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A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization [article]

Ramakrishnan Kannan and Grey Ballard and Haesun Park
2015 arXiv   pre-print
To our knowledge, our algorithm is the first high-performance parallel algorithm for NMF.  ...  Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A ≈ W H.  ...  The main contribution of this work is a new, high-performance parallel algorithm for non-negative matrix factorization.  ... 
arXiv:1509.09313v1 fatcat:uhxr5bd73berxotxgrhdrdpofm

A high-performance parallel algorithm for nonnegative matrix factorization

Ramakrishnan Kannan, Grey Ballard, Haesun Park
2016 Proceedings of the 21st ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming - PPoPP '16  
We propose a high-performance distributed-memory parallel algorithm that computes the factorization by iteratively solving alternating non-negative least squares (NLS) subproblems for W and H.  ...  Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A ≈ WH.  ...  We also thank NSF for the travel grant to present this work in the conference through the grant CCF-1552229.  ... 
doi:10.1145/2851141.2851152 dblp:conf/ppopp/KannanBP16 fatcat:udekzdd7ffgqhajv3apnbbxfmi

Collaborative Filtering Recommendation Using Nonnegative Matrix Factorization in GPU-Accelerated Spark Platform

Bing Tang, Linyao Kang, Li Zhang, Feiyan Guo, Haiwu He, Shah Nazir
2021 Scientific Programming  
However, as the size of the matrix increases, the processing speed of nonnegative matrix factorization is very slow.  ...  To solve this problem, this paper proposes a parallel algorithm based on GPU for NMF in Spark platform, which makes full use of the advantages of in-memory computation mode and GPU acceleration.  ...  Parallel Nonnegative Matrix Factorization Nonnegative Matrix Factorization.  ... 
doi:10.1155/2021/8841133 fatcat:6tf7qm7zwzce3ebcas7r6dvum4

Semi-nonnegative Matrix Factorization Algorithm Based on Genetic Algorithm Initialization

M. Chouh, K. Boukhetala
2016 International Journal of Machine Learning and Computing  
In the present paper, we proposed a semi-nonnegative matrix factorization algorithm based on genetic algorithm (GA) initialization which has larger searching area and gives the best initialization for  ...  Index Terms-Semi-nonnegative matrix factorization, genetic algorithm, initialization.  ...  algorithm appear) as new initialization variant for nonnegative matrix factorization is presented, and in [12] , we can find an improved nonnegative matrix factorization algorithm based on genetic algorithm  ... 
doi:10.18178/ijmlc.2016.6.4.603 fatcat:6gunrtsgqbb6jcitspichsms7i

Dictionary Learning Based on Nonnegative Matrix Factorization Using Parallel Coordinate Descent

Zunyi Tang, Shuxue Ding, Zhenni Li, Linlin Jiang
2013 Abstract and Applied Analysis  
This is accomplished by posing the sparse representation of nonnegative signals as a problem of nonnegative matrix factorization (NMF) with a sparsity constraint.  ...  Numerical experiments demonstrate that the proposed algorithm performs better than the conventional nonnegative K-SVD (NN-KSVD) algorithm and several other algorithms for comparison.  ...  In recent years, nonnegative matrix factorization (NMF) [2, 16] has been widely applied to data analyses having nonnegativity constraints since NMF can factorize a nonnegative matrix into a product of  ... 
doi:10.1155/2013/259863 fatcat:v2dvawu46vewxasunhlqfppvpm

Parallel Nonnegative Matrix Factorization with Manifold Regularization

Fudong Liu, Zheng Shan, Yihang Chen
2018 Journal of Electrical and Computer Engineering  
Nonnegative matrix factorization (NMF) decomposes a high-dimensional nonnegative matrix into the product of two reduced dimensional nonnegative matrices.  ...  For constructing the adjacency matrix in manifold regularization, we propose a two-step distributed graph construction method, which is proved to be equivalent to the batch construction method.  ...  Conclusion In this paper, we proposed a parallel nonnegative matrix factorization with regularization method (PNMF-M) which introduced manifold regularization into conventional NMF and parallelized it  ... 
doi:10.1155/2018/6270816 fatcat:thc46qcap5gljfrzpjq37kxx5u

A Parallel Nonnegative Tensor Factorization Algorithm for Mining Global Climate Data [chapter]

Qiang Zhang, Michael W. Berry, Brian T. Lamb, Tabitha Samuel
2009 Lecture Notes in Computer Science  
This prompts a trend of parallelizing the existing algorithms and methods by mathematicians and computer scientists.  ...  Numerical experiments were performed on a NASA global sea surface temperature dataset and result factors were analyzed and discussed.  ...  Parallel Nonnegative Tensor Factorization In nonnegative tensor factorization (NTF), high-dimensional data, such as global sea surface temperature, is factored directly and is approximated by a sum of  ... 
doi:10.1007/978-3-642-01973-9_45 fatcat:vnftufnpxjed5fimqxcb2zfyqm

Parallel Nonnegative CP Decomposition of Dense Tensors [article]

Grey Ballard and Koby Hayashi and Ramakrishnan Kannan
2018 arXiv   pre-print
We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensor data that can enforce nonnegativity of the computed  ...  low-rank factors.  ...  Likewise, the parallelization approach for tensor methods is not a straightforward application of parallel matrix computation algorithms.  ... 
arXiv:1806.07985v1 fatcat:qx6g7qsrxvfsll2hu464cdvqsi

Accelerated Stochastic Gradient for Nonnegative Tensor Completion and Parallel Implementation [article]

Ioanna Siaminou, Ioannis Marios Papagiannakos, Christos Kolomvakis, Athanasios P. Liavas
2021 arXiv   pre-print
We adopt the alternating optimization framework and solve each nonnegative matrix completion problem via a stochastic variation of the accelerated gradient algorithm.  ...  We believe that our approach is a very competitive candidate for the solution of very large nonnegative tensor completion problems.  ...  Parallel Implementation of AO accelerated stochastic NMC In Algorithm 3, we provide a high level algorithmic sketch of the accelerated stochastic gradient for NMC.  ... 
arXiv:2109.09534v1 fatcat:noeeuc4vwzes7g23oraq3xcqhi

bioNMF: a web-based tool for nonnegative matrix factorization in biology

E. Mejia-Roa, P. Carmona-Saez, R. Nogales, C. Vicente, M. Vazquez, X. Y. Yang, C. Garcia, F. Tirado, A. Pascual-Montano
2008 Nucleic Acids Research  
Nonnegative matrix factorization (NMF) has been established as a very effective method to reveal information about the complex latent relationships in experimental data sets.  ...  This online tool provides a user-friendly interface, combined with a computational efficient parallel implementation of the NMF methods to explore the data in different analysis scenarios.  ...  Formally, the nonnegative matrix decomposition can be described as V % WH, where V 2 R m  n is a positive data matrix with m variables and n objects, W 2 R m  k are the reduced k basis vectors or factors  ... 
doi:10.1093/nar/gkn335 pmid:18515346 pmcid:PMC2447803 fatcat:rg5zeastkvaxto3qbqws24iefy

Parallel and distributed algorithms

Guillaume Aupy, Xueyan Tang
2018 Concurrency and Computation  
We introduce the papers submitted to the special issue of Computation, Concurrency: Practice and Experience on parallel and distributed algorithms.  ...  Fox, for his kind support and guidance. We hope that you will enjoy reading this special issue.  ...  ACKNOWLEDGEMENTS We would like to express sincere appreciation to all the authors and the reviewers for their contributions to this special issue.  ... 
doi:10.1002/cpe.4663 fatcat:bvcbtlidejc7nlmwia3m4broq4

Matrix factorizations at scale: A comparison of scientific data analytics in spark and C+MPI using three case studies

Alex Gittens, Aditya Devarakonda, Evan Racah, Michael Ringenburg, Lisa Gerhardt, Jey Kottalam, Jialin Liu, Kristyn Maschhoff, Shane Canon, Jatin Chhugani, Pramod Sharma, Jiyan Yang (+5 others)
2016 2016 IEEE International Conference on Big Data (Big Data)  
We examine three widely-used and important matrix factorizations: NMF (for physical plausability), PCA (for its ubiquity) and CX (for data interpretability).  ...  We perform scaling experiments on up to 1600 Cray XC40 nodes, describe the sources of slowdowns, and provide tuning guidance to obtain high performance.  ...  Nonnegative Matrix Factorization: Nonnegative matrix factorizations (NMFs) provide interpretable low-rank matrix decompositions when the columns of A are nonnegative and can be viewed as additive superpositions  ... 
doi:10.1109/bigdata.2016.7840606 dblp:conf/bigdataconf/GittensDRRGKLMC16 fatcat:g3k3fstgobhtrgkmfm6nmd7s6y

Accelerated parallel and distributed algorithm using limited internal memory for nonnegative matrix factorization

Duy Khuong Nguyen, Tu Bao Ho
2016 Journal of Global Optimization  
This research designs a fast fully parallel and distributed algorithm using limited internal memory to reach high NMF performance for large datasets.  ...  Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation.  ...  Therefore, in this chapter, we propose an accelerated parallel and distributed algorithm to learn NMF models W for large datasets. 2.2 Related work of nonnegative matrix factorization NMF algorithms can  ... 
doi:10.1007/s10898-016-0471-z fatcat:x6nyvaic5fhaxk5r7mf6hxvm6m

Improving Neutron-Gamma Discrimination with Stilbene Organic Scintillation Detector Using Blind Nonnegative Matrix and Tensor Factorization Methods

Hanane Arahmane, El-Mehdi Hamzaoui, Rajaa Cherkaoui El Moursli
2019 Journal of Spectroscopy  
In order to perform highly qualified neutron-gamma discrimination in mixed radiation field, we investigate the application of blind source separation methods based on nonnegative matrix and tensor factorization  ...  The computation of the performance index of separability of each tested nonnegative algorithm has allowed to select Second-Order NMF algorithm and NTF-2 model as the most efficient techniques for discriminating  ...  Amiri for his interest, support, and valuable contribution to this work, as well as Pr. Y. Ben Maissa for his reviews and valuable suggestions.  ... 
doi:10.1155/2019/8360395 fatcat:dejebkk4f5duxjhgl4kb6vggna

Randomized nonnegative matrix factorization

N. Benjamin Erichson, Ariana Mendible, Sophie Wihlborn, J. Nathan Kutz
2018 Pattern Recognition Letters  
Nonnegative matrix factorization (NMF) is a powerful tool for data mining.  ...  By deriving a smaller matrix from the nonnegative input data, a more efficient nonnegative decomposition can be computed.  ...  Acknowledgments We would like to express our gratitude to the two anonymous reviewers for their helpful feedback which allowed us improve the manuscript.  ... 
doi:10.1016/j.patrec.2018.01.007 fatcat:f7vwfex45fa7xlmddrqgytbuhe
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