  In this paper, two modern adaptive signal processing techniques, Empirical
Intrinsic Geometry and Synchrosqueezing transform, are applied to quantify
different dynamical features of the respiratory and electroencephalographic
signals. We show that the proposed features are theoretically rigorously
supported, as well as capture the sleep information hidden inside the signals.
The features are used as input to multiclass support vector machines with the
radial basis function to automatically classify sleep stages. The effectiveness
of the classification based on the proposed features is shown to be comparable
to human expert classification -- the proposed classification of awake, REM,
N1, N2 and N3 sleeping stages based on the respiratory signal (resp.
respiratory and EEG signals) has the overall accuracy $81.7\%$ (resp. $89.3\%$)
in the relatively normal subject group. In addition, by examining the
combination of the respiratory signal with the electroencephalographic signal,
we conclude that the respiratory signal consists of ample sleep information,
which supplements to the information stored in the electroencephalographic
signal.
