An Optimal Method for the Initialization of Non-negative Matrix Factorization (NMF) ⋆

An optimization method of the NMF algorithm initialization is proposed. This optimization method can be easily integrated with the existing initialization methods of NMF algorithm. The strategy is based on the geometric interpretation of NMF, in the convex hull, the intersection point between the connect of two points and the corresponding boundary of probability simplex, is used to update the initial basis vectors corresponding point in the matrix, so that the base vector matrix extended, and it can better contain the original matrix. Many numerical examples show that, compared with the original initialization, this method can obtain better results.