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Friday, July 20, 2012 |
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Fast and Robust Algorithms for Separable Nonnegative Matrix Factorization |
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Nonnegative Matrix Factorization (NMF) is a linear dimensionality
reduction technique for nonnegative data. It consists in approximating a
nonnegative data matrix with the product of two low-rank nonnegative
matrices. NMF has become a very popular technique in data mining and machine
learning because it automatically extracts meaningful features through a
sparse and part-based representation. Although NMF is NP-hard in general, it
has been shown very recently that it is possible to compute an optimal
solution under the assumption that the input nonnegative data matrix is
separable (i.e., there exists a cone spanned by a small subset of the
columns containing all columns). Current approaches solving the separable
NMF problem are either computationally expensive or not robust to noise. In
this talk, we first introduce NMF and illustrate its usefulness with some
application examples (namely, image processing, text mining and
hyperspectral data analysis). Then, we present a new family of fast and
robust recursive algorithms for separable NMF problems.
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