Nonnegative Matrix Factorization with low-rank regularization for automatic feature extraction.
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In machine learning, Nonnegative Matrix Factorization (NMF) is a method of dimensionality reduction where the nonnegative constraints in NMF impose only additive combinations. One of the challenges in MFN is to determine the rank of the factorization; the correct choice of the rank would allow us to extract better features and thus promote a part-based representation of the data.
In this work, we propose to include a diagonal matrix D and minimize the rank of factorization through the penalization of the elements in the diagonal of D. We derive an iterative algorithm with closed formulas by alternately minimizing local cost functions.
We demonstrate the efficacy of our algorithm by performing experiments on synthetic data, images, texts, and gene expressions data sets. We show that our proposed algorithm not only estimates the factors with high precision but by minimizing the rank of factorization, our algorithm can learn interpretable features from the data.