Topological Data Analysis and Graph-Based Learning for Multimodal Recommendation

Multimodal recommendation systems are becoming increasingly vital for delivering personalized content by utilizing various data sources, including text, images, and user interaction histories. However, current multimodal methods face challenges such as modality heterogeneity, data sparsity, and feature redundancy, which can result in less effective performance when dealing with complex, high-dimensional datasets. In this study, we present a new framework that combines Topological Data Analysis (TDA) with graph-based learning to improve multimodal recommendations (TDA-MMRec). Our approach captures higher-order dependencies and global structural patterns in multimodal data, enhancing the robustness and expressiveness of the representations we learn. By using persistent homology, we extract topological descriptors that convey stable structural information across different modalities, addressing the issues of sparsity and redundancy. We also introduce a modality-aware strategy for constructing graphs, which integrates features derived from TDA into multimodal similarity graphs to maintain both local and global structural properties. Furthermore, we propose a topological pruning technique that refines graph structures by removing redundant connections while preserving essential topological information, enhancing computational efficiency. Extensive experiments on large-scale multimodal datasets indicate that our TDA-augmented framework significantly outperforms leading multimodal recommendation models on key ranking metrics, including Precision@20, Recall@20, and NDCG@20. Our ablation studies confirm that topological descriptors are essential in boosting representation learning, especially in cold-start scenarios where traditional methods struggle due to data sparsity.