Paper ID: 2410.22978

Graph Integration for Diffusion-Based Manifold Alignment

Jake S. Rhodes, Adam G. Rustad

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.

Submitted: Oct 30, 2024