Graph-Driven Multimodal Information Model for Robust Feature Fusion

Leveraging multimodal data, which includes a variety of imaging modalities, laboratory tests, and clinical records, has garnered significant interest in AI-based medical diagnostics and prognostics. Existing multimodal methodologies primarily strive to improve performance by exploiting either the unique or shared properties of different modalities, typically integrating features across these sources. We present a novel theoretical framework, Unified DMDFC-DA, that seamlessly integrates Dynamic Multimodal Data Filtration and Compression (DMDFC) with Domain Adaptation (DA) for robust multimodal learning across domains. Our approach addresses the fundamental challenges of information distillation and distribution alignment in a unified manner, providing a rigorous mathematical foundation for cross-domain, multimodal learning tasks. We derive a unified information-geometric bound that elegantly captures both the domain adaptation aspect through KL-divergence and the information distillation aspect via conditional mutual information, demonstrating how reducing domain discrepancy and distilling relevant information jointly contribute to improved generalization. Our theoretical analysis establishes asymptotic optimality with precise convergence rates, showing that the framework achieves perfect information distillation and domain alignment as the sample size approaches infinity. We prove a minimax lower bound that connects our framework to the fundamental limits of learning in domain adaptation scenarios, demonstrating its near-optimal performance. Leveraging advanced concepts from information theory, optimal transport, and statistical learning theory, we provide comprehensive generalization bounds and characterize the framework’s behavior in high-dimensional feature spaces. Extensive experiments on challenging multimodal medical datasets validate our theoretical findings, showcasing the framework’s superior performance and robustness compared to existing methods, particularly in scenarios with limited data and noisy or redundant modalities. This work establishes Unified DMDFC-DA as a principled and effective approach for multimodal domain adaptation tasks, with strong theoretical guarantees and practical efficacy in critical applications such as medical diagnostics and prognostics.