# View-Aware Contrastive Learning for Incomplete Tabular Data with Low-Label Regimes
## 3 Materials and Method
### Data Augmentation
Given a missing feature \(x_{i}\) and a neighborhood \(N_{i}\) of the sample, the imputed value is calculated as  
\[\hat{x}_{i}=\frac{\sum_{j\in N_{i}}w_{ij}x_{i,j}}{\sum_{j\in N_{i}}w_{ij}}, \tag{2}\]  
where \(w_{ij}\) denotes the similarity-based weight between sample \(i\) and \(j\) and where \(x_{i,j}\) is the observed value of feature \(i\) in sample \(j\). This approach helps to preserve local data structure and mitigates the information loss associated with simple imputation. Standardization is another widely used preprocessing technique in machine learning, particularly when features have different units or scales. It transforms features to a standard range, which facilitates convergence and improves training stability. The standardization process involves subtracting the mean and dividing by the standard deviation:  
\[x_{i}^{\prime}=\frac{x_{i}-\mu_{i}}{\sigma_{i}} \tag{3}\]  
where \(x_{i}^{\prime}\) is the standardized value, \(x_{i}\) is the original feature value, and \(\mu_{i}\) and \(\sigma_{i}\) respectively denote the mean and standard deviation of feature \(i\). This normalization ensures that all features contribute equally during model training, avoiding dominance by features with larger magnitudes. For categorical variables, common encoding techniques include label encoding and embedding mappings. While label encoding assigns integer values to categories, it may introduce unintended ordinal relationships. Thus, embedding mappings are preferred for unordered categories, especially in deep learning. The key idea is to represent each category with a dense vector in a continuous space. For \(C\) categories, the embedding process is defined as follows:  
\[\mathbf{e}_{c}=\text{Emb}(\text{Category}(c)) \tag{4}\]  
where \(\mathbf{e}_{c}\in\mathbb{R}^{d}\) is the embedding vector for category \(c\) and Emb represents the embedding layer. These embeddings are learnable parameters within the network, enabling the model to capture semantic relationships among categories while maintaining context. Data augmentation is a technique used to enhance model generalization by generating synthetic training samples. In SSL, it not only expands the training distribution but also encourages the model to learn robust and generalizable patterns. For structured data, effective augmentation strategies include feature subset resampling, feature masking, additive noise injection, and GANSO [52]. Feature subset resampling involves randomly selecting subsets of features to create diverse training instances. This encourages the model to focus on varying combinations of input dimensions, thereby mitigating overfitting and promoting robustness. The process can be expressed as follows:  
\[\tilde{x}=x[S] \tag{5}\]  
where \(S\) denotes a randomly selected subset of features and \(\tilde{x}\) represents the resulting sample. By repeatedly sampling different subsets, the model learns from a wider range of feature patterns and has improved generalization to unseen data. Feature masking is another widely adopted augmentation strategy, and is particularly effective in self-supervised settings. During training, a subset of features is randomly masked and the model is tasked with reconstructing the features from the remaining context. This forces the model to capture inter-feature dependencies and enhances its robustness against missing data. The reconstruction can be formulated as  
\[\hat{x}_{i}=f(x_{\backslash i};\theta), \tag{6}\]  
where \(x_{\backslash i}\) is the input with the \(i\)-th feature masked, \(\hat{x}_{i}\) is the predicted value, \(f\) is the mapping function, and \(\theta\) denotes model parameters. This strategy enables the model to infer missing information from partial observations, which is crucial when dealing with real-world incomplete datasets. The technique of additive noise injection improves robustness by simulating real-world perturbations during training. Random noise sampled from a predefined distribution is added to the input features, creating noisy variations that the model must learn to tolerate.