# A Novel Criticality Analysis Method for Assessing Obesity Treatment Efficacy
## 3 Methodology
### The Classification Decision Boundary of SVM  
The decision boundary of an SVM classifier is determined by the support vectors, which are the data points closest to the boundary. Parameters \(C\) and \(\sigma\), also known as regularisation and kernel parameters, respectively, control the width of the margin and the shape of the decision boundary. For instance, when \(\sigma\) is set to 0.1 and \(C\) is set to 1, the decision boundary becomes complex and more influenced by the individual data points. The width of the margin becomes relatively small and the classifier more sensitive to the presence of outliers, as the algorithm tries to minimise misclassification errors. Moreover, when \(\sigma\) is set to 0.1 and \(C\) is set to 10, the decision boundary is even more complex as \(C\) has a greater influence on the decision boundary. The width of the margin is even smaller and the classifier is even more sensitive to outliers. Furthermore, when \(\sigma\) is set to 0.1 and \(C\) is set to 0.1, the decision boundary is relatively simple as \(C\) has a much smaller influence on the decision boundary. The width of the margin is relatively large and the classifier is less sensitive to outliers.  
The classification boundaries of the SVM model are depicted in Figures 16-18 using the best classification parameters, enabling the model to accurately categorise participants into the appropriate group.  
The overall performance of the proposed SVM model is evaluated in Figure 19, where the best classification parameters (\(\sigma=0.1\) and \(C=0.1\)) result in the optimal generalisation performance. The 6-week evaluation of the SVM shows fluctuating accuracy in classifying participants into the healthy control and obesity groups. A high accuracy reflects consistent participant characteristics, facilitating accurate classification by the SVM, whereas a low accuracy indicates high variability in participant characteristics, making classification  
Figure 16: The boundary that separates the healthy control walk patterns from the obesity patterns in an SVM model, with RCC control parameters \(f_{p}=1\), \(f_{g}=1\), \(x_{p}=-1\), \(x_{g}=-1\), \(\mu_{f}=2\), and \(\sigma=0.1\) and \(C=0.1\) for \(w_{1}\) and \(\sigma=0.1\) and \(C=1\) for \(w_{2}\), is shown.  
Figure 17: The boundary that separates the healthy control walk patterns from the obesity patterns in an SVM model, with RCC control parameters \(f_{p}=1\), \(f_{g}=1\), \(x_{p}=-1\), \(x_{g}=-1\), \(\mu_{f}=2\), and \(\sigma=0.1\) and \(C=1\) for \(w_{3}\) and \(w_{4}\), is shown.  
challenging. In individuals with obesity, the influence of various factors, including walk speed, affects the results depicted in Figure 19. The figure demonstrates that the highest accuracy is observed during the initial week, but experiences a significant decline in the third week. Subsequently, there is a slight improvement in the fourth week, followed by further declines in the fifth and sixth weeks. The fluctuation in the accuracy of the SVM model during the 6-week period, despite the uniform diet and exercise regimen followed by the participants, could be attributed to various reasons such as variations in compliance levels, where some participants may have been more diligent in adhering to the regimen than others, leading to different classifications into healthy control or obesity groups. Other factors include individual differences such as genetics, medical history, and personal habits, measurement inaccuracies, and changes in any of the systems (metabolic, neuromuscular, cardiovascular) altering participant characteristics over time, even when following the prescribed diet and exercise regimen. Participants' stress levels or health status could impact their classification as it could alter variables affecting their gait and hence classification into healthy control or obesity groups.