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Activity Number: 123
Type: Contributed
Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistics in Imaging
Abstract #311691 View Presentation
Title: Fast Exact Bootstrap Principal Component Analysis for P>1 Million: Leveraging Low-Dimensional Structure Across High-Dimensional Bootstrap Samples
Author(s): Aaron Fisher*+ and Brian Scott Caffo and Vadim Zipunnikov
Companies: and Johns Hopkins University and Johns Hopkins University
Keywords: Principal Component Analysis (PCA) ; Bootstrap ; High Dimensional ; Singular Value Decomposition (SVD) ; Electroencephalography (EEG) ; Computation
Abstract:

Many have suggested a bootstrap procedure for quantifying uncertainty in principal component analysis (PCA) results. However, when the number of measurements per subject (p) is much larger than the number of subjects (n), the challenge of calculating and storing the leading K principal components from each bootstrap sample can be computationally infeasible (computational complexity O(Bpn^2), where B is the number of bootstrap samples). To address this, we outline methods for fast, exact calculation of bootstrap standard errors (complexity O(pKn^2+KBn^2)), and fast, exact calculation of all bootstrap principal components (complexity O(BpnK)). We leverage the fact that all bootstrap samples occupy the same n-dimensional subspace as the original sample. As a result, all bootstrap principal components also occupy same n-dimensional subspace, and can be efficiently represented by their low dimensional coordinates in that subspace. Several uncertainty metrics can be computed solely based on these low dimensional coordinates, without calculating or storing the p-dimensional bootstrap components. Fast bootstrap PCA is applied to a dataset of sleep electroencephalography (EEG) recordings.


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