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Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases and other information retrieval and clustering applications. In this report, we define an exact version of NMF. Then we establish several results about exact NMF: (1) that it is equivalent to a problem in polyhedral combinatorics; (2) that it is NP-hard; and (3) that a polynomial-time local search heuristic exists.
In this paper, we present several descent methods that can be applied to nonnegative matrix factorization and we analyze a recently developped fast block coordinate method called Rank-one Residue Iteration (RRI). We also give a comparison of these di
Fully unsupervised topic models have found fantastic success in document clustering and classification. However, these models often suffer from the tendency to learn less-than-meaningful or even redundant topics when the data is biased towards a set
For most of the state-of-the-art speech enhancement techniques, a spectrogram is usually preferred than the respective time-domain raw data since it reveals more compact presentation together with conspicuous temporal information over a long time spa
In the Nonnegative Matrix Factorization (NMF) problem we are given an $n times m$ nonnegative matrix $M$ and an integer $r > 0$. Our goal is to express $M$ as $A W$ where $A$ and $W$ are nonnegative matrices of size $n times r$ and $r times m$ respec
We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $mathbf{P}^Tmathbf{A}mathbf{P} = mathbf{L}mathbf{D}mathbf{L}^T