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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.
Numerical Analysis, Algorithm design and analysis, Mathematical Software, Mathematics of Computing, Feature extraction or construction, Remote sensing, Applications, Pattern Recognition, Computing Methodologies, Database Applications, Database Management, Information Technology and Systems, Computations on matrices, Numerical Algorithms and Problems, Analysis of Algorithms and Problem Complexity, Numerical algorithms, General, Numerical Analysis, Numerical Linear Algebra

N. A. Gillis and S. Vavasis, "Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization," in IEEE Transactions on Pattern Analysis & Machine Intelligence.
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