Structure anchor graph learning for multi-view clustering

With the growth of data and diverse data sources, clustering large-scale multi-view data has emerged as a prominent topic in the field of machine learning. Anchor graph is an efficient strategy to improve the scalability of graph based multi-view clustering methods because it can capture the essence of the entire dataset by utilizing only a small set of representative anchor points. However, most existing anchor graph based methods encounter at least one of the following two challenges: the first one is the separation of anchor selection from the anchor graph construction process, while the second one is the requirement of an additional clustering step to generate the indicator matrix. Both of the separated steps can potentially lead to suboptimal solutions. In this paper, we propose structure anchor graph learning for multi-view clustering (SAGL), which jointly addresses the two challenges within a unified learning framework. Specifically, instead of utilizing the fixed anchors selected during the pre-processing step, SAGL jointly learns the consensus anchors in the latent space, and constructs anchor graph by assigning larger similarity values to sample-anchor pairs with shorter distances. Meanwhile, by manipulating the connected components of the anchor graph with rank constraint, SAGL obtains the anchor graph with clear cluster structure that can directly reveal the indicator of samples without any post-processing step. As a result, it becomes a truly one-stage end-to-end learning problem. In addition, a simple yet effective transformation is introduced to convert vector-sum-from to matrix-multiplication-form with trace operation, which leads an efficient optimization algorithm. Extensive experiments on several real-world multi-view datasets demonstrate the effectiveness and efficiency of the proposed methods over other state-of-the-art MvC methods.