A weighted non-negative matrix factorization for local representations

The paper presents an improvement of the classical Non-negative Matrix Factorization (NMF) approach for dealing with local representations of image objects. NHF, when applied to global data representations such as faces presents a high ability to represent local features of the original data in an unsupervised way. However, when applied to local representations, NMF generates redundant basis. This work implements an improvement on the original NMF approach by incorporating prior knowledge in the form of a weight matrix extracted from the training data. A detailed mathematical description of the inclusion of this weight matrix is provided, and results demonstrating its advantages are included. Furthermore, the original NMF approach lacks a hierarchy of the elements of the estimated basis. A technique to determine an ordered set of discriminant basis is also presented. Finally, the effectiveness of the weighted approach with respect to the classical approach is experimentally compared. This is done by implementing a clustering algorithm that automatically extracts object parts from the NMF representation of an image database corresponding to newspapers.