Embedding of time series data by using Dynamic Time Warping distances

We propose an approach to embedding time series data in a vector space based on the distances obtained from Dynamic Time Warping (DTW), and classifying them in the embedded space. Under the problem formulation in which both labeled data and unlabeled data are given beforehand, we consider three embeddings: embedding in a Euclidean space by MDS, embedding in a pseudo-Euclidean space, and embedding in a Euclidean space by the Laplacian eigenmap technique. We have found through analysis and experiment that embedding by the Laplacian eigenmap method leads to the best classification results. Furthermore, the proposed approach with Laplacian eigenmap embedding gives better performance than the k nearest neighbor method. © 2006 Wiley Periodicals, Inc.