K-Nearest Neighbor Nonnegative Matrix Factorization for Learning a Mixture of Local SOM Models

Abstract

In this work we present a modified Nonnegative Matrix Factorization (NMF) method for learning a mixture of local SOM models. The proposed method approximates a data point with a linear combination of its k-nearest neighbor prototypes. This allows obtaining a low quantization error and at the same time keeping the interpretability of the prototypes. The results of the new method are compared with those obtained using non-negative least squares, NMF and SOM, using four benchmark data sets. Two metrics are used to assess the performance of the different approaches. The proposed k-nn NMF method obtained the lowest relative local quantization error, while keeping a global quantization error similar to the best alternative methods. © Springer International Publishing Switzerland 2014.