K-Tensors: Clustering Positive Semi-Definite Matrices

06/10/2023
by   Hanchao Zhang, et al.
0

This paper introduces a novel self-consistency clustering algorithm (K-Tensors) designed for positive-semidefinite matrices based on their eigenstructures. As positive semi-definite matrices can be represented as ellipses or ellipsoids in ^p, p ≥ 2, it is critical to maintain their structural information to perform effective clustering. However, traditional clustering algorithms often vectorize the matrices, resulting in a loss of essential structural information. To address this issue, we propose a distance metric that is specifically based on the structural information of positive semi-definite matrices. This distance metric enables the clustering algorithm to consider the differences between positive semi-definite matrices and their projection onto the common space spanned by a set of positive semi-definite matrices. This innovative approach to clustering positive semi-definite matrices has broad applications in several domains, including financial and biomedical research, such as analyzing functional connectivity data. By maintaining the structural information of positive semi-definite matrices, our proposed algorithm promises to cluster the positive semi-definite matrices in a more meaningful way, thereby facilitating deeper insights into the underlying data in various applications.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset