Topoembedx framework enables learning from complex higher order data
TopoEmbedX: A General Framework for Representation Learning on Topological Domains
Machine Learning
Summary
Some datasets involve complex relationships that go beyond simple pairwise connections, such as groups interacting together rather than just pairs. The authors introduce TopoEmbedX, a software framework that can convert these complicated topological structures into simple numeric forms called embeddings. These embeddings help computers understand and work with such complex data for tasks like classification or predicting outcomes. TopoEmbedX combines existing methods and adds new algorithms to do this uniformly for many types of structures.
What this means in practice
- •For data scientists: Use TopoEmbedX to embed complex relational data for improving classification and regression models.
- •For network analysts: Analyze higher-order relationships in network data with embeddings from TopoEmbedX to reveal patterns beyond simple graphs.
Authors
Florian Frantzen, Ibrahem AlJabea, Ines Henriques-Cadby, Theodore Papamarkou, Mustafa Hajij, Michael T. Schaub
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.