# A Novel Criticality Analysis Method for Assessing Obesity Treatment Efficacy
## 5 Discussion  
The primary aim of the comprehensive study was to assess the effectiveness of obesity treatment interventions through the application of a unique CA approach. Simultaneously,  
Figure 19: The classification performance of SVM over a 6-week (\(w_{1}\)-\(w_{6}\)) period is presented.  
Figure 18: The SVM decision 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 \(C=10\) for \(w_{5}\) and \(\sigma=0.1\) and \(C=1\) for \(w_{6}\), is shown.  
the investigation delved into the intricate dynamics of gait patterns, particularly within the context of obesity. This multifaceted exploration sought to provide a deeper understanding of gait patterns and evaluate the potential of the CA methodology combined with SVM classification in gait analysis within the context of obesity treatment assessment. This multidimensional exploration sought to not only quantify gait variability, but also ascertain the robustness of our CA-SVM methodology for gait classification. Throughout the 6-week study period, SVM classification accuracy exhibited significant fluctuations, with the highest accuracy recorded in the initial week, followed by substantial declines in Weeks 3 through 6. These fluctuations highlight the dynamic nature of SVM model's ability to categorise gait patterns over time. Notably, these variations are not arbitrary but reflect shifts in participant characteristics that significantly impact classification outcomes.  
All participants adhered to a uniform diet and exercise regimen during the study, making it evident that individual factors beyond the protocol influenced gait patterns and SVM classifications each week. Factors such as compliance, genetics, medical history, stress levels, or changes in metabolic/neuromuscular systems likely played a role. The SVM accuracy metric robustly quantifies the influence of these individual characteristics on classification performance. ROC curves and AUC values provide insights into the model's proficiency in distinguishing between healthy and obese gait patterns. Optimal model performance occurred under specific parameter settings, \(\sigma=0.1\) and \(C=1\) or \(10\), where AUC values were maximised. These results confirm the exceptional generalisation capabilities of the SVM model when applied to unseen data and underscore the effectiveness of our CA-SVM methodology in extracting relevant features from gait data.  
Visual representations, in the form of phase plots, vividly illustrate the distinctions between healthy and obese gait patterns achieved through the CA method. The phase plots reveal that obese gait patterns are characterised by slower and more labored movements, while healthy gait patterns are smoother and more fluid. These differences align with expectations, given the increased joint stress and stiffness associated with obesity. Phase plots affirm that CA effectively distinguishes between the two groups by revealing interpretable spatio-temporal gait characteristics.  
The spatio-temporal analysis quantifying variability in gait progression over a 6-week period offers valuable insights. Notably, wider variability is observed among obese participants compared to their healthy counterparts. This underscores CA's capacity to elucidate subtle yet evolving patterns through phase plot analysis and its competence in quantifying gait variability. Lastly, classification accuracy results, ranging from 78.2% to 90%, strongly validate the efficacy of the CA method in dimensionality reduction and data representation, enhancing classification performance. CA successfully transforms complex gait patterns into lower-dimensional trajectories discernible by the SVM algorithm, leading to high accuracy. This demonstrates CA's proficiency in extracting essential features and capturing nonlinear relationships, enabling precise classification and establishing it as an effective data representation strategy.