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Regularized matrix data clustering and its application to image analysis
Author(s) -
Gao Xu,
Shen Weining,
Zhang Liwen,
Hu Jianhua,
Fortin Norbert J.,
Frostig Ron D.,
Ombao Hernando
Publication year - 2021
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.13354
Subject(s) - interpretability , cluster analysis , computer science , covariance matrix , estimator , algorithm , computation , separable space , regularization (linguistics) , expectation–maximization algorithm , covariance , matrix (chemical analysis) , pattern recognition (psychology) , mathematics , artificial intelligence , mathematical optimization , statistics , maximum likelihood , mathematical analysis , materials science , composite material
We propose a novel regularized mixture model for clustering matrix‐valued data. The proposed method assumes a separable covariance structure for each cluster and imposes a sparsity structure (eg, low rankness, spatial sparsity) for the mean signal of each cluster. We formulate the problem as a finite mixture model of matrix‐normal distributions with regularization terms, and then develop an expectation maximization type of algorithm for efficient computation. In theory, we show that the proposed estimators are strongly consistent for various choices of penalty functions. Simulation and two applications on brain signal studies confirm the excellent performance of the proposed method including a better prediction accuracy than the competitors and the scientific interpretability of the solution.