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

Spectral clustering (SC) is one of the most widely used methods for data clustering. It first finds a low-dimensional embedding U of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on U^T to get the final clustering result. In this paper, we observe that, in the ideal case, UU^T should be block diagonal and thus sparse. Therefore, we propose the sparse SC (SSC) method that extends the SC with sparse regularization on UU^T. 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 multipliers Furthermore, we propose the pairwise SSC that 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.