Fast and Robust Sparsity-Aware Block Diagonal Representation

TL;DR

This paper introduces FRS-BDR, a novel method for recovering block diagonal affinity matrices in clustering tasks, robustly handling outliers and noise while accurately estimating cluster structures and numbers.

Contribution

The paper proposes a robust, sparsity-aware block diagonal representation method that jointly estimates cluster memberships and the number of clusters, improving robustness and efficiency.

Findings

Outperforms existing methods in clustering accuracy

Demonstrates robustness against outliers and noise

Reduces computation time in real-world applications

Abstract

The block diagonal structure of an affinity matrix is a commonly desired property in cluster analysis because it represents clusters of feature vectors by non-zero coefficients that are concentrated in blocks. However, recovering a block diagonal affinity matrix is challenging in real-world applications, in which the data may be subject to outliers and heavy-tailed noise that obscure the hidden cluster structure. To address this issue, we first analyze the effect of different fundamental outlier types in graph-based cluster analysis. A key idea that simplifies the analysis is to introduce a vector that represents a block diagonal matrix as a piece-wise linear function of the similarity coefficients that form the affinity matrix. We reformulate the problem as a robust piece-wise linear fitting problem and propose a Fast and Robust Sparsity-Aware Block Diagonal Representation (FRS-BDR) method, which jointly estimates cluster memberships and the number of blocks. Comprehensive experiments on a variety of real-world applications demonstrate the effectiveness of FRS-BDR in terms of clustering accuracy, robustness against corrupted features, computation time and cluster enumeration performance.