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Neurodegenerative diseases have shown an increasing incidence in the older population in recent years. A significant amount of research has been conducted to characterize these diseases. Computational methods, and particularly machine learning techniques, are now very useful tools in helping and improving the diagnosis as well as the disease monitoring process. In this paper, we provide an in-depth review on existing computational approaches used in the whole neurodegenerative spectrum, namely for Alzheimer's, Parkinson's, and Huntington's Diseases, Amyotrophic Lateral Sclerosis, and Multiple System Atrophy. We propose a taxonomy of the specific clinical features, and of the existing computational methods. We provide a detailed analysis of the various modalities and decision systems employed for each disease. We identify and present the sleep disorders which are present in various diseases and …