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[Preprint]. 2024 Sep 14:arXiv:2409.09469v1.

Hyperedge Representations with Hypergraph Wavelets: Applications to Spatial Transcriptomics

Xingzhi Sun  1 , Charles Xu  1 , João F Rocha  1 , Chen Liu  1 , Benjamin Hollander-Bodie  1 , Laney Goldman  2 , Marcello DiStasio  1 , Michael Perlmutter  3 , Smita Krishnaswamy  1
Affiliations

Hyperedge Representations with Hypergraph Wavelets: Applications to Spatial Transcriptomics

Xingzhi Sun et al. ArXiv. .

Abstract

In many data-driven applications, higher-order relationships among multiple objects are essential in capturing complex interactions. Hypergraphs, which generalize graphs by allowing edges to connect any number of nodes, provide a flexible and powerful framework for modeling such higher-order relationships. In this work, we introduce hypergraph diffusion wavelets and describe their favorable spectral and spatial properties. We demonstrate their utility for biomedical discovery in spatially resolved transcriptomics by applying the method to represent disease-relevant cellular niches for Alzheimer's disease.

Keywords: Alzheimer’s disease; hyperedge; hypergraph; representation learning; spatial transcriptomics; wavelets.

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Figures

Fig. 1.
Fig. 1.
Conceptual illustrations. a. Creation of a hypergraph and the bipartite expansion. b. Diffusion (Lazy Random Walks) on the expanded graph.
Fig. 2.
Fig. 2.
We represent spatial transcriptomics data as a hypergraph. Physically proximate collections of cells play functional roles, motivating the use of hyperedges to represent cellular niches.
Fig. 3.
Fig. 3.
A. Hypergraphs clustered over tissue sample. B. PHATE [34] space colored by spectral clustering. C. Distribution of cell types on each cluster
Fig. 4.
Fig. 4.
Visualization of pairs of cellular neighborhood representations derived from hypergraph wavelets at different Braak stages, projected into two dimensions using PHATE [34]. Blue points represent cellular neighborhoods at the Braak stage indicated by the column name, while orange points correspond to the stage indicated by the row name.
See this image and copyright information in PMC

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