Fast dynamic time warping using low-rank matrix approximations

Abstract

Dynamic Time Warping (DTW) is a computationally intensive algorithm and computation of a local (Euclidean) distance matrix between two signals constitute the majority of the running time of DTW. In earlier work, a matrix multiplication based formulation for computing the Euclidean distance matrix was proposed leading to faster DTW. In this work, we propose the use of (i) direct low-rank factorization of template matrix and (ii) optimal low-rank factorization of the Euclidean distance matrix, leading to further computational speedup without significantly affecting accuracy. We derive a condition for achieving computational savings using low-rank factorizations. We analyze the condition for achieving computational savings over these low-rank factorizations by using separate low-rank factors for each class of templates to further reduce the rank within each class. We show that, using per-class factors, we can achieve significant average rank reduction with further computational savings for applications with high inter class variability in the feature space. We observe that our low-rank factorization methods result in lesser errors in the Euclidean distance matrix compared to Principal Component Analysis (PCA). We analyze the error behavior using spoken digit and heart auscultation sound datasets and achieve speedups of upto 4.59x for spoken digit recognition task on a dual core mobile CPU.