Efficient model selection in switching linear dynamic systems by graph clustering

TL;DR

This paper introduces a graph clustering approach to reduce the complexity of switching linear dynamic systems, enabling more efficient model selection with quantifiable error bounds.

Contribution

It proposes a novel graph-based clustering method for SLDS that reduces mode cardinality offline, improving computational efficiency while maintaining controllable error levels.

Findings

Clustering reduces model complexity effectively.

Error due to clustering can be quantified exactly.

Numerical results confirm the approach's effectiveness.

Abstract

The computation required for a switching Kalman Filter (SKF) increases exponentially with the number of system operation modes. In this paper, a computationally tractable graph representation is proposed for a switching linear dynamic system (SLDS) along with the solution of a minimum-sum optimization problem for clustering to reduce the switching mode cardinality offline, before collecting measurements. It is shown that upon perfect mode detection, the induced error caused by mode clustering can be quantified exactly in terms of the dissimilarity measures in the proposed graph structure. Numerical results verify that clustering based on the proposed framework effectively reduces model complexity given uncertain mode detection and that the induced error can be well approximated if the underlying assumptions are satisfied.