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Probabilistic PARAFAC2.

Philip J H Jørgensen1, Søren F Nielsen1, Jesper L Hinrich1

  • 1Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kongens Lyngby, Denmark.

Entropy (Basel, Switzerland)
|August 29, 2024
PubMed
Summary
This summary is machine-generated.

We developed two probabilistic formulations for Parallel Factor Analysis 2 (PARAFAC2) to enhance robustness in multimodal data analysis. These methods improve noise handling and factor determination for complex datasets.

Keywords:
PARAFAC2multi-way modelingorthogonality constrainttensor decompositionvariational inference

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Area of Science:

  • Multivariate data analysis
  • Chemometrics
  • Signal processing

Background:

  • Parallel Factor Analysis 2 (PARAFAC2) is a multimodal factor analysis model designed for multi-way data with incomparable observation units.
  • Challenges exist in probabilistic treatment of PARAFAC2 due to complex factor loading decompositions required for model fitting.

Purpose of the Study:

  • To develop fully probabilistic formulations of the PARAFAC2 model.
  • To enhance robustness to noise and provide principled factor number determination.
  • To compare probabilistic approaches against conventional direct fitting methods.

Main Methods:

  • Developed two probabilistic formulations of PARAFAC2.
  • Employed variational Bayesian inference procedures.
  • First formulation: orthogonal mean factor loadings for closed-form updates.
  • Second formulation: orthogonal factor loadings using matrix Von Mises-Fisher distribution.

Main Results:

  • Probabilistic PARAFAC2 formulations demonstrated increased robustness to noise compared to direct fitting.
  • The new methods showed better performance with model order misspecification.
  • Effectiveness validated on synthetic, fluorescence spectroscopy, and GC-MS data.

Conclusions:

  • Probabilistic PARAFAC2 offers a robust framework for multi-way data analysis.
  • The developed methods effectively account for uncertainty in complex datasets.
  • This approach holds promise for advanced chemometric and signal processing applications.