On the initialization of the DNMF algorithm

TLDR: A way to significantly improve the speed of the algorithm convergence by constructing initial basis images that meet the sparseness and orthogonality requirements and approximate the final minimization solution is provided.

Abstract: A subspace supervised learning algorithm named discriminant non-negative matrix factorization (DNMF) has been recently proposed for classifying human facial expressions. It decomposes images into a set of basis images and corresponding coefficients. Usually, the algorithm starts with random basis image and coefficient initialization. Then, at each iteration, both basis images and coefficients are updated to minimize the underlying cost function. The algorithm may need several thousands of iterations to obtain cost function minimization. We provide a way to significantly improve the speed of the algorithm convergence by constructing initial basis images that meet the sparseness and orthogonality requirements and approximate the final minimization solution. To experimentally evaluate the new approach, we have applied DNMF using the random and the proposed initialization procedure to recognize six basic facial expressions. While fewer iteration steps are needed with the proposed initialization, the recognition accuracy remains within satisfactory levels.