Complementary roles of MRI, US, and CEUS. Magnetic resonance imaging (MRI) provides excellent soft tissue contrast and high diagnostic accuracy for preoperative assessment of myometrial and cervical invasion in endometrial cancer. Ultrasound (US) is the primary screening method due to its low cost and reasonable sensitivity; endometrial thickness below 5 mm carries a high negative predictive value. Contrast-enhanced ultrasound (CEUS) enables real-time microvascular imaging that neither standard US nor MRI can provide, making multimodal fusion theoretically superior to any single modality.
The missing modality problem. In clinical practice, not all patients have complete multi-modality data due to high examination costs, long MRI queuing times, or contrast agent contraindications. Conventional multi-modality fusion algorithms require complete data and must either discard incomplete patient records (wasting valuable diagnostic information) or impute missing values (introducing noise). With limited disease-specific datasets, discarding incomplete cases substantially increases overfitting risk.
Motivation for latent relation shared learning. A model that can exploit both complete and incomplete multi-modality samples simultaneously - learning a shared latent space that preserves modality-specific and cross-modality consistent features - would make full use of all available patient data without requiring complete records. This is particularly important for rare cancers where training data are inherently limited.
Clinical staging focus. The study focuses on differentiating endometrial cancer at stages IA, IB, and II. Stage IA and IB (sub-classes of FIGO stage I differing by depth of myometrial invasion) are clinically challenging to distinguish on imaging and require accurate preoperative assessment to guide surgical management, including the decision for lymphadenectomy.
Dataset composition. The TTHEC dataset comprised 117 endometrial cancer patients (mean age 55.3 years) from Beijing Tiantan Hospital, with 43 stage IA, 36 stage IB, and 38 stage II patients. An additional 1,228 normal uterine samples were collected as normal controls. Each patient sample included up to three imaging modalities: MRI, ultrasound, and CEUS, but not all patients had complete multi-modality data. CEUS had the highest missing rates (5.3%-7.0% across stages).
Three classification tasks. The study addressed three tasks of increasing complexity: (1) three-class classification (normal control vs. stage I vs. stage II), (2) four-class classification (normal control vs. stage IA vs. stage IB vs. stage II), and (3) binary classification (stage IA vs. stage IB). Stage IA vs. stage IB is clinically the most challenging distinction, as the two stages differ only in the depth of myometrial invasion.
Latent relation shared learning framework. The framework maps all complete and incomplete multi-modality samples into a shared latent space. For complete multi-modality data, a discriminative low-rank latent subspace model finds shared feature representations across all modalities simultaneously. For incomplete data, the framework extends this to incorporate partial modality information without discarding samples, using graph Laplacian regularization to preserve local geometric structure and prevent overfitting.
Baseline comparisons. The proposed method was compared against six baselines: KCCA and DCCA (canonical correlation analysis methods), MDcR (multi-view feature learning with Hilbert-Schmidt independence criterion), Least_iMSF and Logi_iMSF (incomplete multi-view learning with least-squared and logical loss), and iMVWL (incomplete multi-view weak-label learning). Evaluation used 10-fold cross-validation repeated 30 times, with accuracy, sensitivity, specificity, and AUC as metrics. Data augmentation (flipping, cropping, contrast modification, random noise) increased images from 117 to 3,158 samples.
Overall classification performance. The proposed method outperformed all six baselines across all three classification tasks. For NC vs. stage I vs. stage II, accuracy was 80.1% and AUC was 0.823. For NC vs. stage IA vs. stage IB vs. stage II, accuracy was 78.2% and AUC was 0.791. For the binary stage IA vs. stage IB task, accuracy reached 84.1% and AUC was 0.877 - the strongest result across all configurations.
Comparison to best baselines. The closest competing method was iMVWL, which achieved ACC 79.8% and AUC 0.813 for the three-class task, and ACC 82.5% and AUC 0.828 for the binary task. The proposed method improved binary task accuracy by 1.6 percentage points and AUC by 0.049 over iMVWL. Importantly, methods using only complete multi-modality data (KCCA, DCCA, MDcR) substantially underperformed incomplete multi-modality methods, confirming the value of using all available data.
Benefit of incomplete multi-modality learning over complete-only. The proposed method using incomplete data (ACC 80.1%) substantially outperformed its own complete-data-only variant (ACC 73.1%) in the three-class task, demonstrating that incomplete samples contain genuinely useful information that improves model performance when incorporated rather than discarded. This gap was consistent across all three tasks.
Effect of Laplacian regularization. Ablation removing the Laplacian regularization term reduced accuracy from 80.1% to 58.3% for the three-class task and from 84.1% to 67.7% for the binary task, confirming that graph Laplacian-based local geometric structure preservation is critical to the framework's performance and generalization ability.
Modality contribution analysis. Single-modality experiments showed that MRI alone achieved the highest individual performance: ACC 72.1% and AUC 0.818 for the three-class task, ACC 75.8% and AUC 0.862 for the binary task. US achieved ACC 70.1% and AUC 0.805, and CEUS achieved ACC 71.3% and AUC 0.815 for the three-class task. MRI maps the most effective information to the latent space among the three modalities.
Modality combination effects. Adding any second modality to MRI improved accuracy. MRI+CEUS (ACC 78.9%) outperformed MRI+US (ACC 78.5%) for the three-class task, consistent with CEUS providing more complementary vascular information than standard US. The full MRI+US+CEUS combination achieved the highest accuracy across all three tasks, confirming that each modality contributes unique, non-redundant information to the shared latent space.
Robustness under different missing rates. As the missing rate increased from 10% to 30%, all methods showed performance decreases, but the proposed method maintained the smallest declines. At 30% MRI missing rate for the binary task, the method achieved ACC 78.0% and AUC 0.800, compared to iMVWL's ACC 75.8% and AUC 0.781. The method demonstrated particularly strong robustness when US or CEUS were missing, compared to MRI missing scenarios.
MRI has the greatest impact when missing. Among the three modalities, missing MRI caused the largest performance drop compared to missing US or CEUS, confirming that MRI contributes the most distinctive and irreplaceable information to the latent space. This finding has practical implications: when only limited imaging is available, MRI should be prioritized if possible.
Multi-modality latent subspace formulation. The core framework maps original multi-modality feature matrices into a shared latent space V through basis matrices Uv for each modality, minimizing reconstruction error across all views simultaneously. A multi-label classifier W then maps from the label-dependent latent space to the output class labels. The optimization problem is not jointly convex and is solved using an alternating optimization approach that updates V, W, and Uv sequentially until convergence.
Graph Laplacian regularization. To preserve local geometric structure - similarity between nearby samples in the latent space - graph Laplacian regularization is incorporated using label similarity-based affinities computed from the p-nearest neighbors of each sample. This term prevents the latent subspace from losing topological relationships between similar patients, reducing overfitting and improving generalization. Removing this term dramatically degraded performance, confirming its critical role.
Incomplete multi-modality extension. The framework is extended to incomplete data by splitting the feature matrix for each modality into complete-sample and incomplete-sample components. Both are jointly projected into the shared latent space, allowing incomplete samples to contribute to learning the shared representation without introducing additional noise parameters. The Sylvester equation AV + VB = C provides an efficient closed-form solution for the latent variable update step.
Hyperparameter settings. Trade-off parameters alpha, beta, and gamma were set to 10^-1, 10^-1, and 10^-2 respectively to balance reconstruction error, Laplacian regularization, and classifier regularization. The latent subspace dimension k was set to 1000, and the nearest neighbor number p was set to 20. These values were determined through systematic ablation experiments analyzing the sensitivity of model accuracy and AUC to each parameter.
Core contribution. This study proposes the first incomplete multi-modality fusion method for endometrial cancer staging that combines MRI, US, and CEUS without requiring complete datasets. The latent relation shared framework achieves 84.1% accuracy and AUC 0.877 for the clinically critical stage IA vs. stage IB differentiation, outperforming all six competing methods while handling missing modality rates up to 30%.
Clinical deployment advantages. Unlike methods that discard incomplete records, the framework makes full use of all available patient imaging, which is essential for rare cancers with inherently limited training data. The method's robustness under high missing rates directly addresses a major real-world barrier to multi-modality AI deployment in hospitals where not all patients can access all imaging modalities.
Limitations and future work. The dataset was limited to 117 EC patients from a single center, restricting generalizability. Only endometrial cancer staging was annotated, excluding patients with other concurrent uterine pathologies. Future work will explore fusion of imaging data with medical text data and extend the framework to incorporate disease correlations with other gynecological conditions to further improve four-class classification accuracy.