Clustering of LTI Systems in the Presence of Output Measurement Outliers: A Variational EM Method

Abstract

In this letter, we consider the clustering of LTI systems in the presence of output measurement outliers, and moreover the collected input-output data for each system is short and/or has low signal-to-noise ratio. To address the problem, we propose a Dirichlet process Student’s $t$ mixture regression model (DPSMRM). Then a variational expectation-maximization method with adaptive truncation level is used for the inference of DPSMRM. Finally, we show the convergence of the accepted evidence lower bound sequence. The proposed method has the advantage that it can leverage the prior knowledge to mitigate the large variance of model estimates. Monte Carlo simulations show that under the considered setting, the proposed method outperforms other methods in terms of average clustering accuracy when the relative size and the occurrence probability of outliers are large.