Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 26, Issue 6, Pages 1121-1133Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2014.2333876
Keywords
Dynamic time warping (DTW); edit distance; kernel definiteness; support vector machine (SVM); time series classification
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Funding
- French Ministry of Research
- Brittany Region
- General Council of Morbihan
- European Regional Development Fund
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This paper proposes some extensions to the work on kernels dedicated to string or time series global alignment based on the aggregation of scores obtained by local alignments. The extensions that we propose allow us to construct, from classical recursive definition of elastic distances, recursive edit distance (or time-warp) kernels that are positive definite if some sufficient conditions are satisfied. The sufficient conditions we end up with are original and weaker than those proposed in earlier works, although a recursive regularizing term is required to get proof of the positive definiteness as a direct consequence of the Haussler's convolution theorem. Furthermore, the positive definiteness is maintained when a symmetric corridor is used to reduce the search space, and thus the algorithmic complexity, which is quadratic in the worst case. The classification experiment we conducted on three classical time-warp distances (two of which are metrics), using support vector machine classifier, leads to the conclusion that when the pairwise distance matrix obtained from the training data is far from definiteness, the positive definite recursive elastic kernels outperform in general the distance substituting kernels for several classical elastic distances we have tested.
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