Network representations often cannot fully account for the structural richness of complex systems spanning multiple levels of organisation. Recently proposed high-order information-theoretic signals are well-suited to capture synergistic phenomena that transcend pairwise interactions; however, the exponential-growth of their cardinality severely hinders their applicability. In this work, we combine methods from harmonic analysis and combinatorial topology to construct efficient representations of high-order information-theoretic signals. The core of our method is the diagonalisation of a discrete version of the Laplace-de Rham operator, that geometrically encodes structural properties of the system. We capitalise on these ideas by developing a complete workflow for the construction of hyperharmonic representations of high-order signals, which is applicable to a wide range of scenarios.
@article{arxiv.2010.01117,
title = {Hyperharmonic analysis for the study of high-order information-theoretic signals},
author = {Anibal M. Medina-Mardones and Fernando E. Rosas and Sebastián E. Rodríguez and Rodrigo Cofré},
journal= {arXiv preprint arXiv:2010.01117},
year = {2021}
}