Semi-supervised multi-view clustering by label relaxation based non-negative matrix factorization

Semi-supervised multi-view clustering in the subspace has attracted sustained attention. The existing methods often project the samples with the same label into the same point in the low dimensional space. This hard constraint-based method magnifies the dimension reduction error, restricting the subsequent clustering performance. To relax the labeled data during projection, we propose a novel method called label relaxation-based semi-supervised non-negative matrix factorization (LRSNMF). In our method, we first employ the Spearman correlation coefficient to measure the similarity between samples. Based on this, we design a new relaxed non-negative label matrix for better subspace learning, instead of the binary matrix. Also, we derive an updated algorithm based on an alternative iteration rule to solve the proposed model. Finally, the experimental results on three real-world datasets (i.e., MSRC, ORL1, and ORL2) with six evaluation indexes (i.e., accuracy, NMI, purity, F-score, precision, and recall) show the advantages of our LRSNMF, with comparison to the state-of-the-art methods.