Noname manuscript No. (will be inserted by the editor) Non-linear Assessment of Gait Impairments of Patients with Parkinson’s Disease using Entropy, Complexity, and Poincar´ e Section-based Features. P. A. P´ erez-Toro · J. C. V´ asquez-Correa · T. Arias-Vergara · J. R. Orozco-Arroyave · E.N¨oth Received: date / Accepted: date Abstract Parkinson’s Disease is a progressive disor- der of the nervous system that affects the motor sys- tem of the patients, producing several impairments in muscles and limbs. One of the major manifestations of the disease appears in gait, and typically causes dis- ability of the patients. Gait assessment appears as an useful tool to support the diagnosis process and to eval- uate the neurological state of the patients. The gait of the patients is mainly evaluated from signals captured with inertial sensors attached to the limbs of the pa- tients, where kinematics features are commonly com- puted. On the other hand, there are non-linear effects of the gait process that cannot be properly characterized with the kinematic features. This study proposes the use several non-linear dynamics features to assess the gait impairments of Parkinson’s patients. We consider classical non-linear features such as the correlation di- mension, the largest Lyapunov exponent, and the Hurst exponent, among others. In addition we propose a novel non-linear analysis based on applying a Gaussian mix- ture model to find clusters in Poincar´ e sections. The non-linear dynamics features are used to discriminate between Parkinson’s patients and healthy subjects, and P. A. P´ erez-Toro, J. C. V´asquez-Correa, T. Arias-Vergara, and J. R. Orozco-Arroyave are with Faculty of Engineering, University of Antioquia UdeA, Medell´ ın, Colombia. J. C. V´ asquez-Correa, T. Arias-Vergara, J. R. Orozco- Arroyave, and E.N¨oth are with Pattern Recognition Lab, Friedrich-Alexander-Universit¨at Erlangen-N¨ urnberg, Germany. T. Arias-Vergara is with Ludwig-Maximilians-University, Munich, Germany. *Corresponding author: jcamilo.vasquez@udea.edu.co to classify patients in several stages of the disease. The results indicate that it is possible to discriminate be- tween patients and healthy subjects with accuracies up to 88% and to classify patients in several stages of the disease with accuracies up to 65%. As far as we know, this is one of the first studies that considers a full non- linear dynamics analysis to assess the gait impairments of patients with Parkinson’s disease. Keywords Parkinson’s Disease · Non-linear Dynam- ics · Poincare Section · Gait assessment · Classification · Prediction · Inertial Sensors 1 Introduction Parkinson’s disease (PD) is a neuro-degenerative disor- der characterized by the progressive loss of dopamin- ergic neurons in the mid brain [1]. The motor symp- toms include lack of coordination, tremor, rigidity and postural instability. Gait impairments appear in most of patients and include freezing, shuffling, and festi- nating gait. The standard scale to evaluate the neu- rological state of the patients is the Movement Disor- der Society-Unified Parkinson’s Disease Rating Scale (MDS-UPDRS) [2]. The third section of the scale con- tains 14 items to evaluate the deficits in the lower limbs of the patients. The therapy mainly focuses on treating the symptoms of the patients with individual medica- tion. This medication always has to be adjusted accord- ing to the current stage of disease. Gait changes are a hallmark of PD, where the main symptoms include reductions in speed, decreased step length, altered cadence, and increased gait variability. While gait abnormalities are not pronounced in the early stages, their prevalence and severity increases with