activities Supervised classification of time series C 1 C 2 C 3 C 2 C 3 C 1 ALGORITHM CLASSIFIER ? C 2 TRAINING SET

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Time Series Data Mining Challenges Time Series Data Mining Activities Anomaly/outlier detection

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Time Series Data Mining Challenges Time Series Data Mining Activities Segmentation

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Time Series Data Mining Challenges Clustering Outline of the presentation 1 Time Series Data Mining Activities 2 Clustering 3 (Early) Supervised Classification 4 Outlier/Anomaly Detection 5 Conclusions and Future Work

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Time Series Data Mining Challenges Clustering Time series clustering. Examples CLUSTERING ALGORITHM

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Time Series Data Mining Challenges Clustering Time series clustering: hierarchical, partitional we need a DISTANCE 0 100 200 300 400 Series 1 Series 2 Series 3 Series 4 Series 5 Series 6 Series 7 Series 8 Series 9 k-means

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Time Series Data Mining Challenges Clustering Distance between time series Rigid Distance Flexible Distance

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Time Series Data Mining Challenges Clustering Euclidean Distance (ED) D(X, Y) = n i=1 (xi − yi )2 Easy to compute Only for series with the same distance Does not consider the time Sensitivity to noise

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Time Series Data Mining Challenges Clustering Dynamic Time Warping (DTW) Takes into account the ordered sequence (time) It can deal with series of different sizes Computationally expensive O(min{m, n}2)

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Time Series Data Mining Challenges Clustering Euclidean Distance vs Dynamic Time Warping EUCLIDEAN DTW 6 6

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Time Series Data Mining Challenges Clustering Alternatives to calculate distances Calculating distances Represent each series by means of a set of features and calculate the distance between the features Learn a parametric model for each series and calculate the distance between the parameters

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Time Series Data Mining Challenges Clustering Distances between series Remarks There is not best distance (no free lunch) Each problem requires a different distance The distance to be used needs to be in agreement with out knowledge about what is far and what is close Hint: try with several distances Challenge: Design a method to the (semi)automatic selection of a distance

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Time Series Data Mining Challenges Clustering ...Come back to clustering: K-means k-medois k-means k-medoids

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Time Series Data Mining Challenges Clustering Remarks on clustering Recent papers on the computation of a mean series Alternate clustering methods: graph-based, spectral... Challenge: Multivariate time series clustering almost unexplored

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Time Series Data Mining Challenges (Early) Supervised Classification Outline of the presentation 1 Time Series Data Mining Activities 2 Clustering 3 (Early) Supervised Classification 4 Outlier/Anomaly Detection 5 Conclusions and Future Work

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Time Series Data Mining Challenges (Early) Supervised Classification Supervised Classification of Time Series General-purpose classifiers Specific TS classifiers FEATURES C FEATURES CLASSIFIER SERIES C SERIES CLASSIFIER

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Time Series Data Mining Challenges (Early) Supervised Classification General-purpose classifiers Each series is considered an instance Each time stamp is considered a feature t1 t2 t3 . . . tn C x11 x12 x13 . . . x1n c1 x21 x22 x23 . . . x2n c2 . . . . . . . . . . . . . . . . . . xm1 xm2 xm3 . . . xmn c2

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Time Series Data Mining Challenges (Early) Supervised Classification General-purpose classifiers Each series is considered an instance Each time stamp is considered a feature t2 t1 t3 . . . tn C x12 x11 x13 . . . x1n c1 x22 x21 x23 . . . x2n c2 . . . . . . . . . . . . . . . . . . xm2 xm1 xm3 . . . xmn c2

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Time Series Data Mining Challenges (Early) Supervised Classification General-purpose classifiers Each series is considered an instance Each time stamp is considered a feature t2 t1 t3 . . . tn C x12 x11 x13 . . . x1n c1 x22 x21 x23 . . . x2n c2 . . . . . . . . . . . . . . . . . . xm2 xm1 xm3 . . . xmn c2 CHALLENGE I When to use general-purpose and when time-series specific?

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Time Series Data Mining Challenges (Early) Supervised Classification What is relevant in TSC? PROBLEM I PROBLEM II

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Time Series Data Mining Challenges (Early) Supervised Classification What is relevant in TSC? PROBLEM I PROBLEM II SHAPE

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Time Series Data Mining Challenges (Early) Supervised Classification What is relevant in TSC? PROBLEM I PROBLEM II SHAPE LOCATION

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Time Series Data Mining Challenges (Early) Supervised Classification A taxonomy of time series classification methods Taxonomy Distance-based classifiers Model-based classfiers Feature-based classifiers Shapelets-based classifiers

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Time Series Data Mining Challenges (Early) Supervised Classification Distance-based time series classification General Schema Define a distance between time series Use classifiers based on distances: 1-NN ...

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Time Series Data Mining Challenges (Early) Supervised Classification 1-Nearest Neighbour (1-NN) Easy to understand Better results with higher number of series Computational cost Challenge: What distance??? C 1 C 2 C 3 C 2 C 3 C 1 ? C 2 (d 1 d 2 d 3 d 4 d 5 d 6 ) MINIMUM DISTANCE

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Time Series Data Mining Challenges (Early) Supervised Classification Distance-based time series classification. General Approach CLASIFICADOR SERIES C DISTANCE MATRIX ... ... ... ... ... ... C SERIES CLASSIFIER DISTANCES ...

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Time Series Data Mining Challenges (Early) Supervised Classification Distance-based time series classification. General Approach CLASIFICADOR SERIES C DISTANCE MATRIX ... ... ... ... ... ... C SERIES CLASSIFIER DISTANCES ... VECTORS!

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Time Series Data Mining Challenges (Early) Supervised Classification Distance-based time series classification. General Approach Any algorithm based on distance could be applied It depends on the number of series in training Computationally expensive CLASIFICADOR SERIES C DISTANCE MATRIX ... ... ... ... ... ... C SERIES CLASSIFIER DISTANCES ... VECTORS!

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Time Series Data Mining Challenges (Early) Supervised Classification Feature-based time series classification CLASIFICADOR SERIES C FEATURES ... ... ... ... ... ... C SERIES CLASSIFIER FEATURES ...

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Time Series Data Mining Challenges (Early) Supervised Classification Feature-based time series classification Features Statistics: mean, variance Autorregresive coefficients Fourier coefficients Shift, trend, ... CLASIFICADOR SERIES C FEATURES ... ... ... ... ... ... C SERIES CLASSIFIER FEATURES ...

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Time Series Data Mining Challenges (Early) Supervised Classification Feature-based time series classification Representation independent on the number of series Interpretable representation Challgenge: what feature to use? CLASIFICADOR SERIES C FEATURES ... ... ... ... ... ... C SERIES CLASSIFIER FEATURES ...

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Time Series Data Mining Challenges (Early) Supervised Classification Shapelets-based classification Lij could be distance or presence Computationally expensive When the shapelets are relevant extremely good results Easy to interpret Shapelet 2

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Time Series Data Mining Challenges (Early) Supervised Classification Model-based time series classification SERIES C SERIES PREDICTION MODEL I PREDICTION MODEL II PREDICTION MODEL III What is the most probable model?

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Time Series Data Mining Challenges (Early) Supervised Classification Model-based time series classification Good results with an appropriate model Choice of model Existence of model SERIES C SERIES PREDICTION MODEL I PREDICTION MODEL II PREDICTION MODEL III What is the most probable model?

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Time Series Data Mining Challenges (Early) Supervised Classification Early time series classification Examples Early activity recognition Early disease recognition in electrocardiograms Early detection of sepsis in newborn Early detection of failures in machines (predictive maintenance)

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Time Series Data Mining Challenges (Early) Supervised Classification Early time series classification Balance between accuracy and earlyness C 1 C 2 C 3 C 2 C 3 C 1 ALGORITHM C 2 TRAINING SET ? ? Wait for more data CLASSIFIER EARLY

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Time Series Data Mining Challenges (Early) Supervised Classification Early time series classification t1 2 t C1 C2 C3 t3 ... ... ... T1 T2 T3

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Time Series Data Mining Challenges (Early) Supervised Classification Early time series classification t1 2 t C1 C2 C3 t3 ... ... ... T1 T2 T3

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Time Series Data Mining Challenges (Early) Supervised Classification Early time series classification t1 2 t C1 C2 C3 t3 ... ... ... T1 T2 T3 Output BLUE class

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Time Series Data Mining Challenges (Early) Supervised Classification Multivariate time series classification CHALLENGE

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Time Series Data Mining Challenges Outlier/Anomaly Detection Outline of the presentation 1 Time Series Data Mining Activities 2 Clustering 3 (Early) Supervised Classification 4 Outlier/Anomaly Detection 5 Conclusions and Future Work

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Time Series Data Mining Challenges Outlier/Anomaly Detection Outlier vs Anomaly

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Time Series Data Mining Challenges Outlier/Anomaly Detection Type of outlier: point outlier

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Time Series Data Mining Challenges Outlier/Anomaly Detection Type of outlier: subsequence outlier

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Time Series Data Mining Challenges Outlier/Anomaly Detection Type of outlier: series outlier

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Time Series Data Mining Challenges Outlier/Anomaly Detection Outlier detection method: basic |xt − ˆ xt| < τ

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Time Series Data Mining Challenges Outlier/Anomaly Detection Outlier detection method: basic |xt − ˆ xt| < τ Median

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Time Series Data Mining Challenges Outlier/Anomaly Detection Outlier detection method: basic |xt − ˆ xt| < τ MAD

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Time Series Data Mining Challenges Outlier/Anomaly Detection Outlier detection method: basic |xt − ˆ xt| < τ Model

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Time Series Data Mining Challenges Outlier/Anomaly Detection An overview of outlier/anomaly detection

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Time Series Data Mining Challenges Conclusions and Future Work Outline of the presentation 1 Time Series Data Mining Activities 2 Clustering 3 (Early) Supervised Classification 4 Outlier/Anomaly Detection 5 Conclusions and Future Work

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Time Series Data Mining Challenges Conclusions and Future Work Almost unexplored lands Challenges Time series subset selection Learning in weakly environments: semi-supervised, multi-label, crowd learning Theoretical bounds on learning: assumptions on the generating model

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Time Series Data Mining Challenges Conclusions and Future Work Collaboration Usue Mori (UPV/EHU), Amaia Abanda (BCAM) Ane Blazque (Ikerlan), Angel Conde (Ikerlan) Aritz Perez (BCAM), Izaskun Oregui (Tecnalia), Javier del Ser (Tecnalia) Josu Ircio (Ikerlan), Aizea Lojo (Ikerlan)

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Time Series Data Mining Challenges Conclusions and Future Work Time Series Data Mining Challenges Jose A. Lozano Basque Center for Applied Mathematics (BCAM) University of the Basque Country UPV/EHU MACsPro, Vienna, March 21-23, 2019