# Semi-Supervised Deep Subspace Embedding for Binary Classification of Sella Turcica
## 2 Materials and Methods
### Experimental Settings  
The proposed methodology is executed using Python 3.10, PyTorch 1.12.0, and CUDA 11.3 on a Windows 10 platform. All the input frames are resized to uniform dimensions of \(256\times 256\) pixels. The model is trained using the AdamW optimizer, with a learning rate of \(2.5\times 10^{-5}\) and a weight decay of \(10^{-4}\). AdamW is chosen for its improved weight decay management, which mitigates the overfitting risk by separating the decay factor from the gradient updates. The training process incorporates diffusion timesteps of \(T=1000\), employing a linear schedule that ranges from an initial \(\beta_{1}\) of \(10^{-4}\) to a final \(\beta_{T}\) of 0.02. The training is carried out on a Nvidia RTX 3080 GPU for 75,000 iterations, with batch sizes varying between 6 and 8, depending on the memory constraints.  
An important aspect of the study is selecting the appropriate evaluation methods for classification algorithms. In single-label learning, classification is viewed as correct or incorrect. However, binary or multilabel classification allows for partially correct or inaccurate results, enabling a more nuanced analysis [73]. Various metrics, including accuracy, recall, average precision, and F1 score, are employed to assess the model's performance. The confusion matrix provides insights into the distribution of true positives, false positives, true negatives, and false negatives during both the training and testing phases, offering a comprehensive view of the model's accuracy.  
The receiver operating characteristic (ROC) curve is used to evaluate the model's classification performance across our dataset and the IEEE ISBI 2015 datasets for testing and validation. The ROC curve effectively demonstrates the model's ability to differentiate between classes. Furthermore, t-SNE is employed as a dimensionality reduction technique. The t-SNE plot visually illustrates the model's capability to cluster bridging and non-bridging ST structures in a lower-dimensional space. t-SNE is integrated as an evaluation tool to provide a qualitative perspective on data separability and clustering, complementing quantitative metrics such as accuracy and the ROC curve.  
Following this, a detailed representation of the evaluation methods for SSLDSE is provided. Let \(SL=\{(SL_{i},SL_{j})\}_{i=1}^{n}\) denote a Hybrid Case Base dataset, where \(SL_{i}\) represents the labeled dataset, and \(h(L_{i})\) indicates the label classifier. The variable \(n\) denotes the total number of instances within the dataset, and \(I\lceil\cdot\rceil\) acts as the indicator function.  
Accuracy: It represents the proportion of labels that have been correctly classified:  
\[Accuracy=\frac{1}{n}\sum_{i=1}^{n}\biggl{(}\frac{\left|SL_{i}\cap h(L_{i}) \right|}{\left|SL_{i}\cup h(L_{i})\right|}\biggr{)}, \tag{7}\]  
Recall: It quantifies the average percentage of relevant labels correctly identified for instances classified as appropriate:  
\[Recall=\frac{1}{n}\sum_{i=1}^{n}\frac{\left|SL_{i}\cap h(L_{i})\right|}{\left| SL_{i}\right|}, \tag{8}\]Average Precision: It represents the mean proportion of relevant labels that are ranked higher than a particular label:  
\[\textit{Average precision}=\frac{1}{n}\sum_{i=1}^{n}\frac{1}{|SL_{i}^{l}|}\sum_{ sl_{i}\in SL_{i}^{l}}\frac{\left|\left\{\underline{sl_{q}\in SL_{i}^{l}:R_{i}( sl_{q}\leq R_{i}(sl_{i}))}\right\}\right|}{R_{i}(sl_{i})}, \tag{9}\]  
where \(R_{i}(sl_{i})\) represents the predicted rank of label \(sl_{i}\); for instance, \(l_{i}\). For each label \(sl_{i}\), precision is calculated as the ratio of correctly ranked labels \(sl_{q}\) (those with \(R_{i}(sl_{q})<R_{i}(sl_{i})\)) up to \(sl_{i}\), with the average taken across all instances and labels.  
F1 score: This metric, derived from precision and recall, offers a weighted evaluation. It is often considered a more reliable performance indicator than using precision and recall individually:  
\[\text{F1-score}=2\times\frac{\text{precision}\times\text{recall}}{\text{ precision}+\text{recall}}, \tag{10}\]