Non-negative matrix factorization implementation using graphic processing units

Abstract

Non-Negative Matrix Factorization (NMF) algorithms decompose a matrix, containing only non-negative coefficients, into the product of two matrices, usually with reduced ranks. The resulting matrices are constrained to have only non-negative coefficients. NMF can be used to reduce the number of characteristics in a dataset, while preserving the relevant information that allows for the reconstruction of the original data. Since negative coefficients are not allowed, the original data is reconstructed through additive combinations of the parts-based factorized matrix representation. A Graphics Processing Unit (GPU) implementation of the NMF algorithms, using both the multiplicative and the additive (gradient descent) update rules is presented for the Euclidean distance as well as for the divergence cost function. The performance results on an image database demonstrate extremely high speedups, making the GPU implementations excel by far the CPU implementations. © 2010 Springer-Verlag Berlin Heidelberg.