Semi-Supervised Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a popular method for low-rank approximation of nonnegative matrix, providing a useful tool for representation learning that is valuable for clustering and classification. When a portion of data are labeled, the performance of clustering or classification is improved if the information on class labels is incorporated into NMF. To this end, we present semi-supervised NMF (SSNMF), where we jointly incorporate the data matrix and the (partial) class label matrix into NMF. We develop multiplicative updates for SSNMF to minimize a sum of weighted residuals, each of which involves the nonnegative 2-factor decomposition of the data matrix or the label matrix, sharing a common factor matrix. Experiments on document datasets and EEG datasets in BCI competition confirm that our method improves clustering as well as classification performance, compared to the standard NMF, stressing that semi-supervised NMF yields semi-supervised feature extraction.