Robust Consensus Anchor Learning for Efficient Multi-view Subspace Clustering

As a leading unsupervised classification algorithm in artificial intelligence, multi-view subspace clustering segments unlabeled data from different subspaces. Recent works based on the anchor have been proposed to decrease the computation complexity for the datasets with large scales in multi-view clustering. The major differences among these methods lie on the objective functions they define. Despite considerable success, these works pay few attention to guaranting the robustness of learned consensus anchors via effective manner for efficient multi-view clustering and investigating the specific local distribution of cluster in the affine subspace. Besides, the robust consensus anchors as well as the common cluster structure shared by different views are not able to be simultaneously learned. In this paper, we propose Robust Consensus anchors learning for efficient multi-view Subspace Clustering (RCSC). We first show that if the data are sufficiently sampled from independent subspaces, and the objective function meets some conditions, the achieved anchor graph has the block-diagonal structure. As a special case, we provide a model based on Frobenius norm, non-negative and affine constraints in consensus anchors learning, which guarantees the robustness of learned consensus anchors for efficient multi-view clustering and investigates the specific local distribution of cluster in the affine subspace. While it is simple, we theoretically give the geometric analysis regarding the formulated RCSC. The union of these three constraints is able to restrict how each data point is described in the affine subspace with specific local distribution of cluster for guaranting the robustness of learned consensus anchors. RCSC takes full advantages of correlation among consensus anchors, which encourages the grouping effect and groups highly correlated consensus anchors together with the guidance of view-specific projection. The anchor graph construction, partition and robust anchor learning are jointly integrated into a unified framework. It ensures the mutual enhancement for these procedures and helps lead to more discriminative consensus anchors as well as the cluster indicator. We then adopt an alternative optimization strategy for solving the formulated problem. Experiments performed on eight multi-view datasets confirm the superiority of RCSC based on the effectiveness and efficiency.

As a leading unsupervised classification algorithm in artificial intelligence, multi-view subspace clustering segments unlabeled data from different subspaces. Recent works based on the anchor have been proposed to decrease the computation complexity for the datasets with large scales in multi-view clustering. Despite considerable success, these works pay few attention to guaranting the robustness of learned consensus representative data samples via effective manner for efficient multi-view clustering. In this paper, we propose Robust Consensus anchors learning for efficient multi-view Subspace Clustering (RCSC). We first show that if the data are sufficiently sampled from independent subspaces, and the objective function meets some conditions, the achieved graph constructed by representative data samples has the block-diagonal structure. Experiments performed on eight multi-view datasets confirm the superiority of RCSC based on the effectiveness and efficiency.