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Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization

Nicolas Gillis (ngillis***at***uwaterloo.ca)
Stephen A. Vavasis (vavasis***at***math.uwaterloo.ca)

Abstract: In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns), which is equivalent to the hyperspectral unmixing problem under the linear mixing model and the pure-pixel assumption. We present a family of fast recursive algorithms, and prove they are robust under any small perturbations of the input data matrix. This family generalizes several existing hyperspectral unmixing algorithms and hence provides for the first time a theoretical justification of their better practical performance.

Keywords: nonnegative matrix factorization, algorithms, separability, robustness, hyperspectral unmixing, linear mixing model, pure-pixel assumption.

Category 1: Applications -- Science and Engineering (Data-Mining )


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Entry Submitted: 08/06/2012
Entry Accepted: 08/06/2012
Entry Last Modified: 08/10/2012

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