Nonnegative decomposition of functional count data

We present a novel decomposition of nonnegative functional count data that draws on concepts from nonnegative matrix factorization. Our decomposition, which we refer to as NARFD (nonnegative and regularized function decomposition), enables the study of patterns in variation across subjects in a high...

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Bibliographic Details
Published in:Biometrics Vol. 76; no. 4; pp. 1273 - 1284
Main Authors: Backenroth, Daniel, Shinohara, Russell T., Schrack, Jennifer A., Goldsmith, Jeff
Format: Journal Article
Language:English
Published: United States Blackwell Publishing Ltd 01.12.2020
Subjects:
Accelerometers
Algorithms
data collection
Decomposition
functional data
Functionals
Multiplication
nonnegative matrix factorization
Physical activity
principal component analysis
Principal components analysis
accelerometers
nonnegative matrix factorization
functional data
ISSN:0006-341X, 1541-0420, 1541-0420
Online Access:Get full text
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Summary:We present a novel decomposition of nonnegative functional count data that draws on concepts from nonnegative matrix factorization. Our decomposition, which we refer to as NARFD (nonnegative and regularized function decomposition), enables the study of patterns in variation across subjects in a highly interpretable manner. Prototypic modes of variation are estimated directly on the observed scale of the data, are local, and are transparently added together to reconstruct observed functions. This contrasts with generalized functional principal component analysis, an alternative approach that estimates functional principal components on a transformed scale, produces components that typically vary across the entire functional domain, and reconstructs observations using complex patterns of cancellation and multiplication of functional principal components. NARFD is implemented using an alternating minimization algorithm, and we evaluate our approach in simulations. We apply NARFD to an accelerometer dataset comprising observations of physical activity for healthy older Americans.
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ISSN:0006-341X
1541-0420
1541-0420
DOI:10.1111/biom.13220