• Corpus ID: 120622630

Nonnegative matrix factorization : complexity, algorithms and applications

@inproceedings{Gillis2011NonnegativeMF,
  title={Nonnegative matrix factorization : complexity, algorithms and applications},
  author={Nicolas Gillis},
  year={2011}
}
Linear dimensionality reduction techniques such as principal component analysis are powerful tools for the analysis of high-dimensional data. In this thesis, we explore a closely related problem, namely nonnegative matrix factorization (NMF), a low-rank matrix approximation problem with nonnegativity constraints. More precisely, we seek to approximate a given nonnegative matrix with the product of two low-rank nonnegative matrices. These nonnegative factors can be interpreted in the same way as… 
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References

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TLDR
This paper shows that when the matrix to be factored is not required to be nonnegative, the corresponding problem (R1NF) becomes NP-hard and designs a new type of biclique finding algorithm based on the application of a block-coordinate descent scheme to R1NF.
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TLDR
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TLDR
An algorithm called rank-one downdate (R1D) is proposed for computing an NMF that is partly motivated by the singular value decomposition, and establishes a theoretical result that maximizing this objective function corresponds to correctly classifying articles in a nearly separable corpus.
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TLDR
A class of optimized local algorithms which are referred to as Hierarchical Alternating Least Squares (HALS) algorithms, which work well for NMF-based blind source separation (BSS) not only for the over-determined case but also for an under-d determined (over-complete) case if data are sufficiently sparse.
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TLDR
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