# DentalArch: AI-Based Arch Shape Detection in Orthodontics
## 2 Materials and Methods
### Data Augmentation and Dataset Composition  
In the process of training the DentalArch software, a total of 200 data points with corresponding labels were utilized. These data points were derived from meticulous manual evaluations conducted by orthodontic professionals, including their manual measurements.  
To enhance the robustness of the dataset and facilitate more effective model training, data augmentation techniques were employed. Specifically, measurements of the same dental models at different time points were incorporated as part of the augmentation process. This temporal variation in the dataset allowed for the representation of natural changes that may occur over time, contributing to a more dynamic and comprehensive training set.  
The decision to refrain from introducing synthetic data was made to prevent any potential contamination of the dataset and to maintain a high level of relevance to the clinical context [37]. All data points used in the training process accurately represented the variations and complexities encountered in actual orthodontic practice.  
Furthermore, the augmentation process, utilizing measurements from different time points, enabled the expansion of the dataset without compromising its authenticity [38]. This approach contributed to a more comprehensive and diverse set of training examples, reflecting the dynamic nature of dental arch shapes over time.  
By leveraging these carefully collected and temporally augmented datasets, DentalArch was trained on a rich and varied array of real-world scenarios, enhancing its ability to generalize and make accurate predictions in a clinical setting.  
\begin{table}
\begin{tabular}{l l} \hline
**Category** & **Techniques** \\ \hline Decision trees & Fine tree \\  & Medium tree \\  & Coarse tree \\ \hline Discriminant analysis & Linear discriminant \\  & Quadratic discriminant \\ \hline Naive Bayes classifiers & Gaussian naive Bayes \\  & Kernel naive Bayes \\ \hline Support vector machines & Linear SVM \\  & Quadratic SVM \\  & Cubic SVM \\  & Fine Gaussian SVM \\  & Medium Gaussian SVM \\  & Coarse Gaussian SVM \\ \hline Nearest neighbor classifiers & Fine KNN \\  & Medium KNN \\  & Coarse KNN \\  & Cosine KNN \\  & Cubic KNN \\  & Weighted KNN \\ \hline Ensemble classifiers & Boosted trees \\  & Bagged trees \\  & Subspace discriminant \\  & Subspace KNN \\  & RUSBoost trees \\ \hline Neural network classifiers & Narrow neural network \\  & Medium neural network \\  & Wide neural network \\  & Bilayered neural network \\  & Trilayered neural network \\ \hline \end{tabular}
\end{table}
Table 2: List of machine learning techniques tested in this work.  
2.4.1. Model Selection and Implementation  
After evaluating the machine learning techniques, the method with the highest accuracy was selected for the implementation of DentalArch.  
2.4.2. Model Validation  
To validate the developed DentalArch software, we employed a k-fold cross-validation with a value of k equal to 5. This approach was chosen to rigorously assess the model's performance while preventing overfitting and ensuring its generalizability. In k-fold cross-validation, the dataset is divided into five distinct subsets, or \"folds\". The model is trained on four of these folds and tested on the remaining one in each iteration. This process is repeated five times, with a different fold serving as the test set in each iteration.  
While k-fold cross-validation is computationally demanding, it offers several advantages. It maximizes the use of available data, making it particularly valuable when dealing with limited sample sizes. By evaluating the model's performance across different subsets of data, we obtain a robust measure of its effectiveness and its ability to generalize to new, unseen data.