Semiparametric Partial Common Principal Component Analysis for Covariance Matrices

Wang, Bingkai; Luo, Xi; Zhao, Yi; Caffo, Brain S.

doi:10.1101/808527

Cited by 2 publications

(2 citation statements)

References 27 publications

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“…Flury (1984), Benko et al (2009)) and partial common principal component analysis (PCPCA, see e.g. Flury (1987), Schott (1999), Wang et al (2019)) aim to find the common principal component for multi-group multivariate data. Crainiceanu et al (2011) proposed a population value decomposition (PVD) procedure, and the common eigenvectors are obtained from concatenated individual eigenvectors.…”

Section: Existing Fpca Methods For Multivariate Functional Datamentioning

confidence: 99%

Filtrated Common Functional Principal Components for Multivariate Functional data

Jiao

Frostig

Ombao

2021

Preprint

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Local field potentials (LFPs) are signals that measure electrical activity in localized cortical regions from multiple implanted tetrodes in the human or animal brain. They can be treated as multivariate functional data (i.e., curves observed at many tetrodes spread across a patch on the surface of the cortex). Most multivariate functional data contain both global features (which are shared in common to all curves) as well isolated features (common only to a small subset of curves). The goal is this paper is to develop a procedure for capturing this common features. We propose a novel tree-structured functional principal component (filt-fPC) model through low-dimensional functional representation, specifically via filtration. A popular approach to dimension reduction of functional data is functional principal components analysis (fPCA). Ordinary fPCA can only capture the major information of one population, but fail to reveal the similarity of variation pattern of different groups, which is potentially related to functional connectivity of brain. One major advantage of the proposed filt-fPC method is the ability to extracting components that are common to multiple groups, and meanwhile preserves the idiosyncratic individual features of different groups, leading to a parsimonious and interpretable low dimensional representation of multivariate functional data. Another advantage is that the extracted functional principal components satisfy the orthonormal property for each set, making filt-fPC scores easy to be obtained. The proposed filt-fPC method was employed to study the impact of a shock (induced stroke) on the functional organization structure of the rat brain. Finally we point to further directions as this filtration idea can also be generalized to other functional statistical models, such as functional regression, classification and functional times series models.

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Section: Existing Fpca Methods For Multivariate Functional Datamentioning

confidence: 99%

Filtrated Common Functional Principal Components for Multivariate Functional data

Jiao

Frostig

Ombao

2021

Preprint

View full text Add to dashboard Cite

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“…A pioneering method for linked data is common principal component analysis (Flury, 1984, PCA), which can identify the same set of orthogonal eigenvectors shared across data sets. CPCA was extended to extract shared signal subspace present across data sets (Flury, 1987) and to determine the number of shared components (Wang and others , 2020). Another extension based on matrix decomposition, population value decomposition (Crainiceanu and others , 2011) extends CPCA to matrix-valued data, e.g., neuroimaging and electrophysiology data.…”

Section: Introductionmentioning

confidence: 99%

Two-stage Linked Component Analysis for Joint Decomposition of Multiple Biologically Related Data Sets

Chen

Caffo

Stein-O’Brien

et al. 2021

Preprint

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Integrative analysis of multiple data sets has the potential of fully leveraging the vast amount of high throughput biological data being generated. In particular such analysis will be powerful in making inference from publicly available collections of genetic, transcriptomic and epigenetic data sets which are designed to study shared biological processes, but which vary in their target measurements, biological variation, unwanted noise, and batch variation. Thus, methods that enable the joint analysis of multiple data sets are needed to gain insights into shared biological processes that would otherwise be hidden by unwanted intra-data set variation. Here, we propose a method called two-stage linked component analysis (2s-LCA) to jointly decompose multiple biologically related experimental data sets with biological and technological relationships that can be structured into the decomposition. The consistency of the proposed method is established and its empirical performance is evaluated via simulation studies. We apply 2s-LCA to jointly analyze four data sets focused on human brain development and identify meaningful patterns of gene expression in human neurogenesis that have shared structure across these data sets. The code to conduct 2s-LCA has been complied into an R package PJD, which is available at https://github.com/CHuanSite/PJD.

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Semiparametric Partial Common Principal Component Analysis for Covariance Matrices

Cited by 2 publications

References 27 publications

Filtrated Common Functional Principal Components for Multivariate Functional data

Filtrated Common Functional Principal Components for Multivariate Functional data

Two-stage Linked Component Analysis for Joint Decomposition of Multiple Biologically Related Data Sets

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