Dataset Information

Principal component analysis of hybrid functional and vector data.

ABSTRACT: We propose a practical principal component analysis (PCA) framework that provides a nonparametric means of simultaneously reducing the dimensions of and modeling functional and vector (multivariate) data. We first introduce a Hilbert space that combines functional and vector objects as a single hybrid object. The framework, termed a PCA of hybrid functional and vector data (HFV-PCA), is then based on the eigen-decomposition of a covariance operator that captures simultaneous variations of functional and vector data in the new space. This approach leads to interpretable principal components that have the same structure as each observation and a single set of scores that serves well as a low-dimensional proxy for hybrid functional and vector data. To support practical application of HFV-PCA, the explicit relationship between the hybrid PC decomposition and the functional and vector PC decompositions is established, leading to a simple and robust estimation scheme where components of HFV-PCA are calculated using the components estimated from the existing functional and classical PCA methods. This estimation strategy allows flexible incorporation of sparse and irregular functional data as well as multivariate functional data. We derive the consistency results and asymptotic convergence rates for the proposed estimators. We demonstrate the efficacy of the method through simulations and analysis of renal imaging data.

SUBMITTER: Jang JH

PROVIDER: S-EPMC9084921 | biostudies-literature | 2021 Oct

REPOSITORIES: biostudies-literature

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Principal component analysis of hybrid functional and vector data.

Jang Jeong Hoon JH

Statistics in medicine 20210623 24

We propose a practical principal component analysis (PCA) framework that provides a nonparametric means of simultaneously reducing the dimensions of and modeling functional and vector (multivariate) data. We first introduce a Hilbert space that combines functional and vector objects as a single hybrid object. The framework, termed a PCA of hybrid functional and vector data (HFV-PCA), is then based on the eigen-decomposition of a covariance operator that captures simultaneous variations of functi ...[more]

PMID: 34160848

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Project description:Electroencephalography (EEG) data possess a complex structure that includes regional, functional, and longitudinal dimensions. Our motivating example is a word segmentation paradigm in which typically developing (TD) children, and children with autism spectrum disorder (ASD) were exposed to a continuous speech stream. For each subject, continuous EEG signals recorded at each electrode were divided into one-second segments and projected into the frequency domain via fast Fourier transform. Following a spectral principal components analysis, the resulting data consist of region-referenced principal power indexed regionally by scalp location, functionally across frequencies, and longitudinally by one-second segments. Standard EEG power analyses often collapse information across the longitudinal and functional dimensions by averaging power across segments and concentrating on specific frequency bands. We propose a hybrid principal components analysis for region-referenced longitudinal functional EEG data, which utilizes both vector and functional principal components analyses and does not collapse information along any of the three dimensions of the data. The proposed decomposition only assumes weak separability of the higher-dimensional covariance process and utilizes a product of one dimensional eigenvectors and eigenfunctions, obtained from the regional, functional, and longitudinal marginal covariances, to represent the observed data, providing a computationally feasible non-parametric approach. A mixed effects framework is proposed to estimate the model components coupled with a bootstrap test for group level inference, both geared towards sparse data applications. Analysis of the data from the word segmentation paradigm leads to valuable insights about group-region differences among the TD and verbal and minimally verbal children with ASD. Finite sample properties of the proposed estimation framework and bootstrap inference procedure are further studied via extensive simulations.

Dataset Information

Principal component analysis of hybrid functional and vector data.

Publications

Principal component analysis of hybrid functional and vector data.

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