Progressive transduction nonnegative matrix factorization for dimensionality reduction

Abstract

Dimensionality reduction is one important technique to find out meaningful representations of data by discovering the underlying structures of data. As one widely applied method, by learning parts-based representations, nonnegative matrix factorization (NMF) has been widely researched and used to various application fields. Compared with the previous methods, this paper presents a novel semi-supervised NMF learning framework, called progressive transduction NMF (PTNMF), that learns a robustly discriminative representation by introducing a progressive transduction structure. Specifically, a progressive transduction based scheme is employed to gradually update the representations of unlabeled points according to the similarity between the labeled and unlabeled data points. This is helpful to improve the effectiveness of NMF, especially for the case that labeled data is inadequate. The efficiency of the proposed method is discussed both theoretically and empirically. Extensive experiments on several real-world data sets are listed, and the experimental results demonstrate that the proposed algorithm obtains better discriminant ability in comparison to the state-of-the-art methods.