# Graph Integration for Diffusion-Based Manifold Alignment

arXiv: https://arxiv.org/abs/2410.22978 · HTML: https://mlsanity.com/paper/2410.22978/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Builds on (most cited first, 9 of 9)

- [MAGAN: Aligning Biological Manifolds](https://mlsanity.com/paper/1803.00385/) (2018)
- [Kernel Manifold Alignment](https://mlsanity.com/paper/1504.02338/) (2015)
- [Diffusion Transport Alignment](https://mlsanity.com/paper/2206.07305/) (2022)
- [Manifold Matching using Shortest-Path Distance and Joint Neighborhood Selection](https://mlsanity.com/paper/1412.4098/) (2014)
- [MultiView Diffusion Maps](https://mlsanity.com/paper/1508.05550/) (2015)
- [Harmonic Alignment](https://mlsanity.com/paper/1810.00386/) (2018)
- [Manifold Alignment with Label Information](https://mlsanity.com/paper/2210.12774/) (2022)
- [Visualizing High Dimensional Dynamical Processes](https://mlsanity.com/paper/1906.10725/) (2019)
- [Practical Cross-modal Manifold Alignment for Grounded Language](https://mlsanity.com/paper/2009.05147/) (2020)

## Built on by (most cited first, 4 of 4)

- [DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation](https://mlsanity.com/paper/2602.00656/) (2026)
- [Random Forest-Supervised Manifold Alignment](https://mlsanity.com/paper/2411.15179/) (2024)
- [Guided Manifold Alignment with Geometry-Regularized Twin Autoencoders](https://mlsanity.com/paper/2509.22913/) (2025)
- [Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment](https://mlsanity.com/paper/2602.00974/) (2026)

## Abstract (arXiv)

Data from individual observations can originate from various sources or modalities but are often intrinsically linked. Multimodal data integration can enrich information content compared to single-source data. Manifold alignment is a form of data integration that seeks a shared, underlying low-dimensional representation of multiple data sources that emphasizes similarities between alternative representations of the same entities. Semi-supervised manifold alignment relies on partially known correspondences between domains, either through shared features or through other known associations. In this paper, we introduce two semi-supervised manifold alignment methods. The first method, Shortest Paths on the Union of Domains (SPUD), forms a unified graph structure using known correspondences to establish graph edges. By learning inter-domain geodesic distances, SPUD creates a global, multi-domain structure. The second method, MASH (Manifold Alignment via Stochastic Hopping), learns local geometry within each domain and forms a joint diffusion operator using known correspondences to iteratively learn new inter-domain correspondences through a random-walk approach. Through the diffusion process, MASH forms a coupling matrix that links heterogeneous domains into a unified structure. We compare SPUD and MASH with existing semi-supervised manifold alignment methods and show that they outperform competing methods in aligning true correspondences and cross-domain classification. In addition, we show how these methods can be applied to transfer label information between domains.