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

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.

25 pages, 16 Figures; a review of earlier works

References in corpus (20)

• Fast unfolding of communities in large networks
• Modularity and community structure in networks
• Maps of random walks on complex networks reveal community structure
• Resolution limit in community detection
• Comparing community structure identification
• Statistical Mechanics of Community Detection
• Emergence of network features from multiplexity
• Phase transition in the detection of modules in sparse networks
• Graph spectra and the detectability of community structure in networks
• Growing length and time scales in glass forming liquids
• Rigorous Inequalities between Length and Time Scales in Glassy Systems
• Limited resolution in complex network community detection with Potts model approach
• Think Locally, Act Locally: The Detection of Small, Medium-Sized, and Large Communities in Large Networks
• Orbital order in classical models of transition-metal compounds
• (Un)detectable cluster structure in sparse networks
• Probing a critical length scale at the glass transition
• Finding One Community in a Sparse Graph
• Community Detection in Complex Networks by Dynamical Simplex Evolution
• Temporal stability of network partitions
• Global disorder transition in the community structure of large-q Potts systems

Cited by in corpus (4)

• Graph Dynamical Networks for Unsupervised Learning of Atomic Scale Dynamics in Materials
• Machine Learning for Quantum Matter
• Machine-learning Iterative Calculation of Entropy for Physical Systems
• Learning to find order in disorder