Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment

TL;DR

FoSTA is a scalable manifold alignment method that uses forest-induced geometry to denoise data structures and improve cross-domain semantic alignment, especially in biological applications.

Contribution

It introduces a novel forest-guided approach for manifold alignment that enhances semantic structure recovery and alignment accuracy over traditional Euclidean-based methods.

Findings

Improves correspondence recovery in synthetic benchmarks

Enhances label transfer accuracy in biological data

Outperforms existing methods in practical applications

Abstract

Label-supervised manifold alignment bridges the gap between unsupervised and correspondence-based paradigms by leveraging shared label information to align multimodal datasets. Still, most existing methods rely on Euclidean geometry to model intra-domain relationships. This approach can fail when features are only weakly related to the task of interest, leading to noisy, semantically misleading structure and degraded alignment quality. To address this limitation, we introduce FoSTA (Forest-guided Semantic Transport Alignment), a scalable alignment framework that leverages forest-induced geometry to denoise intra-domain structure and recover task-relevant manifolds prior to alignment. FoSTA builds semantic representations directly from label-informed forest affinities and aligns them via fast, hierarchical semantic transport, capturing meaningful cross-domain relationships. Extensive comparisons with established baselines demonstrate that FoSTA improves correspondence recovery and label transfer on synthetic benchmarks and delivers strong performance in practical single-cell applications, including batch correction and biological conservation.