q-Divergence-Based Fuzzy c-Linear Gaussian State Space Model

Abstract

This paper proposes a fuzzy clustering algorithm based on the linear Gaussian state space model (LGSSM), referred to as q-divergence-based fuzzy c-linear Gaussian state space models (QFCLGSSMs) for series data. QFCLGSSMs are constructed from mixtures of linear Gaussian state space models (MLGSSMs), which is a conventional probabilistic clustering algorithm based on LGSSM for series data. QFCLGSSMs are motivated by the relationship between the following clustering algorithms for vectorial data: Gaussian mixture model with identity covariances and q-divergence-based fuzzy c-means. In numerical experiments that use an artificial dataset, we revealed the effects of fuzzification parameters on the fuzziness of clustering results in the proposed algorithm demonstrating the close relationship between the proposed algorithm and the conventional algorithm, MLGSSMs. Moreover, through numerical experiments, using nine real datasets, we demonstrated that the proposed algorithm outperformed the conventional algorithm, MLGSSMs, in terms of clustering accuracy.