Image Classification with Nonnegative Matrix Factorization Based on Spectral Projected Gradient

Nonnegative Matrix Factorization (NMF) is a key tool for model dimensionality reduction in supervised classification. Several NMF algorithms have been developed for this purpose. In a majority of them, the training process is improved by using discriminant or nearest-neighbor graph-based constraints that are obtained from the knowledge on class labels of training samples. The constraints are usually incorporated to NMF algorithms by l(2)-weighted penalty terms that involve formulating a large-size weighting matrix. Using the Newton method for updating the latent factors, the optimization problems in NMF become large-scale. However, the computational problem can be considerably alleviated if the modified Spectral Projected Gradient (SPG) that belongs to a class of quasi-Newton methods is used. The simulation results presented for the selected classification problems demonstrate the high efficiency of the proposed method.