Network Filtering for Big Data: Triangulated Maximally Filtered Graph

TL;DR

The paper introduces TMFG, a fast, scalable network-filtering method that constructs meaningful networks from large datasets, aiding clustering and community detection with online updating capabilities.

Contribution

It presents TMFG, a novel triangulation-based algorithm for network filtering that efficiently handles large data, supports online updates, and improves information retention.

Findings

TMFG is fast and scalable to large datasets.

Supports online updating with local and non-local moves.

Enhances network-based data analysis in big data contexts.

Abstract

We propose a network-filtering method, the Triangulated Maximally Filtered Graph (TMFG), that provides an approximate solution to the Weighted Maximal Planar Graph problem. The underlying idea of TMFG consists in building a triangulation that maximizes a score function associated with the amount of information retained by the network. TMFG uses as weights any arbitrary similarity measure to arrange data into a meaningful network structure that can be used for clustering, community detection and modeling. The method is fast, adaptable and scalable to very large datasets, it allows online updating and learning as new data can be inserted and deleted with combinations of local and non-local moves. TMFG permits readjustments of the network in consequence of changes in the strength of the similarity measure. The method is based on local topological moves and can therefore take advantage of parallel and GPUs computing. We discuss how this network-filtering method can be used intuitively and efficiently for big data studies and its significance from an information-theoretic perspective.