  Nonnegative matrix factorization (NMF) has been widely used to dimensionality
reduction in machine learning. However, the traditional NMF does not properly
handle outliers, so that it is sensitive to noise. In order to improve the
robustness of NMF, this paper proposes an adaptive weighted NMF, which
introduces weights to emphasize the different importance of each data point,
thus the algorithmic sensitivity to noisy data is decreased. It is very
different from the existing robust NMFs that use a slow growth similarity
measure. Specifically, two strategies are proposed to achieve this: fuzzier
weighted technique and entropy weighted regularized technique, and both of them
lead to an iterative solution with a simple form. Experimental results showed
that new methods have more robust feature representation on several real
datasets with noise than exsiting methods.
