Stepwise Covariance-Free Common Principal Components (CF-CPC) With an Application to Neuroscience

Finding the common principal component (CPC) for ultra-high dimensional data is a multivariate technique used to discover the latent structure of covariance matrices of shared variables measured in two or more k conditions. Common eigenvectors are assumed for the covariance matrix of all conditions,...

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Autores principales:	Usama Riaz, Fuleah A. Razzaq, Shiang Hu, Pedro A. Valdés-Sosa
Formato:	article
Lenguaje:	EN
Publicado:	Frontiers Media S.A. 2021
Materias:	Ultra-high Dimensional Data Covariance-free Neuroimaging EEG MEG common principal component (CPC) Neurosciences. Biological psychiatry. Neuropsychiatry RC321-571
Acceso en línea:	https://doaj.org/article/bdc035ecc71047b39a5c6301c4f74fc2
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id	oai:doaj.org-article:bdc035ecc71047b39a5c6301c4f74fc2
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spelling	oai:doaj.org-article:bdc035ecc71047b39a5c6301c4f74fc22021-11-11T12:51:46ZStepwise Covariance-Free Common Principal Components (CF-CPC) With an Application to Neuroscience1662-453X10.3389/fnins.2021.750290https://doaj.org/article/bdc035ecc71047b39a5c6301c4f74fc22021-11-01T00:00:00Zhttps://www.frontiersin.org/articles/10.3389/fnins.2021.750290/fullhttps://doaj.org/toc/1662-453XFinding the common principal component (CPC) for ultra-high dimensional data is a multivariate technique used to discover the latent structure of covariance matrices of shared variables measured in two or more k conditions. Common eigenvectors are assumed for the covariance matrix of all conditions, only the eigenvalues being specific to each condition. Stepwise CPC computes a limited number of these CPCs, as the name indicates, sequentially and is, therefore, less time-consuming. This method becomes unfeasible when the number of variables p is ultra-high since storing k covariance matrices requires O(kp2) memory. Many dimensionality reduction algorithms have been improved to avoid explicit covariance calculation and storage (covariance-free). Here we propose a covariance-free stepwise CPC, which only requires O(kn) memory, where n is the total number of examples. Thus for n < < p, the new algorithm shows apparent advantages. It computes components quickly, with low consumption of machine resources. We validate our method CFCPC with the classical Iris data. We then show that CFCPC allows extracting the shared anatomical structure of EEG and MEG source spectra across a frequency range of 0.01–40 Hz.Usama RiazFuleah A. RazzaqShiang HuPedro A. Valdés-SosaPedro A. Valdés-SosaFrontiers Media S.A.articleUltra-high Dimensional DataCovariance-freeNeuroimagingEEGMEGcommon principal component (CPC)Neurosciences. Biological psychiatry. NeuropsychiatryRC321-571ENFrontiers in Neuroscience, Vol 15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Ultra-high Dimensional Data Covariance-free Neuroimaging EEG MEG common principal component (CPC) Neurosciences. Biological psychiatry. Neuropsychiatry RC321-571
spellingShingle	Ultra-high Dimensional Data Covariance-free Neuroimaging EEG MEG common principal component (CPC) Neurosciences. Biological psychiatry. Neuropsychiatry RC321-571 Usama Riaz Fuleah A. Razzaq Shiang Hu Pedro A. Valdés-Sosa Pedro A. Valdés-Sosa Stepwise Covariance-Free Common Principal Components (CF-CPC) With an Application to Neuroscience
description	Finding the common principal component (CPC) for ultra-high dimensional data is a multivariate technique used to discover the latent structure of covariance matrices of shared variables measured in two or more k conditions. Common eigenvectors are assumed for the covariance matrix of all conditions, only the eigenvalues being specific to each condition. Stepwise CPC computes a limited number of these CPCs, as the name indicates, sequentially and is, therefore, less time-consuming. This method becomes unfeasible when the number of variables p is ultra-high since storing k covariance matrices requires O(kp2) memory. Many dimensionality reduction algorithms have been improved to avoid explicit covariance calculation and storage (covariance-free). Here we propose a covariance-free stepwise CPC, which only requires O(kn) memory, where n is the total number of examples. Thus for n < < p, the new algorithm shows apparent advantages. It computes components quickly, with low consumption of machine resources. We validate our method CFCPC with the classical Iris data. We then show that CFCPC allows extracting the shared anatomical structure of EEG and MEG source spectra across a frequency range of 0.01–40 Hz.
format	article
author	Usama Riaz Fuleah A. Razzaq Shiang Hu Pedro A. Valdés-Sosa Pedro A. Valdés-Sosa
author_facet	Usama Riaz Fuleah A. Razzaq Shiang Hu Pedro A. Valdés-Sosa Pedro A. Valdés-Sosa
author_sort	Usama Riaz
title	Stepwise Covariance-Free Common Principal Components (CF-CPC) With an Application to Neuroscience
title_short	Stepwise Covariance-Free Common Principal Components (CF-CPC) With an Application to Neuroscience
title_full	Stepwise Covariance-Free Common Principal Components (CF-CPC) With an Application to Neuroscience
title_fullStr	Stepwise Covariance-Free Common Principal Components (CF-CPC) With an Application to Neuroscience
title_full_unstemmed	Stepwise Covariance-Free Common Principal Components (CF-CPC) With an Application to Neuroscience
title_sort	stepwise covariance-free common principal components (cf-cpc) with an application to neuroscience
publisher	Frontiers Media S.A.
publishDate	2021
url	https://doaj.org/article/bdc035ecc71047b39a5c6301c4f74fc2
work_keys_str_mv	AT usamariaz stepwisecovariancefreecommonprincipalcomponentscfcpcwithanapplicationtoneuroscience AT fuleaharazzaq stepwisecovariancefreecommonprincipalcomponentscfcpcwithanapplicationtoneuroscience AT shianghu stepwisecovariancefreecommonprincipalcomponentscfcpcwithanapplicationtoneuroscience AT pedroavaldessosa stepwisecovariancefreecommonprincipalcomponentscfcpcwithanapplicationtoneuroscience AT pedroavaldessosa stepwisecovariancefreecommonprincipalcomponentscfcpcwithanapplicationtoneuroscience
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Stepwise Covariance-Free Common Principal Components (CF-CPC) With an Application to Neuroscience

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