Feature Weighted Non-Negative Matrix Factorization.

Non-negative matrix factorization (NMF) is one of the most popular techniques for data representation and clustering and has been widely used in machine learning and data analysis. NMF concentrates the features of each sample into a vector and approximates it by the linear combination of basis vectors, such that the low-dimensional representations are achieved. However, in real-world applications, the features usually have different importance. To exploit the discriminative features, some methods project the samples into the subspace with a transformation matrix, which disturbs the original feature attributes and neglects the diversity of samples. To alleviate the above problems, we propose the feature weighted NMF (FNMF) in this article. The salient properties of FNMF can be summarized as three-fold: 1) it learns the weights of features adaptively according to their importance; 2) it utilizes multiple feature weighting components to preserve the diversity; and 3) it can be solved efficiently with the suggested optimization algorithm. The performance on synthetic and real-world datasets demonstrates that the proposed method obtains the state-of-the-art performance.