Use of Principal Component Analysis in the Frequency Domain for Mapping Electroencephalographic Activities: Comparison with Phase?Encoded Fourier Spectral Analysis

Abstract

Principal component analysis (PCA) can separate multichannel electroencephalographic (EEG) epochs into linearly independent (temporally and spatially noncorrelated) components. Results of PCA include component time-series waveforms and factors representing the contribution of each component to each electrode; these factors may be displayed as contour maps representing the topographic distribution of each component. However, PCA often does not achieve the most useful separation of components. PCA may be performed in the frequency domain to potentially improve results. After inspecting principal components of the frequency spectra, spectral values in a selected frequency range are multiplied by a chosen factor to emphasize (or de-emphasize) these frequencies and PCA is redone, promoting the separation of different frequencies into different components. Phase-encoded Fourier spectral analysis (PEFSA) uses multichannel complex Fourier spectra (amplitude and phase) to obtain positive or negative (phase-encoded) potentials at each electrode for any selected frequency. These may be displayed as a contour map representing the topographic distribution of the selected frequency. Applying both techniques, we found that EEG activities of differing frequency were readily separated by PEFSA, while standard PCA often mixed activities with different frequencies into a single component. However, frequency-domain PCA gave a component whose spatial distribution well matched PEFSA results. PCA is superior to PEFSA for separating activities with overlapping frequencies but differing spatial distributions. Preservation of phase information is an advantage of PEFSA and PCA over topographic maps that represent only amplitude (or power) at a given frequency. PCA or PEFSA maps can serve as a starting point for source localization.