Feature Weighted Non-negative Matrix Factorization
This is an incremental improvement for data representation and clustering in machine learning, addressing feature importance and diversity in NMF applications.
The paper tackles the problem of Non-negative Matrix Factorization (NMF) not accounting for varying feature importances in real-world data, proposing Feature weighted NMF (FNMF) that adaptively learns feature weights and achieves state-of-the-art performance on synthetic and real-world datasets.
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 are usually with different importances. 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 Non-negative Matrix Factorization (FNMF) in this paper. The salient properties of FNMF can be summarized as threefold: 1) it learns the weights of features adaptively according to their importances; 2) it utilizes multiple feature weighting components to preserve the diversity; 3) it can be solved efficiently with the suggested optimization algorithm. Performance on synthetic and real-world datasets demonstrate that the proposed method obtains the state-of-the-art performance.