Discrimination and characterization of Parkinsonian rest tremors by analyzing long-term correlations and multifractal signatures

In this paper, we analyze 48 signals of rest tremor velocity related to 12 distinct subjects affected by Parkinson's disease. The subjects belong to two different groups, formed by four and eight subjects with, respectively, high- and low-amplitude rest tremors. Each subject is tested in four settings, given by combining the use of deep brain stimulation and L-DOPA medication. We develop two main feature-based representations of such signals, which are obtained by considering (i) the long-term correlations and multifractal properties, and (ii) the power spectra. The feature-based representations are initially utilized for the purpose of characterizing the subjects under different settings. In agreement with previous studies, we show that deep brain stimulation does not significantly characterize neither of the two groups, regardless of the adopted representation. On the other hand, the medication effect yields statistically significant differences in both high- and low-amplitude tremor groups. We successively test several different instances of the two feature-based representations of the signals in the setting of supervised classification and (nonlinear) feature transformation. We consider three different classification problems, involving the recognition of (i) the presence of medication, (ii) the use of deep brain stimulation, and (iii) the membership to the high- and low-amplitude tremor groups. Classification results show that the use of medication can be discriminated with higher accuracy, considering many of the feature-based representations. Notably, we show that the best results are obtained with a parsimonious, two-dimensional representation encoding the long-term correlations and multifractal character of the signals.