Optimizing Functional Network Representation of Multivariate Time Series

Abstract

By combining complex network theory and data mining techniques, we provide objective criteria for optimization of the functional network representation of generic multivariate time series. In particular, we propose a method for the principled selection of the threshold value for functional network reconstruction from raw data, and for proper identification of the network's indicators that unveil the most discriminative information on the system for classification purposes. We illustrate our method by analysing networks of functional brain activity of healthy subjects, and patients suffering from Mild Cognitive Impairment, an intermediate stage between the expected cognitive decline of normal aging and the more pronounced decline of dementia. We discuss extensions of the scope of the proposed methodology to network engineering purposes, and to other data mining tasks.

Functional brain networks: great expectations, hard times and the big leap forward

“…Once a series of network metrics are calculated, neuroscientists face the arduous problem of understanding what properties are important [93].…”

“…The amount of information codified in each network can be approximated by the success score achieved in a classification task, where a model is trained to identify subjects belonging to the two considered classes [93]. Not only does this strategy allow identifying the combinations of properties obtaining higher classification scores, but it also affords a quantitative assessment of the degree to which these properties actually discriminate between different experimental conditions.…”

“…First, too high a threshold can prevent the convergence of the sample distribution to the true asymptotic one and therefore the emergence of the corresponding macroscopic property. The percentage of considered links may also not be the one which optimizes data classification based on network properties, and where classification is robust to fluctuations in network parameters [93].…”

“…A qualitatively different strategy consists of selecting the threshold level that optimizes some criterion, e.g. data classification [93].…”

Complex network theory and the brain

“…How to best segment or parcellate the anatomical space and how to accurately sample the underlying dynamical system are two of the main issues encountered. Functional connectivity is generally defined using statistical relationships between activity recorded at different brain sites or sensors, but there is as yet no universally accepted criterion for choosing the most appropriate metric of brain activity out of the set of available ones, and the question of how different connectivity metrics affect the topological properties of the resulting networks is still poorly understood [28,29].…”