Multi-view latent structure learning with rank recovery

Multi-view clustering (MVC) algorithms usually have good performance which benefits from the merit that multi-view data contains more comprehensive information. Generally, most graph-based MVC algorithms adopt a two-step learning strategy, that is, first learn affinity graphs from each view, and then fuse these graphs according to certain criterion to obtain the final consistent affinity graph. Although this strategy can get partial consistent information from multiple views, it still suffers from some drawbacks. 1) Due to the existence of noise and redundant features in the raw data, the structural information in the learned affinity graphs may deviate from the truth; 2) The affinity graphs learned in the first step may constrain each other in the fusion stage, which may lead to further degradation of the final affinity graph. To minimize the impact of the above factors, a new MVC method, multi-view latent structure learning with rank recovery (MLSL), is proposed in this work. Specifically, MLSL recovers a set of low-rank representations from the raw data by low-rank matrix approximation, then learns a consistent embedding space of the raw data from these new representations, and finally learns adaptively the inherent affinity graph from the learned embedding space. In the learning process of MLSL, the low-rank recovery is used to remove the noise of the raw data, the embedding space learning is used to minimize the redundant features, and the single affinity graph learning can avoid graph fusion. Meanwhile, orthogonal constraints are used to ensure that the embedding space have the same rank as the low-rank representations of each view. Schatten p-norm is adopted in low-rank recovery technology to better approximate the rank of matrix. An efficient iterative algorithm is designed to solve the non-convex optimization problem based on the Schatten p -norm. Finally, extensive experiments on nine datasets are performed to evaluate the performance of the proposed algorithm. The experimental results indicate that MLSL can improve the clustering performance on most datasets compared with related recent studies. Meanwhile, the ablation experiments also verify that the low-rank recovery policy in MLSL can improve the multi-view clustering performance.