Our research objectives include artifact removal and electroencephalogram (EEG) data recovery for appropriate mathematical modeling of the Sleep-Wake cycle. Corrupted EEG data have been successfully removed and recovered. Data recovery and artifact elimination have been obtained by implementing the generalized singular value decomposition algorithm in conjunction with the k-nearest neighbor classification scheme, which incorporates feature selection. This research provides the proper segue into the manifestation of a more efficient mathematical model of the Sleep-Wake cycle. It is hypothesized that by modeling the sleep process as a continuum and investigating the transitional stages of sleep on a patient based methodology insight regarding the biological need for sleep may be contributed to the field.