Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment

Label-supervised manifold alignment bridges the gap between unsupervised and correspondence-based paradigms by leveraging shared label information to align multimodal datasets. However, existing methods either rely on label-independent intra-domain geometry or incorporate supervision primarily through the alignment objective, rather than directly constructing task-aware intra-domain affinities. To address this limitation, we introduce FoSTA (Forest-guided Semantic Transport Alignment), which learns supervised forest geometries independently within each domain and uses their shared class-semantic structure to infer cross-domain correspondences without predefined anchors. FoSTA extends RF-GAP affinities to partially labeled data and aligns the resulting semantic representations through scalable hierarchical transport. Extensive comparisons with established baselines demonstrate strong correspondence recovery and semantic structure preservation on synthetic and real-world benchmarks, including multimodal data integration and single-cell batch correction.