Clustering Time Series, Subspace Identification and Cepstral Distances

Abstract

In this paper a methodology to cluster time series based on measurement data is described. In particular, we propose a distance for stochastic models based on the concept of subspace angles within a model and between two models. This distance is used to obtain a clustering over the set of time series. We show how it is related to the mutual information of the past and the future output processes, and to a previously defined cepstral distance. Finally, the methodology is applied to the clustering of time series of power consumption within the Belgian electricity grid.