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Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment

Adrien Aumon, Myriam Lizotte, Guy Wolf, Kevin R. Moon, Jake S. Rhodes

TL;DR

FoSTA introduces forest-guided semantic transport for label-supervised manifold alignment, replacing Euclidean intra-domain geometry with task-adaptive forest affinities and using fast semantic transport via HiRef to infer cross-domain correspondences under partial labels. It constructs semantic representations from forest-based affinities, solves a scalable optimal transport problem in semantic space, and propagates correspondences to form cross-domain affinities before embedding with Landmark PHATE. The method achieves superior label transfer and correspondence recovery on synthetic benchmarks and strong biological conservation with competitive batch correction in single-cell data, highlighting the practical benefits of task-aware geometry for scalable multimodal alignment. By avoiding dense OT and diffusion preprocessing, FoSTA delivers near-linear scalability and robust performance in realistic partially labeled settings, with clear directions for extending to partially overlapping label spaces and alternative transport formulations.

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.

Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment

TL;DR

FoSTA introduces forest-guided semantic transport for label-supervised manifold alignment, replacing Euclidean intra-domain geometry with task-adaptive forest affinities and using fast semantic transport via HiRef to infer cross-domain correspondences under partial labels. It constructs semantic representations from forest-based affinities, solves a scalable optimal transport problem in semantic space, and propagates correspondences to form cross-domain affinities before embedding with Landmark PHATE. The method achieves superior label transfer and correspondence recovery on synthetic benchmarks and strong biological conservation with competitive batch correction in single-cell data, highlighting the practical benefits of task-aware geometry for scalable multimodal alignment. By avoiding dense OT and diffusion preprocessing, FoSTA delivers near-linear scalability and robust performance in realistic partially labeled settings, with clear directions for extending to partially overlapping label spaces and alternative transport formulations.

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.
Paper Structure (22 sections, 25 equations, 3 figures, 4 tables)

This paper contains 22 sections, 25 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Guided manifold learning with tree ensembles
  4. Manifold alignment approaches
  5. Methods
  6. Problem formulation
  7. Label-informed intra-domain affinities
  8. Learning correspondences via semantic transport
  9. Cross-domain affinities through correspondence propagation
  10. Joint embedding
  11. Complexity analysis
  12. Empirical Results
  13. Multimodal alignment for data integration
  14. Batch effect removal in single-cell genomics
  15. Conclusion and discussion
  16. ...and 7 more sections

Figures (3)

  • Figure 1: Overview of FoSTA. (a) Given two (partially labeled) domains $\mathcal{X}_A$ and $\mathcal{X}_B$, we compute semi-supervised, label-informed RF-GAP intra-domain affinities $W_A$ and $W_B$ to capture task-relevant neighborhood structure (Section \ref{['subsec:intradomain']}). (b) We form class-wise semantic profiles and map samples from both domains to a shared, $\ell_2$-normalized semantic space, which defines a cross-domain semantic cost (Section \ref{['subsec:transport']}). (c) Using this cost, HiRef estimates an efficient bijective transport plan $\mathbf{T}$ between domains (Section \ref{['subsec:transport']}). (d) We propagate correspondences through $\mathbf{T}$ to build cross-domain affinities $W_{AB}$ and $W_{BA}$ consistent with the intra-domain graphs (Section \ref{['subsec:cross-domain']}). (e) Finally, we compute a joint low-dimensional embedding from the resulting block affinity matrix (Section \ref{['subsec:joint_embedding']}).
  • Figure 2: Biological preservation (bio) vs. batch correction (batch) scores lueckenBenchmarkingAtlaslevelData2022 for simulated batch effect removal on lung single-cell data vieirabragaCellularCensusHuman2019. The legend is ordered according to average method ranks in these two aspects, with FoSTA leading the average ranking (as 1st in bio and 3rd in batch) followed by scANVI (1st in batch but 4th in bio) and others.
  • Figure 3: Embeddings of the simulated batch integration task. Left column: data before correcting for batch effects, visualized with RF-PHATE rhodes2023gaining supervised by cell type labels. Right column: resulting embbedding after applying FoSTA to correct the batch effects. The plots are colored by simulated batch (top), and cell type (bottom). FoSTA mixes the batches well, while preserving the biological structure of the data.