Hodge-Aware Contrastive Learning

A Möllers, A Immer, V Fortuin, E Isufi
ICASSP, 2024
Overview

Abstract

Simplicial complexes prove effective in modeling data with multi-way dependencies, such as data defined along the edges of networks or within other higher-order structures. Their spectrum can be decomposed into three interpretable subspaces via the Hodge decomposition, resulting foundational in numerous applications. We leverage this decomposition to develop a contrastive self-supervised learning approach for processing simplicial data and generating embeddings that encapsulate specific spectral information.

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