Embedded Anchors Coupled Low-Rank Tensor Learning for Multi-View Intrinsic Subspace Clustering

Multi-view subspace clustering mines fusion maps that reflect the underlying structure of views in low-dimensional subspace. It has been broadly popularized for its capability to consolidate multi-view information effectively. The cubic time complexity of both graph construction and spectral clustering has greatly hindered the application of these algorithms to large-scale scenarios. Several research approaches have dramatically improved the clustering productivity by employing the anchor sampling mechanism. However, existing methods do not consider that large-scale data often includes extensive noise and anomalous information, which inevitably degrades the clustering performance by performing the selection of anchors in the primitive data space. Besides, these methods do not reveal the high-order relationships concealed behind multi-view data and recover the global low-rank of the anchor graphs. Given this, we present a new approach called embedded anchors coupled low-rank tensor learning for multi-view intrinsic subspace clustering (ALTMSC). Specifically, we firstly map the multi-view data to a clean feature space through the feature transfer matrix, and adaptively accomplish anchor learning and the construction of embedded anchor graphs. As such, we can obtain high-quality anchor graphs. In addition, to enhance cross-view global consistency, we learn multiple intrinsic anchor graphs via rank-preserving decomposition to diminish the negative impact of view-specific statistical properties on consistency. Then, these intrinsic anchor maps are stacked into a third-order tensor with tensor nuclear norm constraint that can fully explore the high-order relationships between views. Compared with existing approaches, extensive experiments on eight datasets confirm the supremacy of ALTMSC.