K-Tensors: Clustering Positive Semi-Definite Matrices

• URL: http://arxiv.org/abs/2306.06534v5
• Date: Sat, 30 Aug 2025 05:17:41 GMT
• Title: K-Tensors: Clustering Positive Semi-Definite Matrices
• Authors: Hanchao Zhang, Xiaomeng Ju, Baoyi Shi, Lingsong Meng, Thaddeus Tarpey,
• Abstract summary: This paper presents a new clustering algorithm for symmetric positive semi-definite (SPSD) matrices, called K-Tensors.<n>We show that the proposed clustering algorithm is self-consistent under mild distribution assumptions and converges to a local optimum.<n>We demonstrate the use of the algorithm through an application to resting-state functional magnetic resonance imaging (rs-fMRI) data from the Human Connectome Project.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper presents a new clustering algorithm for symmetric positive semi-definite (SPSD) matrices, called K-Tensors. The method identifies structured subsets of the SPSD cone characterized by common principal component (CPC) representations, where each subset corresponds to matrices sharing a common eigenstructure. Unlike conventional clustering approaches that rely on vectorization or transformations of SPSD matrices, thereby losing critical geometric and spectral information, K-Tensors introduces a divergence that respects the intrinsic geometry of SPSD matrices. This divergence preserves the shape and eigenstructure information and yields principal SPSD tensors, defined as a set of representative matrices that summarize the distribution of SPSD matrices. By exploring its theoretical properties, we show that the proposed clustering algorithm is self-consistent under mild distribution assumptions and converges to a local optimum. We demonstrate the use of the algorithm through an application to resting-state functional magnetic resonance imaging (rs-fMRI) data from the Human Connectome Project, where we cluster brain connectivity matrices to discover groups of subjects with shared connectivity structures.

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