Joint correntropy metric weighting and block diagonal regularizer for robust multiple kernel subspace clustering

Abstract Nonlinear kernel-based subspace clustering methods that can reveal the multi-cluster nonlinear structure of samples are an emerging research topic. However, the existing kernel subspace clustering methods have the following three flaws: 1) their clustering performance is largely determined by the chosen kernel function; 2) they may lack robustness in the presence of non-Gaussian noise and impulsive noise; and 3) their learned affinity matrix can not hold the desired block diagonal property for clustering purpose, which possibly leads to incorrect clustering when using spectral clustering. In this paper, we propose a Joint Robust Multiple Kernel Subspace Clustering (JMKSC) method for data clustering, which has two primary innovations. First, our multiple kernel weighting strategy introduces the correntropy metric weighting instead of a fixed, or inappropriately assigned weighting, which is more robust to the non-Gaussian noise and contributes to learning the optimal consensus kernel. Second, our method encourages acquiring an affinity matrix with the optimal block diagonal property based on the block diagonal regularizer (BDR) and the self-expressiveness property. Experiments on several different types of datasets confirm that the proposed JMKSC significantly outperforms several state-of-the-art single kernel and multiple kernel subspace clustering methods in terms of accuracy, NMI and purity.