  We propose a novel unsupervised approach for sleep dynamics exploration and
automatic annotation by combining modern harmonic analysis tools. Specifically,
we apply diffusion-based algorithms, diffusion map (DM) and alternating
diffusion (AD) algorithms, to reconstruct the intrinsic geometry of sleep
dynamics by reorganizing the spectral information of an electroencephalogram
(EEG) extracted from a nonlinear-type time frequency analysis tool, the
synchrosqueezing transform (SST). The visualization is achieved by the
nonlinear dimension reduction properties of DM and AD. Moreover, the
reconstructed nonlinear geometric structure of the sleep dynamics allows us to
achieve the automatic annotation purpose. The hidden Markov model is trained to
predict the sleep stage. The prediction performance is validated on a publicly
available benchmark database, Physionet Sleep-EDF [extended] SC* and ST*, with
the leave-one-subject-out cross validation. The overall accuracy and macro F1
achieve 82:57% and 76% in Sleep-EDF SC* and 77.01% and 71:53% in Sleep-EDF ST*,
which is compatible with the state-of-the-art results by supervised
learning-based algorithms. The results suggest the potential of the proposed
algorithm for clinical applications.
