AUTHOR=Riaz Usama , Razzaq Fuleah A. , Hu Shiang , Valdés-Sosa Pedro A. 

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

JOURNAL=Frontiers in Neuroscience

VOLUME=Volume 15 - 2021

YEAR=2021

URL=https://www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2021.750290

DOI=10.3389/fnins.2021.750290

ISSN=1662-453X

ABSTRACT=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(kn^2) 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<