A group refactorization procedure for sleep electroencephalography

[WORKING DRAFT] In order to relate health and disease to brain state, patterns of activity in the brain must be phenotyped. In this regard, polysomnography datasets present both an opportunity and a challenge, as although sleep data are extensive and multidimensional, features of the sleep EEG are known to correlate with clinical outcomes. Machine learning methods for rank reduction are attractive means for bringing the phenotyping problem to a manageable size. The whole-night power spectrogram is nonnegative, and so applying nonnegative matrix factorization (NMF) to separate spectrograms into time and frequency factors is a natural choice for dimension reduction. However, NMF converges differently depending on initial conditions, and there is no guarantee that factors obtained from one individual will be comparable with those from another, hampering inter-individual analysis. We therefore reseed time-frequency NMF with group frequency factors obtained from the entire sample. This "refactorization" extends classical frequency bands to frequency factors. The group reseeding procedure coerces factors into equivalence classes, making them comparable across individuals. By comparing frequency factor properties, we illustrate age-related effects on the sleep EEG. The procedure can presumably be adapted to higher resolutions, e.g. to local field potential datasets, for characterizing individual time-frequency events.