# View-Aware Contrastive Learning for Incomplete Tabular Data with Low-Label Regimes
## 3 Materials and Method
### Proposed Method
#### 3.3.1 Multi-View Encoder  
Within the proposed SSL framework, the multi-view encoder serves as a core component responsible for partitioning and encoding feature subspaces of structured sparse inputs. Its design aims to uncover latent structural information from diverse feature combinations across multiple perspectives, thereby enhancing the generalization capability in downstream representation learning and predictive tasks. As illustrated in Figure 1, the original input is represented by a rating matrix \(R_{d}\in\mathbb{R}^{u_{d}\times l_{d}}\), where \(u_{d}\) denotes the number of users and \(I_{d}\) is the number of items. Because such matrices typically contain substantial missing values, direct encoding would result in incomplete information and reduced representational capacity. To address this, a Gumbel-Softmax module is introduced to perform multi-view partitioning of the original features in a differentiable manner. This module applies soft sampling to split \(R_{d}\) along the feature dimension into \(k\) subspaces, resulting in submatrices \(\tilde{R}_{d}^{1}\), \(\tilde{R}_{d}^{2},\ldots,\tilde{R}_{d}^{k}\). This approach retains global semantic structure while introducing perturbations that enrich representational diversity, simulating potential latent subfeature distributions found in practice. Each submatrix is then passed through a structurally identical but independently parameterized encoder network \(g_{i}(\cdot)\) to generate the corresponding latent representation \(z_{d}^{i}=g_{i}(\tilde{R}_{d}^{i})\), where \(i=1,\ldots,k\).  
Each encoder adopts a two-layer nonlinear feedforward neural network. The first layer performs a linear transformation with hidden dimensionality \(d_{\text{hidden}}=128\), followed by a ReLU activation. The second layer maps the output to a latent vector of dimension \(d_{\text{latent}}=64\). The complete encoding operation is formally defined as follows:  
\[z_{d}^{i}=g_{i}(\tilde{R}_{d}^{i})=\text{ReLU}(W_{2}^{(i)}\cdot\text{ReLU}(W _{1}^{(i)}\cdot\text{vec}(\tilde{R}_{d}^{i})+b_{1}^{(i)})+b_{2}^{(i)}) \tag{9}\]  
where \(W_{1}^{(i)}\in\mathbb{R}^{128\times n_{i}}\) and \(W_{2}^{(i)}\in\mathbb{R}^{64\times 128}\), while \(n_{i}\) represents the flattened dimension of \(\tilde{R}_{d}^{i}\). This decoupling strategy enables each view to independently capture higher-order feature correlations within its subspace while mitigating the risk of representation bias due to dominant features. The multi-view encoder design offers both theoretical significance and practical value. First, by introducing subspace-level distribution perturbations, it improves the model's robustness under diverse augmentation strategies and alleviates disruptions caused by missing entries in tabular data. Second, although all views share the same architectural design, their parameters remain unshared. This enables each to learn unique statistical patterns during training, enhancing the discriminative power of latent representations. Furthermore, the collection of \(z_{d}^{i}\) embeddings serves as input for subsequent contrastive learning and weighted fusion, facilitating the construction of interpretable and disentangled multimodal embedding spaces. In practice, the number of views \(k\) and the feature subset size for each view are treated as critical hyperparameters. Experimental results demonstrate that a moderate increase in \(k\) enhances the model's capacity to characterize complex structural patterns, while excessive partitioning leads to overly sparse subspaces, with a negative impact on encoder performance. Therefore, \(k\) is empirically set to 4, with each encoder receiving a randomly sampled 25% of the feature set. A joint optimization involving contrastive loss and masked prediction loss ensures that all view-specific embeddings converge toward a unified semantic space.  
Figure 1: Illustration of the view-disentangled encoder module. \(\otimes\) means dot and \(\oplus\) means plus.