# Semi-Supervised Deep Subspace Embedding for Binary Classification of Sella Turcica
## 2 Materials and Methods
### Proposed Semi-Supervised Deep Subspace Embedding (SSLDSE) Architecture
#### 2.3.2 Semi-Supervised Learning with Deep Subspace Descriptor  
In typical classification tasks, a CNN is designed to generate predictions \(p_{i}\) for \(i=1,...,n\) by utilizing a labeled dataset \(SL_{i}=\{SL_{i}\in SL\}_{1}^{n}\). This is achieved by mapping a high-dimensional data space \(SL\) to a smaller space using techniques such as max-pooling and fully convolutional layers. As the dimensions of each layer are reduced, the essential information of the data is distilled, effectively transforming each layer into a feature embedding of the data. On the other hand, clustering algorithms aim to organize an unlabeled dataset \(SL_{i}=\{SL_{i}\in SL\}_{1}^{n}\) into \(x\) clusters, represented by their means \(\mu_{j}\) for \(j=1,...,k\). Unlike supervised CNNs, clustering algorithms do not require labels to form clusters [24]. However, they suffer from the curse of dimensionality and perform better when the dimensionality of data space \(SL\) is reduced. The primary goal of this study is to combine the advantages of both methods: the powerful capabilities of a deep CNN and the label-free clustering capabilities of a robust clustering algorithm based on unsupervised deep embedding [66]. By merging these approaches, the study addresses the limitations typically associated with clustering algorithms [67; 68]. Within this framework, the CNN learns a mapping from data \(SL\) to a lower-dimensional embedding \(Z\). At the same time, the clustering algorithm groups the data points into clusters from this lower-dimensional embedding. These two tasks--embedding, learning, and clustering--are conducted simultaneously. [Algorithmic Framework]The framed algorithm follows this structure by applying stochastic augmentation to dataset SL, then processing it through a transfer learning approach using the Inception-ResNet-v2 network with fine-tuning and dropout [59; 60; 61]. The output from this network is then passed through a deep subspace descriptor, specifically, the deep embedding clustering algorithm [69; 70], which further reduces the dimensionality and generates embeddings \(SL_{i}\) as illustrated in Figure 4.  
To effectively integrate labeled and unlabeled data, our approach employs a sophisticated semi-supervised learning framework that maximizes the utility of both datasets. This integration occurs through several key steps:  
* Data Augmentation: Both labeled \(SL_{i}\) and unlabeled \(SL_{i}\) datasets undergo stochastic augmentation. This step enhances the diversity and robustness of the training samples by introducing variations in the data, such as rotations, translations, and noise, which helps the model generalize better to unseen data. * Feature Extraction: Features from both labeled and unlabeled datasets are extracted using the Inception-ResNet-v2 network. This deep learning model is fine-tuned to adapt to the specific task at hand, ensuring that the extracted features are relevant and informative for distinguishing between bridging and non-bridging ST shapes. * Joint Training: The extracted features from both datasets are jointly utilized in the training process. The model performs supervised learning for the labeled data \(SL_{i}\), using the ground truth labels to guide the learning process. This helps the model to learn the direct mappings from input features to the desired output labels. Simultaneously, the unlabeled data \(SL_{i}\) are used in unsupervised learning, where the model learns to identify and group similar patterns within the data. This unsupervised learning process aids in discovering the underlying structure of the data, which might not have been apparent from the labeled data alone. Figure 4: The figure illustrates a comprehensive framework of the proposed SSLOSE that integrates labeled (\(SL_{i}\)) and unlabeled case databases (\(SL_{i}\)). Features are extracted using Kullback–Leibler divergence, mean (\(\mu\)), and standard deviation (\(\sigma\)), forming a Hybrid Database. The data undergo stochastic augmentation and are processed through an Inception-ResNet-V2 model.