Anchor-Based Multiview Subspace Clustering With Anchor-wise and Class-wise Alignments

Multiview subspace clustering has shown promising performance in multimedia and data mining applications. However, its employment in large-scale datasets is limited due to its quadratic or even cubic computational complexity. The anchor graph strategy, which selects a few important samples (anchors) to represent the whole data for different views, has been introduced to address this challenge. These methods rely on a heuristic assumption that the correspondence and class structures between the sets of anchors across different views are the same. This assumption ignores the difference in the ordering of anchors with respect to their associated classes and the number of anchors belonging to the same class from different views. As a result, this can lead to unsatisfactory clustering results due to incorrect anchorwise and classwise alignments. To tackle this issue, this article proposes an anchor-based multiview subspace clustering with anchorwise and classwise alignments (AMCA²) method. Specifically, the proposed method simultaneously aligns and fuses multiple anchor graphs anchor wisely and class wisely via learning permutation matrices and utilizing the Hadamard product. To further enhance the clustering performance of AMCA², we propose a novel anchor selection method called kernel anchor selection (KAS) to select more representative anchors. Extensive experiments on ten benchmark datasets are conducted to show the superiority and effectiveness of AMCA² over the state-of-the-art methods.