Nonnegative Tensor Representation With Cross-View Consensus for Incomplete Multi-View Clustering

Abstract

Tensors capture the multi-dimensional structure of multi-view data naturally, resulting in richer and more meaningful data representations. This produces more accurate clustering results for challenging incomplete multi-view clustering (IMVC) tasks. However, previous tensor learning-based IMVC (TLIMVC) methods often build a tensor representation by simply stacking view-specific representations. Consequently, the learned tensor representation lacks good interpretability since each entry of it could not directly reveals the similarity relationship of the corresponding two samples. In addition, most of them only focus on exploring the high-order correlations among views, while the underlying consensus information is not fully exploited. To this end, we propose a novel TLIMVC method named Nonnegative Tensor Representation with Cross-view Consensus (NTRC $^{2}$ ) in this paper. Specifically, a nonnegative constraint and view-specific consensus are jointly integrated into the framework of the tensor based self-representation learning, which enables the method to simultaneously explore the consensus and complementary information of multi-view data more fully. An Augmented Lagrangian Multiplier based optimization algorithm is derived to optimize the objective function. Experiments on several challenging benchmark datasets verify our NTRC $^{2}$ method's effectiveness and competitiveness against state-of-the-art methods.