Efficient Orthogonal Multi-view Subspace Clustering

Multi-view subspace clustering targets at clustering data lying in a union of low-dimensional subspaces. Generally, an n X n affinity graph is constructed, on which spectral clustering is then performed to achieve the final clustering. Both graph construction and graph partitioning of spectral clustering suffer from quadratic or even cubic time and space complexity, leading to difficulty in clustering large-scale datasets. Some efforts have recently been made to capture data distribution in multiple views by selecting key anchor bases beforehand with k-means or uniform sampling strategy. Nevertheless, few of them pay attention to the algebraic property of the anchors. How to learn a set of high-quality orthogonal bases in a unified framework, while maintaining its scalability for very large datasets, remains a big challenge. In view of this, we propose an Efficient Orthogonal Multi-view Subspace Clustering (OMSC) model with almost linear complexity. Specifically, the anchor learning, graph construction and partition are jointly modeled in a unified framework. With the mutual enhancement of each other, a more discriminative and flexible anchor representation and cluster indicator can be jointly obtained. An alternate minimizing strategy is developed to deal with the optimization problem, which is proved to have linear time complexity w.r.t. the sample number. Extensive experiments have been conducted to confirm the superiority of the proposed OMSC method. The source codes and data are available at https://github.com/ManshengChen/Code-for-OMSC-master.