State-Space Time-Series Clustering and Inference Using Discrepancies Based on the Kullback-Leibler Information and the Mahalanobis Distance

• Activity Number: 692
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Eric Foster*+ and Joseph Cavanaugh
• Companies: The University of Iowa and University of Iowa
• Keywords: Kalman Smoothing ; Kullback-Leibler Information ; Mahalanobis Distance ; State Space Model ; Time Course Experiment ; Time Series Analysis

Abstract

Time series applications frequently arise in biomedicine, genetics, and bioinformatics that require the clustering of multiple series into homogeneous groups. Both nonparametric and parametric techniques have been formulated; the latter are often based on discrepancy measures developed within a suitable modeling framework. For the purpose of clustering state-space processes, Bengtsson and Cavanaugh proposed the use of a discrepancy based on a Kullback-Leibler information measure. This measure is derived using the joint distribution of the collection of smoothed values for the states, computed via the Kalman filter smoother. In this work, we formulate a Mahalanobis distance version of the joint Kullback-Leibler based discrepancy. For comparison purposes, we contrast these measures to counterparts derived using the observed series as opposed to the smoothed series. Our initial simulation results indicate that the measures based on the smoothed series outperform those based on the observed series. Furthermore, we develop an iterative estimation routine based on the dissimilarity matrices that improves model parameter estimation in settings where short time series are observed.