B-Spline Smoothing of Feature Vectors in Nonnegative Matrix Factorization

Rafal Zdunek, Andrzej Cichocki, Tatsuya Yokota

Abstract: Nonnegative Matrix Factorization (NMF) captures nonnegative, sparse and parts-based feature vectors from the set of observed nonnegative vectors. In many applications, the features are also expected to be locally smooth. To incorporate the information on the local smoothness to the optimization process, we assume that the features vectors are conical combinations of higher degree B-splines with a given number of knots. Due to this approach the computational complexity of the optimization process does not increase considerably with respect to the standard NMF model. The numerical experiments, which were carried out for the blind spectral unmixing problem, demonstrate the robustness of the proposed method.