Early Prediction of Parkinson’s Disease by Using MathematicalModeling and Hilbert Transform

This research introduces a hybrid mathematical-deep learning framework for the early ‎prediction of Parkinson’s Disease (PD) using hand-drawn spiral and wave imagery. The ‎grayscale pictures were changed using the Hilbert Transform to get amplitude and phase details ‎that show the severity of the tremor and how it moves in an irregular way. We combined these ‎attributes with the original photos and ran them through three Transformer backbones: Swin-T, ‎ViT-B/16, and BEiT-B/16. The experimental findings showed that Swin-T exhibited superior ‎performance, achieving an AUC of 0.983, sensitivity of 0.951, and accuracy of 94.1%. This ‎was followed by ViT-B/16, which attained an AUC of 0.972. In contrast, BEiT-B/16 ‎underperformed, recording an AUC of 0.613. Combining Hilbert-based mathematical modeling ‎with Transformer designs creates a strong and understandable way to do early PD screening ‎without surgery. Furthermore, the limitations resulting from the tiny clinical dataset are ‎explicitly examined, and a stability–separability formalism is given to assess the resilience and ‎discriminative strength of Hilbert-derived features‎.