Multifrontal Non-negative Matrix Factorization

Sao, Piyush; Kannan, Ramakrishnan {ramki}

doi:10.1007/978-3-030-43229-4_46

Title: Multifrontal Non-negative Matrix Factorization

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Abstract

Non-negative matrix factorization (Nmf) is an important tool in high-performance large scale data analytics with applications ranging from community detection, recommender system, feature detection and linear and non-linear unmixing. While traditional Nmf works well when the data set is relatively dense, however, it may not extract sufficient structure when the data is extremely sparse. Specifically, traditional Nmf fails to exploit the structured sparsity of the large and sparse data sets resulting in dense factors. We propose a new algorithm for performing Nmf on sparse data that we call multifrontal Nmf (Mf-Nmf) since it borrows several ideas from the multifrontal method for unconstrained factorization (e.g. LU and QR). We also present an efficient shared memory parallel implementation of Mf-Nmf and discuss its performance and scalability. We conduct several experiments on synthetic and realworld datasets and demonstrate the usefulness of the algorithm by comparing it against standard baselines. We obtain a speedup of 1.2x to 19.5x on 24 cores with an average speed up of 10.3x across all the real world datasets.

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^[1];

^[1]

ORNL

Publication Date:: 2020-03-01

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1649537

DOE Contract Number:: AC05-00OR22725

Resource Type:: Conference

Resource Relation:: Journal Volume: 12043; Conference: 13th International Conference on Parallel Processing and Applied Mathematics (PPAM) - BIALYSTOK, , Poland - 9/8/2019 12:00:00 PM-9/11/2019 4:00:00 AM

Country of Publication:: United States

Language:: English

Citation Formats


                    Sao, Piyush, and Kannan, Ramakrishnan. Multifrontal Non-negative Matrix Factorization.  United States: N. p., 2020. 
        Web.  doi:10.1007/978-3-030-43229-4_46.

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                    Sao, Piyush, & Kannan, Ramakrishnan. Multifrontal Non-negative Matrix Factorization.  United States.  https://doi.org/10.1007/978-3-030-43229-4_46

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                    Sao, Piyush, and Kannan, Ramakrishnan. 2020.  
        "Multifrontal Non-negative Matrix Factorization".  United States.  https://doi.org/10.1007/978-3-030-43229-4_46.  https://www.osti.gov/servlets/purl/1649537.

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@article{osti_1649537,

  title        = {Multifrontal Non-negative Matrix Factorization},

  author       = {Sao, Piyush and Kannan, Ramakrishnan},

  abstractNote = {Non-negative matrix factorization (Nmf) is an important tool in high-performance large scale data analytics with applications ranging from community detection, recommender system, feature detection and linear and non-linear unmixing. While traditional Nmf works well when the data set is relatively dense, however, it may not extract sufficient structure when the data is extremely sparse. Specifically, traditional Nmf fails to exploit the structured sparsity of the large and sparse data sets resulting in dense factors. We propose a new algorithm for performing Nmf on sparse data that we call multifrontal Nmf (Mf-Nmf) since it borrows several ideas from the multifrontal method for unconstrained factorization (e.g. LU and QR). We also present an efficient shared memory parallel implementation of Mf-Nmf and discuss its performance and scalability. We conduct several experiments on synthetic and realworld datasets and demonstrate the usefulness of the algorithm by comparing it against standard baselines. We obtain a speedup of 1.2x to 19.5x on 24 cores with an average speed up of 10.3x across all the real world datasets.},

  doi          = {10.1007/978-3-030-43229-4_46},

  url          = {https://www.osti.gov/biblio/1649537},
  journal      = {},

  issn         = {0302-9743},

  number       = ,

  volume       = 12043,

  place        = {United States},

  year         = {2020},

  month        = {3}

}

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