A reproducing kernel Hilbert space framework for pairwise time series distances

Authors:
Zhengdong Lu;Todd K. Leen;Yonghong Huang;Deniz Erdogmus
Affiliations:
Oregon Health & Science University, Beaverton, OR;Oregon Health & Science University, Beaverton, OR;Oregon Health & Science University, Beaverton, OR;Oregon Health & Science University, Beaverton, OR
Venue:
Proceedings of the 25th international conference on Machine learning
Year:
2008

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Abstract

A good distance measure for time series needs to properly incorporate the temporal structure, and should be applicable to sequences with unequal lengths. In this paper, we propose a distance measure as a principled solution to the two requirements. Unlike the conventional feature vector representation, our approach represents each time series with a summarizing smooth curve in a reproducing kernel Hilbert space (RKHS), and therefore translate the distance between time series into distances between curves. Moreover we propose to learn the kernel of this RKHS from a population of time series with discrete observations using Gaussian process-based non-parametric mixed-effect models. Experiments on two vastly different real-world problems show that the proposed distance measure leads to improved classification accuracy over the conventional distance measures.