Learning latent features by nonnegative matrix factorization combining similarity judgments

Nonnegative matrix factorization (NMF) is a popular method for learning low-rank approximation of nonnegative matrix. However, aiming at seeking the low-rank approximation from the viewpoint of data reconstruction, NMF may produce unfavorable performances in classification and clustering tasks. In this paper, we develop a novel modification of NMF (called NMFCSJ) by incorporating the similarity judgments of data points into NMF, and then performs a collective factorization on the data matrix and a weighted similarity matrix with a closely related factor matrix. With the superiority of additive clustering, the proposed method NMFCSJ exploits the latent features hidden in the original data. Experiments show that NMFCSJ improves the classification performance on two face databases and achieves better clustering accuracy for semi-supervised or unsupervised document clustering on 9 documents datasets from CLUTO toolkit.