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Time Warp Edit Distance
Marteau [2009] proposed the Time Warp Edit Distance (TWED) another elastic similarity metric (i.e. can handle shifts in time series). TWED elas-ticity is controlled by a parameter called stiffness using time stamp dif-ferences as part of the local matching cost. An infinite stiffness makes the distance equivalent to the ED, whereas a null stiffness is similar to DTW without warping window. A second parameter is involved in TWED, it corre-sponds to penalty for insertion or deletion operations, similarly to the pre-viously seen edit distance. TWED has three operations: delete_xi, delete_x‘ and match.
Move-Split-Merge
Stefan et al. [2013] introduced the Move-Split-Merge (MSM), which is based on a set of operations: move, split and merge. move is equivalent to a substitution (i.e. changes the value of an element), split will double an element (i.e. add the same element right after itself) and merge merges two consecutive elements into one. Each operations has an associated cost c, except the move operation which cost corresponds to the absolue value of the difference between the original element and the new one. The distance between two time series corresponds to the cost of the cheapest sequence of operations that transforms the first time series into the second one. MSM is a distance metric which is robust to temporal shifts and which is able to deal with time series of different lengths and multivariate time series.
Global Alignment Kernel
Cuturi et al. [2007] proposed a kernel to handle the time series align-ment problem. This DTW-inspired kernel aligns time series using the soft-minimum of all alignment costs in order to define a positive definite kernel. It has a quadratic complexity of O(n2), which is similar to the DTW measure. Definition 1.9 (Global Alignment Kernel). The Global Alignment Kernel (GAK) kGAK between two time series xi and x‘ is defined as kGAK(xi; x‘) = X (1.16).
Feature-based Time Series Classifiers
Feature-based methods extract features from time series before the clas-sification step where a classifier can be used on the extracted features. Many different works have been proposed with different kind of features. In this section, we first start by introducing time series representations that are used in the literature. Then, we review the most relevant feature-based time series classifiers. Finally, we present some shapelet-based algorithms.
Time Series Representations
Time series classification can be performed on both raw and transformed time series. The most natural representation of time series is the raw rep-resentation, i.e. the ordered list of valued data points. However, there are many tasks for which a representation that highlights some specificities of time series is the most suitable one, e.g. frequency for speech recognition. Due to the wide range of possible applications for time series data, numer-ous representations have been proposed by the time series community from Fourier and Wavelet Transformations to SIFT-based Representation, through Piecewise Approximations. In the following, we focus on the most well-known time series representations.
Table of contents :
Résumé en Français
La classification de séries temporelles
Travaux sur les algorithmes de classification de séries temporelles .
Contents
List of Publications
List of Symbols and Acronyms
Introduction
Motivation
Contributions
Organisation
1 Time Series Classification State-of-the-Art
1.1 Basic Definitions and Notations
1.2 Distance-based Time Series Classifiers
1.3 Feature-based Time Series Classifiers
1.4 Ensemble Classifiers for Time Series
1.5 Summary on Time Series Classification Algorithms
1.6 Model Selection and Evaluation
1.7 Other challenging problems related to Time Series Classification
2 TSC based on Local Features Representation
2.1 Related Work
2.2 (Dense) Bag-of-Temporal-SIFT-Words Algorithm
2.3 Experiments on UCR/UEA datasets
3 Improving TS Shapelets based on Adversarial Examples
3.1 Related Work
3.2 Link between CNNs and LTS
3.3 The proposed method
3.4 Experiments on UEA / UCR datasets
3.5 Discussion
4 Time Series Classification: Remote Sensing Applications
4.1 Remote Sensing (Time Series) Data
4.2 TiSeLac Dataset
4.3 Brazilian Amazon Dataset
4.4 TiSeLaC Dataset versus Brazilian Amazon Dataset
4.5 Experiments on Remote Sensing Time Series datasets
4.6 Conclusion
Conclusion and Perspectives
Results Summary
Perspectives
Bibliography .
