One-Step Adaptive Graph Learning for Incomplete Multiview Subspace Clustering

Abstract

Incomplete multiview clustering (IMVC) optimally integrates complementary information within incomplete multiview data to improve clustering performance. Several one-step graph-based methods show great potential for IMVC. However, the low-rank structures of similarity graphs are neglected at the initialization stage of similarity graph construction. Moreover, further investigation into complementary information integration across incomplete multiple views is needed, particularly when considering the low-rank structures implied in high-dimensional multiview data. In this paper, we present one-step adaptive graph learning (OAGL) that adaptively performs spectral embedding fusion to achieve clustering assignments at the clustering indicator level. We first initiate affinity matrices corresponding to incomplete multiple views using spare representation under two constraints, i.e., the sparsity constraint on each affinity matrix corresponding to an incomplete view and the degree matrix of the affinity matrix approximating an identity matrix. This approach promotes exploring complementary information across incomplete multiple views. Subsequently, we perform an alignment of the spectral block-diagonal matrices among incomplete multiple views using low-rank tensor learning theory. This facilitates consistency information exploration across incomplete multiple views. Furthermore, we present an effective alternating iterative algorithm to solve the resulting optimization problem. Extensive experiments on benchmark datasets demonstrate that the proposed OAGL method outperforms several state-of-the-art approaches.