Inference of hidden structures in complex physical systems by multi-scale clustering

TL;DR

This paper explores the use of community detection, a statistical physics approach, for identifying hidden structures in complex physical systems through multi-scale clustering, with applications in materials diagnosis and image segmentation.

Contribution

It introduces a multiresolution community detection method to uncover structures at various scales in complex systems, highlighting its phase behavior and correlation analysis.

Findings

Community detection reveals significant patterns at multiple scales.

The method exhibits phase transitions similar to NP-hard problems.

Correlations between solvers enhance structure identification.

Abstract

We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the quest of partitioning a complex system involving many elements into optimally decoupled subsets or communities of such elements. We review a multiresolution variant which is used to ascertain structures at different spatial and temporal scales. Significant patterns are obtained by examining the correlations between different independent solvers. Similar to other combinatorial optimization problems in the NP complexity class, community detection exhibits several phases. Typically, illuminating orders are revealed by choosing parameters that lead to extremal information theory correlations.