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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.06534 |
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| _version_ | 1866908510151770112 |
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| author | Zhang, Hanchao Ju, Xiaomeng Shi, Baoyi Meng, Lingsong Tarpey, Thaddeus |
| author_facet | Zhang, Hanchao Ju, Xiaomeng Shi, Baoyi Meng, Lingsong Tarpey, Thaddeus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06534 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | K-Tensors: Clustering Positive Semi-Definite Matrices Zhang, Hanchao Ju, Xiaomeng Shi, Baoyi Meng, Lingsong Tarpey, Thaddeus Machine Learning Methodology 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. |
| title | K-Tensors: Clustering Positive Semi-Definite Matrices |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2306.06534 |