Batch kernel SOM and related Laplacian methods for social network analysis

TL;DR

This paper introduces a kernel-based batch Self Organizing Map method utilizing Laplacian-derived kernels to analyze large social network graphs, aiding in discovering community structures and relationships.

Contribution

It presents a novel application of kernel SOM combined with Laplacian spectral methods for social network analysis, enhancing understanding of graph structures.

Findings

Effective in revealing community structures in social networks

Combines kernel SOM with spectral graph analysis for improved insights

Applied successfully to medieval social network data

Abstract

Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic tools are required to get a synthetic view of the graph and to reach a good understanding of the underlying problem. In particular, discovering groups of tightly connected vertices and understanding the relations between those groups is very important in practice. This paper shows how a kernel version of the batch Self Organizing Map can be used to achieve these goals via kernels derived from the Laplacian matrix of the graph, especially when it is used in conjunction with more classical methods based on the spectral analysis of the graph. The proposed method is used to explore the structure of a medieval social network modeled through a weighted graph that has been directly built from a large corpus of agrarian contracts.