Incorporating Neighborhood Information During NMF Learning

Michel Kaddouh, Guénaël Cabanes, Younès Bennani

Abstract: Self-Organizing Map is an algorithm that computes a set of artificial neurons to model the distribution of a data-set. This model is composed of a graph of neurons connected by neighborhood links. The main advantage of a SOM model is the conservation of a low-dimensional topology, which allows a visual representation of the data distribution. It is a non-linear projection that preserves the neighborhood, while reducing both the dimensions and the size of the data. In this paper, we propose a modified version of the convex Non-negative Matrix Factorization to compute a similar projection. Experimental results show that the proposed algorithm significantly decreases the topological error in comparison to SOM, without loss of computational speed.