Jointly with researchers from EPFL in Switzerland and at CENTAI Institute in Italy, Federico Battiston, an Associate Professor in CEU’s Department of Network and Data Science, has recently developed a new mathematical and computational framework which allows for analysis of the higher-order organization of multivariate time series data. The higher-order approach was applied to human brain dynamics, financial markets and the spread of different diseases.
The work has been published in Nature Physics and follows another recent publication by Battiston on inferring community structure in networks with higher-order interactions, in Nature Communications.
“Pushing the boundaries of time series analysis towards new mathematical and computational horizons, the work has also the potential to impact fields such as ecology and climate change, where most data comes into the form of time series,” says Battiston.
A variety of diverse phenomena, including signals in the human brain, stock prices in financial markets, or COVID hospitalizations in different countries, are naturally encoded using time series data, that is repeated measurements over a given time interval. It might be natural to ask which regions of the brain activate together, which stocks follow similar price dynamics, and which countries have similar patterns of hospitalisations over time.
Most tools aimed to address such questions rely on pairwise statistics, taking into account the interaction between two variables at a time only. However, in the real-world many interactions are not limited to pairs, but involve three or more agents at a time. This is for instance what happens during epileptic seizures, when multiple regions of the brain get into an hypersynchronous state, suggesting that current pairwise approaches might not be properly suited to describe the dynamics of many real-world phenomena.
The method was able to extract a variety of features which cannot be captured by simple pairwise statistics, including oscillations between chaotic and synchronized neural interactions, early detections of stable or unstable financial periods, or classify different diseases such as flu and pertussis based on their spreading patterns.