Convex Sparse Spectral Clustering: Single-view to Multi-view

TL;DR

This paper introduces a novel sparse regularization approach to spectral clustering, improving efficiency and extending to multi-view data, with demonstrated superior performance on real datasets.

Contribution

It proposes a convex relaxation of sparse spectral clustering and extends the method to multi-view data, enhancing computational efficiency and clustering accuracy.

Findings

Convex SSC can be efficiently solved using ADMM.

Sparse regularization improves clustering performance.

Multi-view extension (PSSC) boosts accuracy on real datasets.

Abstract

Spectral Clustering (SC) is one of the most widely used methods for data clustering. It first finds a low-dimensonal embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on $U^\top$ to get the final clustering result. In this work, we observe that, in the ideal case, $UU^\top$ should be block diagonal and thus sparse. Therefore we propose the Sparse Spectral Clustering (SSC) method which extends SC with sparse regularization on $UU^\top$. To address the computational issue of the nonconvex SSC model, we propose a novel convex relaxation of SSC based on the convex hull of the fixed rank projection matrices. Then the convex SSC model can be efficiently solved by the Alternating Direction Method of \canyi{Multipliers} (ADMM). Furthermore, we propose the Pairwise Sparse Spectral Clustering (PSSC) which extends SSC to boost the clustering performance by using the multi-view information of data. Experimental comparisons with several baselines on real-world datasets testify to the efficacy of our proposed methods.