Full reconstruction of simplicial complexes from binary time-series data

Abstract

Previous efforts on data-based reconstruction focused on complex networks with pairwise or two-body interactions. There is a growing interest in networks with high-order or many-body interactions, raising the need to reconstruct such networks based on observational data. We develop a general framework combining statistical inference and expectation maximization to fully reconstruct 2-simplicial complexes with two- and three-body interactions based on binary time-series data from social contagion dynamics. We further articulate a two-step scheme to improve the reconstruction accuracy while significantly reducing the computational load. Through synthetic and real-world 2-simplicial complexes, we validate the framework by showing that all the connections can be faithfully identified and the full topology of the 2-simplicial complexes can be inferred. The effects of noisy data or stochastic disturbance are studied, demonstrating the robustness of the proposed framework.

Unveiling the higher-order organization of multivariate time series

“…Indeed, examples of these complex patterns are observed in the neuronal activity of the brain, supporting a wide variety of motor and cognitive functions [27,28], in financial markets, where partially synchronized patterns often reflect periods of financial stress [29,30], but also in the co-evolution of biological species [31][32][33]. While the inference of pairwise interactions has a long history [34], researchers have only recently taken the first steps towards reconstructing or filtering higher-order interactions [35][36][37]. To date, it remains unclear to what degree the information encoded in multivariate time series stems from independent individual entities or, rather, from their group interactions.…”