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Accelerating Nonnegative Matrix Factorization Algorithms Using Extrapolation.

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We introduce a novel framework to accelerate nonnegative matrix factorization (NMF) algorithms. This approach enhances speed for NMF, a key technique in data analysis, using extrapolation methods.

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Area of Science:

  • Machine Learning
  • Optimization Algorithms
  • Data Science

Background:

  • Nonnegative matrix factorization (NMF) is a widely used dimensionality reduction technique.
  • Existing NMF algorithms can be computationally intensive, limiting their application on large datasets.
  • Accelerating NMF algorithms is crucial for efficient data analysis.

Purpose of the Study:

  • To propose a general framework for significantly accelerating NMF algorithms.
  • To introduce a novel application of extrapolation schemes in nonconvex NMF.
  • To demonstrate the effectiveness of the proposed framework on existing NMF methods.

Main Methods:

  • A general framework inspired by extrapolation schemes from convex optimization and the method of parallel tangents.
  • Application of extrapolation to exact coordinate descent algorithms for nonconvex NMF problems.
  • Integration with state-of-the-art NMF algorithms like hierarchical alternating least squares (HALS) and alternating nonnegative least squares (ANLS).

Main Results:

  • Significant acceleration of NMF algorithms.
  • Demonstrated performance improvements on synthetic, image, and document datasets.
  • Novel application of extrapolation techniques to nonconvex NMF.

Conclusions:

  • The proposed framework offers a general and effective approach to accelerate NMF algorithms.
  • Extrapolation methods can be successfully applied to nonconvex NMF problems.
  • The accelerated NMF algorithms show improved performance across various data types.