Discriminant analysis using nonnegative matrix factorization for nonparametric multiclass classification

Linear discriminant analysis (LDA) has been applied to many pattern recognition problems. However, a lot of practical problems require nonnegativity constraints. For example, pixels in digital images, term frequencies in text mining, and chemical concentrations in bioinformatics should be nonnegative. In this paper, we propose discriminant analysis using nonnegative matrix factorization (DA/NMF), which is a multiclass classifier that generates nonnegative basis vectors. It does not require any parameter optimization and it is intrinsically appropriate for multiclass classifications. It also provides us with the reliability of classification. DA/NMF can be considered as a novel nonnegative dimension reduction algorithm for supervised machine learning problems since it generates nonnegative low-rank representations as well as nonnegative basis vectors. In addition, it can be thought of as nonnegative LDA or the supervised version of NMF.