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 $\Re^p$, $p \ge 2$, 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.

本文提出了一种自洽聚类算法（K-Tensors），它是针对正半定矩阵的特殊结构所设计的算法，包括了一个专为正半定矩阵的结构信息而设计的距离度量，可在金融和生物医学研究等领域中具有广泛的应用。

K-Tensors：正半定矩阵聚类