Joint learning affinity matrix and representation matrix for robust low-rank multi-kernel clustering

Multi-kernel subspace clustering has attracted widespread attention, because it can process nonlinear data effectively. It usually solves the representation coefficient between data by the subspace clustering optimization model, and then the constructed affinity matrix is input into the spectral clustering method to get the final clustering result. Obviously, the quality of the affinity matrix (graph) has a significant impact on the final clustering result. Unfortunately, there are two deficiencies in the previous multi-kernel subspace clustering methods as follows: 1) this typical two-phase method restricts the learning of the affinity matrix; 2) it does not fully extract the data global structure mapped to the kernel space. In order to solve these two problems simultaneously, a novel low-rank multi-kernel subspace clustering method incorporating a joint learning scheme, namely JALSC, is proposed. The innovation of this method is reflected in the following two aspects: 1) the adaptive local structure is used to learn the representation of the data and the affinity graph in the integrated objective function at the same time. The optimal affinity graph obtained by the one-step learning scheme helps to improve the clustering performance; 2) our method uses a non-convex low-rank approximation function to constrain the consensus kernel to preserve the global structure of the data after mapping to the feature space. A mass of experiments on several commonly used datasets show that JALSC obtains the best clustering performance and has better robustness compared with several advanced multi-kernel clustering methods.