Making clustering in delay-vector space meaningful

Sequential time series clustering is a technique used to extract important features from time series data. The method can be shown to be the process of clustering in the delay-vector space formalism used in the Dynamical Systems literature. Recently, the startling claim was made that sequential time series clustering is meaningless. This has important consequences for a significant amount of work in the literature, since such a claim invalidates these work’s contribution. In this paper, we show that sequential time series clustering is not meaningless, and that the problem highlighted in these works stem from their use of the Euclidean distance metric as the distance measure in the delay-vector space. As a solution, we consider quite a general class of time series, and propose a regime based on two types of similarity that can exist between delay vectors, giving rise naturally to an alternative distance measure to Euclidean distance in the delay-vector space. We show that, using this alternative distance measure, sequential time series clustering can indeed be meaningful. We repeat a key experiment in the work on which the “meaningless” claim was based, and show that our method leads to a successful clustering outcome. Jason R. Chen received the B.E. degree from Sydney University, Australia, in 1991 and then worked mainly in the banking and finance industry until 1997. From 1997 to 2001, he completed the Ph.D. at Australian National University, Canberra, Australia, in robotics. From 2001 to the present, he has been a Research Engineer in the Research School of Information Science and Engineering, at Australian National University. His research interests broadly include robotics, data mining, and AI.