Fast approximate dynamic warping kernels

Abstract

The dynamic time warping (DTW) distance is a popular similarity measure for comparing time series data. It has been successfully applied in many fields like speech recognition, data mining and information retrieval to automatically cope with time deformations and variations in the length of the time dependent data. There have been attempts in the past to define kernels on DTW distance. These kernels try to approximate the DTW distance. However, these have quadratic complexity and these are computationally expensive for large time series. In this paper, we introduce FastDTW kernel, which is a linear approximation of the DTW kernel and can be used with linear SVM. To compute the DTW distance for any given sequences, we need to find the optimal warping path from all the possible alignments, which is a computationally expensive operation. Instead of finding the optimal warping path for every pair of sequences, we learn a small set of global alignments from a given dataset and use these alignments for comparing the given sequences. In this work, we learn the principal global alignments for the given data by using the hidden structure of the alignments from the training data. Since we use only a small number of global alignments for comparing the given test sequences, our proposed approximation kernel is computationally efficient compared to previous kernels on DTW distance. Further, we also propose a approximate explicit featuremap for our proposed kernel. Our results show the efficiency of the proposed approximation kernel.