Semi-supervised Nonnegative Matrix Factorization with Commonness Extraction

摘要

Standard nonnegative matrix factorization extracts nonnegative bases for nonnegative representation, which, however, considers only features, not commonness. In addition, the standard NMF is an unsupervised learning method that cannot fully utilize label information if it exists. In this paper, we present a semi-supervised commonness NMF technique that incorporates samples’ commonness and label information into the optimization model. Naturally, the commonness vector should be constrained by nonnegativity and will degenerate to zero if no commonness exists. We develop a multiplicative update rule to solve the model, which has properties comparable to those of the standard NMF with automatic satisfaction of the nonnegativity constraints, monotonicity without the need for any adjustable learning rate and a low computational overhead. Through experiments on the standard databases, we analyze the behavior of the proposed method, which exhibits a performance that is favorably superior with respect to commonness extraction and clustering accuracy.