# Semi-Supervised Deep Subspace Embedding for Binary Classification of Sella Turcica
## 2 Materials and Methods
### Proposed Semi-Supervised Deep Subspace Embedding (SSLDSE) Architecture
#### 2.3.3 Enhancing Model Robustness with Zero-Shot Classifier  
The concluding phase of the proposed methodology, depicted through the detailed Figure 5 functional architectural framework, involves bolstering model resilience using a zero-shot classifier \(ZsC\) module guided by KL divergence loss [9]. This sophisticated model is engineered to recognize examples from categories absent during training, which is essential when data for certain classes are unavailable or limited. The \(ZsC\) utilizes semantic connections between familiar and unfamiliar classes, allowing the model to extrapolate beyond its training dataset. In our strategy, the classifier employs KL divergence loss to synchronize the learned embeddings with the distribution of known classes, thus enabling the identification of novel classes [71; 72]. **[Zero-Shot Classifier Integrated with KL Divergence]** To execute _ZsC_ using KL divergence loss, a CNN is initially trained on the existing data to extract significant features from the input examples. This pre-trained CNN produces robust feature representations \(f(x)\), which serve as the foundation for subsequent classification tasks. Each class, including both known and unknown categories, is characterized by a semantic vector. These vectors are constructed using deep visual features extracted from pre-trained CNNs and enhanced with supplementary information such as textual descriptions or hierarchical attributes. The semantic vectors encapsulate the characteristics and relationships among various classes within a high-dimensional semantic space, thereby enabling the model to deduce the existence of unseen classes based on their semantic resemblance to familiar categories. The KL divergence loss plays a crucial role in this process by assessing the difference between the predicted probability distribution of input data embeddings and the target distribution defined by semantic vectors of known classes. As outlined in Equation 2, the KL divergence measures the disparity between the predicted distribution \(P(Y_{i}\mid X)\) and the target distribution \(Q(Y_{i})\), and is defined as  
\[D_{KL}(P(Y_{i}\mid X)\parallel Q(Y_{i}))=\sum_{i}P(Y_{i}\mid X)\ln \left(\frac{P(Y_{i}\mid X)}{Q(Y_{i})}\right), \tag{6}\]  
This loss function guides the model in synchronizing the predicted embeddings \(Q_{i}\) with the semantic vectors, ensuring that network weights are adjusted to reduce divergence. This synchronization helps align the embeddings of known classes closely with their corresponding semantic vectors. Through iterative minimization of the KL divergence between predicted and target distributions, the model develops the ability to generalize effectively beyond the training data. This  
Figure 5: The illustrated SSLDSE architectural framework processes labeled (L) and semi-labeled (\(SL_{i}\)) data using Inception-ResNet-V2 as the CNN backbone to extract features (P, Q) and estimate pairwise probability densities (P\({}_{i,j}\), Q\({}_{i,j}\)). KL divergence (\(D_{\text{KL}}(P\parallel Q)\)) minimizes divergence through the optimization of (Y). Manifold learning maps feature matrices (X) to t-SNE representations (Y) while preserving structural relationships. The SSL framework employs deep embedding and clustering (mean: \(\mu_{j}\), covariance: \(\Sigma_{j}\)) for feature representation. The zero-shot classifier constructs semantic vectors and applies KL divergence loss for output prediction (\(O_{i}\)). enables the classifier to map embeddings \(q_{i}\) to appropriate class labels \(O_{i}\), even without explicit examples of those classes. The capacity to identify unseen classes is achieved by utilizing the semantic relationships encoded in the model, allowing it to deduce the existence of new classes based on their resemblance to known classes. This approach enhances the model's resilience and adaptability, enabling it to function effectively in varied and dynamic settings where new classes may continually emerge.