26537 articles – 20365 references  [version française]
Detailed view Article in peer-reviewed journal
Neurocomputing / EEG Neurocomputing 71, 7-9 (2008) 1257-1273
Attached file list to this document: 
PS
villa_etal_N2007.ps(5.5 MB)
PDF
villa_etal_N2007.pdf(933 KB)
Batch kernel SOM and related Laplacian methods for social network analysis
Romain Boulet1, Bertrand Jouve1, Fabrice Rossi2, Nathalie Villa1

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.
1:  IMT - Institut de Mathématiques de Toulouse
2:  INRIA Rocquencourt / INRIA Sophia Antipolis - AxIS
self-organizing map – kernel methods – graphs – data mining – Laplacian – diffusion matrix – spectral clustering