Fast, Exact Bootstrap Principal Component Analysis for p > 1 million.

Area of Science:

• Statistics
• Machine Learning
• Computational Biology

Background:

• Principal Component Analysis (PCA) is widely used for dimensionality reduction.
• Estimating sampling variability of PCA results using bootstrap is computationally intensive, especially with high-dimensional data (p >> n).
• Existing methods struggle with large datasets due to infeasible calculation and storage of bootstrap principal components.

Purpose of the Study:

• To introduce a computationally efficient method for bootstrap PCA.
• To enable accurate estimation of sampling variability in high-dimensional PCA.
• To overcome the computational limitations of traditional bootstrap PCA.

Main Methods:

• Leveraging the n-dimensional subspace of bootstrap samples for efficient representation.
• Calculating bootstrap principal components, eigenvalues, and scores using low-dimensional coordinates.
• Applying the fast bootstrap PCA to electroencephalogram (EEG) and magnetic resonance imaging (MRI) datasets.

Main Results:

• The proposed method allows for fast, exact calculation of bootstrap PCA results.
• Uncertainty metrics can be computed without storing high-dimensional bootstrap components.
• Significant reduction in computation time was observed, e.g., 47 minutes vs. 4 days for MRI data.

Conclusions:

• The developed fast bootstrap PCA method is computationally feasible for high-dimensional datasets.
• This approach enables robust estimation of sampling variability in complex datasets.
• The method has practical implications for fields utilizing large-scale data analysis, such as neuroimaging.