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Multifrontal Non-negative Matrix Factorization

  • Piyush SaoEmail author
  • Ramakrishnan Kannan
Conference paper
  • 137 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12043)

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.

Keywords

Sparse matrix computations Non-negative matrix factorization Data analysis Multifrontal methods 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Oak Ridge National LaboratoryOak RidgeUSA

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