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Nonnegative decomposition of functional count data.

ABSTRACT: 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.

SUBMITTER: Backenroth D

PROVIDER: S-EPMC7375931 | biostudies-literature | 2020 Dec

REPOSITORIES: biostudies-literature

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Nonnegative decomposition of functional count data.

Backenroth Daniel D Shinohara Russell T RT Schrack Jennifer A JA Goldsmith Jeff J

Biometrics 20200203 4

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 ...[more]

PMID: 31970756

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Project description:Large-scale transcriptome data, such as single-cell RNA-sequencing data, have provided unprecedented resources for studying biological processes at the systems level. Numerous dimensionality reduction methods have been developed to visualize and analyze these transcriptome data. In addition, several existing methods allow inference of functional variations among samples using gene sets with known biological functions. However, it remains challenging to analyze transcriptomes with reduced dimensions that are interpretable in terms of dimensions' directionalities, transferrable to new data, and directly expose the contribution or association of individual genes. In this study, we used gene set non-negative principal component analysis (gsPCA) and non-negative matrix factorization (gsNMF) to analyze large-scale transcriptome datasets. We found that these methods provide low-dimensional information about the progression of biological processes in a quantitative manner, and their performances are comparable to existing functional variation analysis methods in terms of distinguishing multiple cell states and samples from multiple conditions. Remarkably, upon training with a subset of data, these methods allow predictions of locations in the functional space using data from experimental conditions that are not exposed to the models. Specifically, our models predicted the extent of progression and reversion for cells in the epithelial-mesenchymal transition (EMT) continuum. These methods revealed conserved EMT program among multiple types of single cells and tumor samples. Finally, we demonstrate this approach is broadly applicable to data and gene sets beyond EMT and provide several recommendations on the choice between the two linear methods and the optimal algorithmic parameters. Our methods show that simple constrained matrix decomposition can produce to low-dimensional information in functionally interpretable and transferrable space, and can be widely useful for analyzing large-scale transcriptome data.

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Nonnegative decomposition of functional count data.

Publications

Nonnegative decomposition of functional count data.

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