TopoEmbedX: A General Framework for Representation Learning on Topological Domains

arXiv (Cornell University)

Abstract

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.

Authors 6

1. Florian Frantzen Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

2. Ibrahem ALJabea

   Louisiana State University

   Affiliation as printed

   Louisiana State University

3. Inês Henriques-Cadby

   University of Manchester

   Affiliation as printed

   The University of Manchester

4. Theodore Papamarkou

   National Technical University of Athens

   Affiliation as printed

   National Technical University of Athens

   PolyShape

5. Mustafa Hajij

   University of San Francisco

   Affiliation as printed

   University of San Francisco

6. Michael T. Schaub Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University