## 4 Discussion and Conclusions
In addition, according to the importance of the left and right directions of each feature and the importance of CSIP coordinates, we found that there was no significant difference in gait symmetry among PD patients, so this symmetry could not be used as a basis for distinguishing disease grades; that is to say, the abnormal gait pattern of PD was not found in only one limb. Considering the complexity of the human body, we analyzed the gait features. The results showed that the persistent entropy model was better than the model without topology data analysis. Although we could get good results by measuring the importance of variables, the training accuracy reached the peak when the proportion of training samples reached 80%. Increasing the number of training samples could not improve the training accuracy. This indicates that the effect of only using gait features to distinguish different PD grades encountered a bottleneck. When the persistent entropy was used as the training sample, the training accuracy of the learner broke through this bottleneck and reached 99.23%. The results showed that the TDA method could further extract the differences between gait features of different disease grades, and improved the discrimination among classes. This was due to the strong nonlinearity and complexity of human walking, and the SVM we used was essentially a linear classifier. The TDA method could map the gait feature data to the high-dimensional space and mine the sample features at a deeper level, which made the sample discrimination increase. Therefore, it was suitable for solving few-shot machine-learning problems related to human gait. Figure 9: The proportion of left foot support between control subjects and PD patients (one subject in each group). In addition, the training cost of samples processed by different methods is also different. The method of persistent entropy can be simplified to represent a class of gait features with only three numbers, which greatly reduces the dimension of the sample and significantly reduces the computation load during training. In the problem of sample balancing, persistent entropy is used to strengthen the discrimination between different classes of samples, which makes the distance between different categories further. This avoids the blindness of the SMOTE algorithm in neighbor selection to a certain extent, and makes the synthesized samples achieve a better training effect. According to the misclassification of severity levels, there are some cases in which normal people are recognized as patients, or low-level cases are identified as high-level cases. This is because when there are too few training samples, the walking speed becomes the most important feature. When the walking speed of the older normal or mild patients is too slow, the learner will mistakenly classify them as a serious manifestation of the disease, resulting in misclassification. When the number of training samples increases, this kind of misclassification can be improved. In summary, this paper proposed a few-shot learning method based on the measurement of permutation-variable importance and topological-imprint persistent entropy. The GRF was used as the basic data, Borderline-SMOTE was used as sample balancing method, and SVM was used as a classifier to identify the grade of PD. The proposed method achieved better results than when using original data. At the same time, the results of our study also indicated the leading factors of the differences among disease grades, which is valuable in further understanding the differential performance of different PD grades, revealing the walking characteristics of PD patients, and guiding the targeted health care. [PERSON] and [PERSON] conceived the key idea; [PERSON] analyzed the data and wrote the original draft; [PERSON] provided valuable suggestions for the experiments and reviewed the article; [PERSON] and [PERSON] designed and carried out the experiments; and [PERSON] provided guidance for the analysis method and revised the paper.