Multilevel Hierarchical Kernel Spectral Clustering for Real-Life Large Scale Complex Networks

TL;DR

This paper introduces a multilevel hierarchical kernel spectral clustering method tailored for large-scale complex networks, enabling efficient detection of multi-level community structures with high quality at various granularities.

Contribution

The paper presents a novel hierarchical clustering approach based on kernel spectral clustering that automatically determines multiple hierarchy levels in large networks.

Findings

Effective detection of multi-level hierarchies in real-world networks

Outperforms state-of-the-art methods like Louvain, OSLOM, and Infomap

Identifies high-quality clusters at multiple scales

Abstract

Kernel spectral clustering corresponds to a weighted kernel principal component analysis problem in a constrained optimization framework. The primal formulation leads to an eigen-decomposition of a centered Laplacian matrix at the dual level. The dual formulation allows to build a model on a representative subgraph of the large scale network in the training phase and the model parameters are estimated in the validation stage. The KSC model has a powerful out-of-sample extension property which allows cluster affiliation for the unseen nodes of the big data network. In this paper we exploit the structure of the projections in the eigenspace during the validation stage to automatically determine a set of increasing distance thresholds. We use these distance thresholds in the test phase to obtain multiple levels of hierarchy for the large scale network. The hierarchical structure in the network is determined in a bottom-up fashion. We empirically showcase that real-world networks have multilevel hierarchical organization which cannot be detected efficiently by several state-of-the-art large scale hierarchical community detection techniques like the Louvain, OSLOM and Infomap methods. We show a major advantage our proposed approach i.e. the ability to locate good quality clusters at both the coarser and finer levels of hierarchy using internal cluster quality metrics on 7 real-life networks.