Comparative factor analysis models for an empirical study of EEG data

This paper (the first in a series) applies new, empirical factor analysis methods to the problem of "banding" EEG power spectra. A measure is introduced for the comparison of factor analysis results (factor loading matrices). The measure, Ambient Matrix Coherence (AC) is "geometrically unbiased", and invariant of so-called "oblique rotations." AC is used in a "stability computation" to find the dimension of the stable factor analysis solution common to several subsets of a given dataset. If the factor analysis model is appropriate, then the correct number of factors is empirically determined in this way. Stability computations were first performed on various simulated datasets to establish the robustness and efficacy of this method (for various noise levels). These techniques were then applied to EEG power spectra datasets for each of 8 leads. Comparison of these results indicated 3 stable factors in common to all 8 leads, an additional less stable factor in common to 5 leads, and weak stability for the six-dimensional solution for one lead.