Enhanced Tensor Low-Rank and Sparse Representation Recovery for Incomplete Multi-View Clustering

Incomplete multi-view clustering (IMVC) has attracted remarkable attention due to the emergence of multi-view data with missing views in real applications. Recent methods attempt to recover the missing information to address the IMVC problem. However, they generally cannot fully explore the underlying properties and correlations of data similarities across views. This paper proposes a novel Enhanced Tensor Low-rank and Sparse Representation Recovery (ETLSRR) method, which reformulates the IMVC problem as a joint incomplete similarity graph learning and complete tensor representation recovery problem. Specifically, ETLSRR learns the intra-view similarity graphs and constructs a 3-way tensor by stacking the graphs to explore the inter-view correlations. To alleviate the negative influence of missing views and data noise, ETLSRR decomposes the tensor into two parts: a sparse tensor and an intrinsic tensor, which models the noise and underlying true data similarities, respectively. Both global low-rank and local structured sparse characteristics of the intrinsic tensor are considered, which enhances the discrimination of similarity matrix. Moreover, instead of using the convex tensor nuclear norm, ETLSRR introduces a generalized nonconvex tensor low-rank regularization to alleviate the biased approximation. Experiments on several datasets demonstrate the effectiveness and superiority of our method compared with the state-of-the-art methods.