Parkinson’s disease (PD) is a progressive neurodegenerative disorder that affects both motor and speech functions. Advances in machine learning and signal processing have enabled non-invasive PD detection through voice analysis. This study proposes a comprehensive mathematical framework for PD classification that integrates topological, statistical, and spectral representations of speech signals. The framework combines topological descriptors derived from persistent homology, statistical measures based on random matrix theory, and spectral features extracted from frequency-domain analysis to capture complementary information about vocal dynamics. A hybrid training strategy was employed, using synthetic speech data generated from real recordings to train the models, while real samples were reserved exclusively for evaluation. Experimental results demonstrate that spectral features, particularly when fused with statistical descriptors, yield the highest discriminative power, achieving 98.00% accuracy and 97.98% F1-score with a multi-layer perceptron classifier. In contrast, topological descriptors provided limited standalone performance, serving instead as complementary components that enrich the overall representation. The findings highlight the potential of combining diverse mathematical representations to improve speech-based PD detection, especially in scenarios with limited access to clinically annotated data.
Parkinson’s disease (PD) is a progressive neurodegenerative disorder that affects both motor and speech functions. Advances in machine learning and signal processing have enabled non-invasive PD detection through voice analysis. This study proposes a comprehensive mathematical framework for PD classification that integrates topological, statistical, and spectral representations of speech signals. The framework combines topological descriptors derived from persistent homology, statistical measures based on random matrix theory, and spectral features extracted from frequency-domain analysis to capture complementary information about vocal dynamics. A hybrid training strategy was employed, using synthetic speech data generated from real recordings to train the models, while real samples were reserved exclusively for evaluation. Experimental results demonstrate that spectral features, particularly when fused with statistical descriptors, yield the highest discriminative power, achieving 98.00% accuracy and 97.98% F1-score with a multi-layer perceptron classifier. In contrast, topological descriptors provided limited standalone performance, serving instead as complementary components that enrich the overall representation. The findings highlight the potential of combining diverse mathematical representations to improve speech-based PD detection, especially in scenarios with limited access to clinically annotated data. Read More
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