**5. Conclusions**

In this paper, a novel IMBEF based automatic sleep stage classification method is proposed. Moreover, a grid search strategy was presented to determine a suitable model order *nDSSM* and a wavelet basis *ωDSSM* for estimating the DSSM among 15 candidate wavelets and 6 candidate model orders. With the same search strategy, a proper wavelet basis *ωLE* and the WPD level *lLE* for LE calculation are determined under 15 candidate wavelets and multilevel decomposition. The fused IMBEFs extracted from the DSSM and LE would be used as the input features of the suitable classifier which can be selected by comparing a variety of classifiers' experiment results. In order to precisely verify the performance of the proposed IMBEF based automatic sleep stage classification method, experiments were carried out on three public databases. The comparison results with other state-of-the-art methods show that the proposed algorithm can achieve higher accuracy.

We demonstrated in this paper measurable improvements in automatic sleep stage classification, providing better understanding and diagnostic of the sleep phenomenon, clearly essential in medical, wellness and other fields.

**Author Contributions:** Conceptualization, H.S. and A.L.; methodology, H.S., A.G. (Allon Guez) and A.L.; software, H.S.; validation, H.S., A.G. (Allon Guez) and A.G. (Aiying Guo); formal analysis, H.S., A.L.; investigation, A.G. (Aiying Guo); resources, F.R.; data curation, A.L.; writing–original draft preparation, H.S. and A.L.; writing–review and editing, H.S., A.G. (Allon Guez) and A.L.; visualization, M.X.; supervision, M.X.; project administration, M.X.; funding acquisition, F.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China grant number 61674100.

**Acknowledgments:** We acknowledge the support provided by the Microelectronics Research and Development Center of Shanghai University.

**Conflicts of Interest:** The authors declare no conflict of interest.
