Robust multiple kernel subspace clustering with block diagonal representation and low-rank consensus kernel

Abstract

Multiple kernel learning (MKL) is widely used to deal with nonlinear clustering problem, because MKL can obtain the optimal consensus kernel by designing kernel weighting strategy, which avoids the limitation of single-kernel learning restricted by the selected kernel function. However, existing MKL subspace clustering algorithms ignore noise and the low-rank structure of the data in the feature space. We propose a new robust multiple kernel subspace clustering algorithm (LRMKSC) with block diagonal representation (BDR) and low-rank consensus kernel (LRCK), which is more systematic and comprehensive for data processing. In particular, (1) to learn the optimal consensus kernel, we design an automatic weighting strategy using Mixture Correntropy Induced Metric (MCIM), which not only sets the optimal weight for each kernel, but also improves the robustness of LRMKSC by suppressing noise; (2) to explore low-rank structure of input data in feature space, we propose the Weighted Truncated Schatten p-Norm (WTSN) and apply it to the low-rank constraint of the optimal consensus kernel; (3) considering the block diagonal property of the affinity matrix, we apply block diagonal constraint to the coefficient matrix. LRMKSC combines MKL, LRCK and BDR to solve these problems simultaneously. Through the interaction of three technologies, the results of other technologies are used in the overall optimal solution to iteratively improve the efficiency of each technology, and finally form an overall optimal algorithm for processing nonlinear structural data. Compared with the most advanced MKL subspace clustering algorithms, extensive experiments on image and text datasets verify the competitiveness of LRMKSC.