# Non-Negative Matrix Factorization Implementation Using Graphic Processing Units

### Authors

### 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.

### Keywords

Non-Negative Matrix Factorization, GPU Computing### Subject

Non-Negative Matrix Factorization### Conference

11th International Conference on Intelligent Data Engineering and Automated Learning, LNCS 6283, Springer, pp. 275-283, September 2010### DOI

### Cited by

#### Year 2015 : 2 citations

Rossi, R. A., & Ahmed, N. K. (2015). Role discovery in networks. Knowledge and Data Engineering, IEEE Transactions on, 27(4), 1112-1131.

Mejía-Roa, E., Tabas-Madrid, D., Setoain, J., García, C., Tirado, F., & Pascual-Montano, A. (2015). NMF-mGPU: non-negative matrix factorization on multi-GPU systems. BMC bioinformatics, 16(1), 1.

#### Year 2014 : 2 citations

Rossi, Ryan A., and Nesreen K. Ahmed. "Role Discovery in Networks." arXiv preprint arXiv:1405.7134 (2014).

Zhang, Yin, et al. "A GPU-accelerated non-negative sparse latent semantic analysis algorithm for social tagging data." Information Sciences (2014).

#### Year 2013 : 1 citations

Ding, Chris. "Nonnegative Matrix Factorizations for Clustering: A Survey." Data Clustering: Algorithms and Applications (2013): 148.

#### Year 2011 : 3 citations

E. Mejía-Roa, C. García, J.I. Gómez, M. Prieto, F. Tirado, R. Nogales and A. Pascual-Montano, Biclustering and Classification Analysis in Gene Expression using Nonnegative Matrix Factorization on Multi-GPU Systems, 11th International Conference on Intelligent Systems Design and Applications, pp. 882-887, 2011

Edgardo Mejía-Roa, Carlos García, José Ignacio Gómez, Manuel Prieto, Christian Tenllado, Alberto D. Pascual-Montano and Francisco Tirado, Parallelism on the Nonnegative Matrix Factorization. In Applications, Tools and Techniques on the Road to Exascale Computing, pp. 421-428 , 2011

Tirado, F. "Parallelism on the Nonnegative Matrix Factorization". Advances in Parallel Computing 22:421-428 (2011)

#### Year 2010 : 1 citations

Pei-Yin Tsai, NMF on CUDA, 2010.