Sleep signals from a polysomnographic database are sequences in nature. Commonly employed analysis and classification methods, however, ignored this fact and treated the sleep signals as non-sequence data. Treating the sleep signals as sequences, this paper compared two powerful unsupervised feature extractors and three sequence-based classifiers regarding accuracy and computational (training and testing) time after 10-folds cross-validation. The compared feature extractors are Deep Belief Networks (DBN) and Fuzzy C-Means (FCM) clustering. Whereas the compared sequence-based classifiers are Hidden Markov Models (HMM), Conditional Random Fields (CRF) and its variants, i.e., Hidden-state CRF (HCRF) and Latent-Dynamic CRF (LDCRF); and Conditional Neural Fields (CNF) and its variant (LDCNF). In this study, we use two datasets. The first dataset is an open (public) polysomnographic dataset downloadable from the Internet, while the second dataset is our polysomnographic dataset (also available for download). For the first dataset, the combination of FCM and CNF gives the highest accuracy (96.75\%) with relatively short training time (0.33 hours). For the second dataset, the combination of DBN and CRF gives the accuracy of 99.96\% but with 1.02 hours training time, whereas the combination of DBN and CNF gives slightly less accuracy (99.69\%) but also less computation time (0.89 hours).