A Method of Initialization for Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a widely-used method for multivariate nonnegative data analysis, due to its ability to learn a parts-based representation. However, the standard NMF algorithm does not always find spatially localized basis images in practice, unless sparseness constraints are employed. In this paper we present a method of structured initialization which enables the standard NMF algorithm to find spatially localized basis images. The initialization method is based on the hierarchical clustering of attributes through a similarity measure reflecting ´closeness to rank-one´. Numerical experiments with face image data, confirm the validity of our initialization method.