A kernel for time series based on global alignments

TL;DR

This paper introduces a new positive definite kernel for time series based on global alignments, extending Dynamic Time Warping, and demonstrates its effectiveness in speech recognition tasks.

Contribution

It develops a novel kernel for time series that considers all possible alignments, providing a positive definite measure suitable for kernel methods.

Findings

Kernel is positive definite under certain conditions

Effective tuning demonstrated for practical applications

Encouraging results on speech recognition tasks

Abstract

We propose in this paper a new family of kernels to handle times series, notably speech data, within the framework of kernel methods which includes popular algorithms such as the Support Vector Machine. These kernels elaborate on the well known Dynamic Time Warping (DTW) family of distances by considering the same set of elementary operations, namely substitutions and repetitions of tokens, to map a sequence onto another. Associating to each of these operations a given score, DTW algorithms use dynamic programming techniques to compute an optimal sequence of operations with high overall score. In this paper we consider instead the score spanned by all possible alignments, take a smoothed version of their maximum and derive a kernel out of this formulation. We prove that this kernel is positive definite under favorable conditions and show how it can be tuned effectively for practical applications as we report encouraging results on a speech recognition task.