Elastic Multi-view Subspace Clustering with Pairwise and High-order Correlations

Multi-view clustering has become an important research topic in machine learning and computer vision communities, which aims at achieving a consensus partition of data points across different views. However, the existing multi-view clustering methods fail to simultaneously consider the pairwise and high-order correlations among different views in the process of obtaining the final results. In this paper, we propose the Elastic multi-view Subspace Clustering with pairwise and high-order Correlations (ESCC) to solve this problem. ESCC simultaneously explores the pairwise and high-order correlations among different views, resulting in a more comprehensive shared representation. ESCC formulates these two kinds of correlations into a unified objective framework, which are able to be jointly optimized to refine each other. As an instantiation, we construct an example of ESCC (e-ESCC) in this work. To be specific, e-ESCC uses the multi-layer neural networks to study the pairwise correlation from multiple views with the guidance of the latent representation. It is also able to help obtain the nonlinear subspaces of the multi-view data. e-ESCC collects multi-view similarity matrices into a tensor and utilizes the low-rank tensor norm to exploit the high-order correlation among different views. The augmented Lagrangian multiplier is adopted to solve the formulated problem of e-ESCC. Experiments on seven data sets validate the superiority of our method over 13 state-of-the-art multi-view clustering methods under six metrics.