Fast Elastic-Net Multi-view Clustering: A Geometric Interpretation Perspective

Multi-view clustering methods have been extensively explored in the last decades. This kind of methods is built on the assumption that the data are sampled from multiple subspaces with low dimension and each group fits into one of these subspaces. The quadratic or cubic computation complexity produced by these methods is inevitable, resulting in the difficulty for clustering multi-view datasets with large scales. Some efforts have been presented to select key anchors beforehand to capture the data distributions in different views. Despite significant progress, these methods pay few attentions to deriving provably scalable and correct method for finding the optimal shared anchor graph from the geometric interpretation perspective. They also ignore to give a well balance between the connectedness and subspace preserving properties of the shared anchor graph. In this paper, we propose the Fast Elastic- Net Multi-view Clustering (FENMC) from a geometric interpretation perspective. We provide the geometric analysis in determining the optimal shared anchor graph based on the introduced elastic-net regularizer for fast multi-view clustering, where the elastic-net regularizer is built on the mixture of L_2 and L_1 norms. We also give a theoretical justification for the balance between the connectedness and subspace preserving properties of the shared anchor graph for multi-view clustering. Our experiments on different datasets show that the proposed method not only obtains the satisfied clustering performance, but also deals with large-scale datasets with high efficiency.