Huberian function applied to neurodegenerative disorder gait rhythm

ABSTRACT

Huberian statistical approach is applied to differentiate three neurodegenerative disorder gait rhythm and presents a method reducing the number of parameters of an autoregressive moving average (ARMA) modeling of the walking signal. Gait rhythm dynamics differ between healthy control, Parkinson's disease, Huntington's disease and amyotrophic lateral sclerosis. Random variables such as the stride interval and its two sub-phases (i.e. swing and stance) present a great variability with natural outliers. Huberian function as a mixture of $L_2$ and $L_1$ norms with low threshold γ is used to present new statistical indicators by deducing the corresponding skewness and kurtosis. The choice of γ is discussed to ensure consistency and convergence of a low-order ARMA estimator of the gait rhythm signal. A mathematical point of view is developed and experimental results are presented.

KEYWORDS:

• Huberian statistical
• Huberian non-parametric probability density function
• mixed kernelfunction
• Gait disorder signal
• natural outlier
• neurodegenerative disease
• low-orderARMA estimator

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Christophe Corbier  http://orcid.org/0000-0002-6832-121X