Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization
This work addresses hyperspectral unmixing and related problems, providing theoretical justification for improved practical performance, though it appears incremental as it generalizes prior algorithms.
The paper tackles the nonnegative matrix factorization problem under the separability assumption, presenting a family of fast recursive algorithms that are proven robust to small data perturbations, generalizing existing hyperspectral unmixing methods.
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.