Neurodegenerative diseases are common progressive nervous system disorders that show intricate clinical patterns. The gait fluctuations reflect the physiology and pathologic alterations in the locomotor control system. Using gait fluctuations for disease state evaluation is an essential way for clinical trials and healthcare monitoring. The classification of gait fluctuations helps improve the life quality and enhance clinical diagnosis ability in neuro-degenerative patients. In this work, we firstly embed the time series of multiple gait fluctuations into the phase space. Then we use persistent homology to extract the topological signatures of barcodes. Together with a random forest classifier, we proposed a topological motion analysis (TMA) framework to analyze the gait fluctuations. Further, we proposed a comprehensive comparison study using the TMA framework in the neuro-degenerative classification tasks for stance-, stride-, and swing-based gait fluctuations. In the tasks of comparing amyotrophic lateral sclerosis (ALS), Huntington's disease (HD), and Parkinson's disease (PD) to the healthy control (HC) group, the bestachieved AUC scores were 0.9135, 0.9906 and 0.9667 respectively, which show the effectiveness of TMA framework. In summary, our study proposed a TMA framework towards gait fluctuations classification in the neuro-degenerative analysis tasks. The proposed method shows promising clinical application value in earlier interventions and state monitoring for neurodegenerative patients.

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