TopoEmbedX：拓扑域表示学习的通用框架

中文摘要 AI 辅助

拓扑结构，如单纯复形、超图和胞腔复形，通过建模高阶关系扩展了标准图模型。这些结构出现在许多现代数据集中，需要专门的方法来生成有意义的嵌入。在本文中，我们介绍了TopoEmbedX，一个将各种拓扑域嵌入到欧几里得空间的统一框架。该包汇集了现有的几种拓扑嵌入算法——DeepCell、Cell2Vec、CellDiff2Vec、HOLE和HOGLEE——并引入了五种新算法：ComplexNetMF、ComplexRep、ComplexRandNE、ComplexWalklets和ComplexHeat。这些算法使用拓扑域的增广Hasse图将著名的图嵌入技术扩展到高阶设置。TopoEmbedX为拓扑表示学习提供了一个清晰、一致且易于使用的框架。实验表明，TopoEmbedX生成的嵌入支持跨多维数据的分类和回归等任务。

英文摘要

Topological structures such as simplicial complexes, hypergraphs, and cell complexes extend standard graph models by modeling higher-order relationships. These structures appear in many modern datasets and require specialized methods for generating meaningful embeddings. In this paper, we introduce TopoEmbedX, a unified framework for embedding a wide range of topological domains into Euclidean spaces. The package brings together several existing topological embedding algorithms---DeepCell, Cell2Vec, CellDiff2Vec, HOLE, and HOGLEE---and introduces five new algorithms: ComplexNetMF, ComplexRep, ComplexRandNE, ComplexWalklets, and ComplexHeat. These algorithms extend well-known graph embedding techniques to higher-order settings using the augmented Hasse graph of a topological domain. TopoEmbedX provides a clear, consistent, and easy-to-use framework for topological representation learning. Experiments show that the embeddings generated by TopoEmbedX support tasks such as classification and regression across multidimensional data.

发表机构

• RWTH Aachen University（亚琛工业大学）
• Louisiana State University（路易斯安那州立大学）
• The University of Manchester（曼彻斯特大学）
• National Technical University of Athens（雅典国立技术大学）
• PolyShape
• University of San Francisco（旧金山大学）

机构由 AI 辅助整理，请以论文原文为准。