Robust Spectral Ensemble Clustering via Rank Minimization.

Ensemble Clustering (EC) is an important topic for data cluster analysis. It targets to integrate multiple Basic Partitions (BPs) of a particular dataset into a consensus partition. Among previous works, one promising and effective way is to transform EC as a graph partitioning problem on the co-association matrix, which is a pair-wise similarity matrix summarized by all the BPs in essence. However, most existing EC methods directly utilize the co-association matrix, yet without considering various noises (e.g., the disagreement between different BPs and the outliers) that may exist in it. These noises can impair the cluster structure of a co-association matrix, and thus mislead the final graph partitioning process. To address this challenge, we propose a novel Robust Spectral Ensemble Clustering (RSEC) algorithm in this article. Specifically, we learn low-rank representation (LRR) for the co-association matrix to uncover its cluster structure and handle the noises, and meanwhile, we perform spectral clustering with the learned representation to seek for a consensus partition. These two steps are jointly proceeded within a unified optimization framework. In particular, during the optimizing process, we leverage consensus partition to iteratively enhance the block-diagonal structure of LRR, in order to assist the graph partitioning. To solve RSEC, we first formulate it by using nuclear norm as a convex proxy to the rank function. Then, motivated by the recent advances in non-convex rank minimization, we further develop a non-convex model for RSEC and provide it a solution by the majorization--minimization Augmented Lagrange Multiplier algorithm. Experiments on 18 real-world datasets demonstrate the effectiveness of our algorithm compared with state-of-the-art methods. Moreover, several impact factors on the clustering performance of our approach are also explored extensively.