Merging Student's-t and Rayleigh distributions regression mixture model for clustering time-series

This paper addresses an efficient scheme for clustering time-series through a novel regression mixture strategy (RMM) that simultaneously utilizes the benefits of the Markov random field (MRF) and mean template. Each component of the proposed RMM is a mixture of Student's-t and non-symmetric Rayleigh distributions. The Student's-t distribution has been validated to be effective in reducing the influence of outliers. Another advantage is it considers the property of time-series in which spatially adjacent voxels have higher probabilities when belonging to the same cluster; thus, this study seeks to impose the spatially interdependent constraints in the form of a prior through a Bayesian theorem. By introducing the non-symmetric Rayleigh distribution, the proposed method has flexibility to fit various types of observed time-series. To optimize the model parameters, the proposed algorithm is formulated as a maximum a posteriori (MAP) estimation problem. An expectation maximization (EM)-type approach is eventually executed to obtain the update equations. Additionally, an efficient energy function is applied in the proposed approach such that the EM-MAP algorithm can be directly applied to calculate the objective function, which makes the proposed approach easier to implement. To illustrate the suitability of the proposed approach, we have extensively compared clustering accuracy, curve square error, and intraclass index with those of existing similarity methods on synthetic spatiotemporal datasets, synthetic fMRI time-series, and real life fMRI time-series.