  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.
