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Nonnegative decomposition of functional count data.

Daniel Backenroth1, Russell T Shinohara2, Jennifer A Schrack3

  • 1Department of Biostatistics, Mailman School of Public Health, Columbia University, New York City, New York.

Biometrics
|January 24, 2020
PubMed
Summary
This summary is machine-generated.

We developed a new method, nonnegative and regularized function decomposition (NARFD), to analyze functional count data. NARFD offers a more interpretable way to study variations in data across subjects.

Keywords:
accelerometersfunctional datanonnegative matrix factorization

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Area of Science:

  • Statistics
  • Data Analysis
  • Functional Data Analysis

Background:

  • Analyzing nonnegative functional count data presents challenges in interpretability.
  • Existing methods like generalized functional principal component analysis can be complex.

Purpose of the Study:

  • To introduce a novel decomposition method, NARFD, for nonnegative functional count data.
  • To enable a more interpretable study of patterns in variation across subjects.

Main Methods:

  • Developed NARFD based on nonnegative matrix factorization concepts.
  • Implemented NARFD using an alternating minimization algorithm.
  • Estimated prototypic modes of variation directly on the observed data scale.

Main Results:

  • NARFD provides local and interpretable modes of variation.
  • Reconstruction of observed functions is achieved through transparent addition of modes.
  • NARFD contrasts with generalized functional principal component analysis in scale and reconstruction complexity.

Conclusions:

  • NARFD offers a more interpretable approach to analyzing functional count data.
  • The method was evaluated through simulations and applied to physical activity data.