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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
Summary
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.
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.
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