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Fast and Robust Recursive Algorithmsfor Separable Nonnegative Matrix Factorization
April 2014 (vol. 36 no. 4)
pp. 698-714
Nicolas Gillis, Dept. of Math. & Operational Res., Univ. de Mons, Mons, Belgium
Stephen A. Vavasis, Dept. of Combinatorics & Optimization, Univ. of Waterloo, Waterloo, ON, Canada
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.
Index Terms:
Algorithm design and analysis,Hyperspectral imaging,Noise,Robustness,Equations,Indexes,Materials,pure-pixel assumption,Nonnegative matrix factorization,algorithms,separability,robustness,hyperspectral unmixing,linear mixing model
Nicolas Gillis, Stephen A. Vavasis, "Fast and Robust Recursive Algorithmsfor Separable Nonnegative Matrix Factorization," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 36, no. 4, pp. 698-714, April 2014, doi:10.1109/TPAMI.2013.226
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