Hyperedge Representations with Hypergraph Wavelets: Applications to Spatial Transcriptomics

Xingzhi Sun, Charles Xu, João F. Rocha, Chen Liu, Benjamin Hollander-Bodie, Laney Goldman, Marcello DiStasio, Michael Perlmutter, Smita Krishnaswamy
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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.
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使用超图小波的 Hyperedge 表示法:空间转录组学应用
在许多数据驱动型应用中,多个对象之间的高阶关系对于捕捉复杂的相互作用至关重要。超图允许边连接任意数量的节点,从而对图进行了泛化,为此类高阶关系的建模提供了一个灵活而强大的框架。在这项工作中,我们介绍了超图扩散小波,并描述了其有利的频谱和空间特性。通过应用这种方法来表示阿尔茨海默病的疾病相关细胞龛,我们展示了它们在空间解析转录组学的生物医学发现中的实用性。
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