Hyperharmonic analysis for the study of high-order information-theoretic signals

• Published in: Journal of physic, complexity Vol. 2; no. 3; pp. 35009 - 35024
• Main Authors: Medina-Mardones, Anibal M, Rosas, Fernando E, Rodríguez, Sebastián E, Cofré, Rodrigo
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.09.2021
• Subjects: harmonic analysis; high-order phenomena; information theory; Laplace operator; signal processing
• ISSN: 2632-072X; 2632-072X
• DOI: 10.1088/2632-072X/abf231

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.