Similarity Learning-Induced Symmetric Nonnegative Matrix Factorization for Image Clustering

Abstract

As a typical variation of nonnegative matrix factorization (NMF), symmetric NMF (SNMF) is capable of exploiting information of the cluster embedded in the matrix of similarity. The traditional SNMF-based methods for clustering first performs the techniques of the similarity learning on input data to learn a matrix of similarity, which is subsequently factorized by SNMF or one of its variants to learn information from the cluster. While these methods have led to satisfactory clustering results, it is suboptimal, since they do not explicitly exploit the fact that processes of the similarity learning and the clustering are depend on each other. In this paper, we describe a new SNMF model, termed similarity learning-induced SNMF (SLSNMF). SLSNMF can be considered as a unified framework that jointly considers these two processes. SLSNMF improves the clustering performance of SNMF by thoroughly exploring the mutual reinforcement between the process of similarity learning and the process of clustering until convergence. We incorporate a constraint into the standard SNMF model to learn the matrices of similarity and cluster simultaneously. Meanwhile, for solving this new model, we use the strategy of alternating iterative and derive an efficient algorithm, whose convergence is theoretically guaranteed. Experimental results over three benchmark image data sets demonstrate that SLSNMF outperforms the state-of-the-art methods for clustering.

Keywords

• Symmetric nonnegative matrix factorization (SNMF)
• nonnegative matrix factorization (NMF)
• clustering
• unsupervised learning