Parkinson's Disease (PD) is often characterized by abnormal gait patterns, which can be objectively and quantitatively diagnosed using Vertical Ground Reaction Force (VGRF) signals. Previous studies have demonstrated the effectiveness of deep learning in VGRF signal analysis. However, the inherent graph structure of VGRF signals has not been adequately considered, limiting the representation of dynamic gait characteristics. To address this, we propose a Multi-Scale Adaptive Directed Graph Neural Network (MS-ADGNN) approach to distinguish the gaits between Parkinson's patients and healthy controls. This method models the VGRF signal as a multi-scale directed graph, capturing the distribution relationships within the plantar sensors and the dynamic pressure conduction during walking. MS-ADGNN integrates an Adaptive Directed Graph Network (ADGN) unit and a Multi-Scale Temporal Convolutional Network (MSTCN) unit. ADGN extracts spatial features from three scales of the directed graph, effectively capturing local and global connectivity. MSTCN extracts multi-scale temporal features, capturing short to long-term dependencies. The proposed method outperforms existing methods on three widely used datasets. In cross-dataset experiments, the average improvements in terms of accuracy, F1-score, and geometric mean are 2.46$\%$, 1.25$\%$, and 1.11$\%$ respectively. Meanwhile, in 10-fold cross-validation experiments, the improvements are 0.78$\%$, 0.83$\%$, and 0.81$\%$ respectively.

Vertical Ground Reaction Force (VGRF) signal obtained from foot-worn sensors, also known as plantar data, provides a highly informative and detailed representation of an individual's gait features. Existing methods, such as CNNs, LSTMs and Transformers, have revealed the efficiency of deep learning in Parkinson's Disease (PD) diagnosis using VGRF signal. However, the intrinsic topologic graph and pressure transmission characteristics of plantar data are overlooked in those approaches, which are essential features for gait analysis. In this paper, we propose to construct a plantar directed topologic graph to fully exploit the plantar topology in gait circles. It can facilitate the expression of gait information by representing sensors as nodes and pressure transmissions as directional edges. Accordingly, an Adaptive Spatio-Temporal Directed Graph Neural Network (AST-DGNN) is proposed to extract the connection features of the plantar directed topologic graph. Each AST-DGNN Unit includes an Adaptive Directed Graph Network (ADGN) block and a Temporal Convolutional Network (TCN) block. In order to capture both local and global spatial relationships among sensor nodes and pressure transmission edges, the ADGN block performs message passing on the plantar directed topologic graph in an adaptive manner. To capture the temporal features of sensor nodes and pressure transmission edges, the TCN block defines a temporal feature extraction process for each node and edge in the graph. Moreover, the data augmentation is introduced for plantar data to improve the generalization ability of the AST-DGNN. Experimental results on Ga, Ju, and Si datasets demonstrate that the proposed method outperforms the existing methods under both cross-dataset validation and mixed-data cross-validation. Especially in cross-dataset validation, there is an average improvement of 2.13%, 7.73%, and 12.27% in accuracy, F1 score, and G-mean, respectively.