Diagonalizing Affinity Matrix to Identify Clustering Structure

Zheng Xing, Weibing Zhao

Keywords: Block diagonal, clustering analysis, affinity matrix

Abstract: Affinity matrix-based clustering constitutes an eminent approach within the domain of data mining. Nevertheless, prior research overlooked the opportunity to directly exploit the block-diagonal structure of the affinity matrix for the purpose of identifying cluster formations. In this paper, we propose an affinity matrix-based clustering strategy, termed as DAM, which employs a traversal algorithm to discern high-density clusters within the graph weighted by the affinity matrix, thereby establishing a traversal sequence. This sequence is subsequently utilized to permute the affinity matrix, thereby revealing its intrinsic block-diagonal structure. Moreover, we introduce an innovative split-and-refine algorithm that autonomously detects all diagonal blocks within the permuted matrix, ensuring theoretical optimality in the presence of well-separated clusters. Extensive evaluations on six real-world benchmark image clustering datasets demonstrate the superiority of our method over contemporary state-of-the-art clustering techniques.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 1860