Clean affinity matrix learning with rank equality constraint for multi-view subspace clustering

The existing multi-view subspace clustering (MVSC) algorithm still has certain limitations. First, the affin-ity matrix obtained by them is not clean and robust enough since the original multi-view data usually contain noise. Second, they also have defects in exploring the consistency between views. To compensate for these two shortcomings, we propose a novel MVSC, i.e., clean affinity matrix learning with rank equal-ity constraint (CAMR) for MVSC. By borrowing the idea from robust principal component analysis (RPCA), the representation matrix of each view obtained by low-rank representation (LRR) is first cleaned up to obtain a cleaner and more robust affinity matrix. In addition, the rank constraint is utilized to explore the same clustering properties between different views. An objective function solution method based on an augmented Lagrange multiplier (ALM) is designed and tested on four widely employed datasets to verify that CAMR has better clustering performance than certain state-of-the-art methods. We provide the code of CAMR at https://github.com/zhaojinbiao/CAMR.(c) 2022 Elsevier Ltd. All rights reserved.