Composite marginal discrepancies for state-space time series clustering

Abstract

We consider the clustering of time series data; specifically, time series that can be modeled in the state space framework. Of primary focus is the pairwise discrepancy between two state space time series. The state space model can be formulated in terms of two equations: the state equation, based on a latent process, and the observation equation. Because the unobserved state process is often of interest, we develop discrepancy measures based on the estimated version of this process. First, discrepancies derived from Kullback-Leibler (KL) information and Mahalanobis distance (MD) measures are proposed using the composite marginal contributions of the smoothed estimates of the unobserved states. In addition, a Euclidean distance based on the smoothed state estimates is formulated. We compare these measures to the Euclidean distance based on the observed data in an example pertaining to the clustering of time course genetic profiles.