Parkinson's disease (PD) and essential tremor (ET) are prevalent movement disorders that mainly affect elderly people, presenting diagnostic challenges due to shared clinical features. While both disorders exhibit distinct speech patterns-hypokinetic dysarthria in PD and hyperkinetic dysarthria in ET-the efficacy of speech assessment for differentiation remains unexplored. Developing technology for automatic discrimination could enable early diagnosis and continuous monitoring. However, the lack of data for investigating speech behavior in these patients has inhibited the development of a framework for diagnostic support. In addition, phonetic variability across languages poses practical challenges in establishing a universal speech assessment system. Therefore, it is necessary to develop models robust to the phonetic variability present in different languages worldwide. We propose a method based on Gaussian mixture models to assess domain adaptation from models trained in German and Spanish to classify PD and ET patients in Czech. We modeled three different speech dimensions: articulation, phonation, and prosody and evaluated the models' performance in both bi-class and tri-class classification scenarios (with the addition of healthy controls). Our results show that a fusion of the three speech dimensions achieved optimal results in binary classification, with accuracies up to 81.4 and 86.2% for monologue and /pa-ta-ka/ tasks, respectively. In tri-class scenarios, incorporating healthy speech signals resulted in accuracies of 63.3 and 71.6% for monologue and /pa-ta-ka/ tasks, respectively. Our findings suggest that automated speech analysis, combined with machine learning is robust, accurate, and can be adapted to different languages to distinguish between PD and ET patients.

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