Approximation of Feature Vectors in Nonnegative Matrix Factorization with Gaussian Radial Basis Functions

Nonnegative Matrix Factorization (NMF) is a feature extraction technique that has already found numerous applications in machine learning and data processing. In some applications, the feature vectors or lateral components can be modeled as linear combinations of basis functions. In this paper, we are concerned with modeling the features with Gaussian Radial Basis Functions (GRBF) that have become very popular for high-dimensional data approximation or multivariate interpolation problems. To estimate the coefficients of a linear combination of GRBFs, one of the NMF subproblems is reformulated to the Quadratic Programming (QP) problem subject to inequality constraints, which is then solved with the active-set method. The experiments carried out for spectral datasets demonstrate that our approach outperforms some wellknown NMF algorithms in terms of Signal-to-Interference Ratio (SIR).