Batch kernel SOM and related Laplacian methods for social network analysis

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

On-line relational SOM for dissimilarity data

International audienceIn some applications and in order to address real world situations better, data may be more complex than simple vectors. In some examples, they can be known through their pairwise dissimilarities only. Several variants of the Self Organizing Map algorithm were introduced to generalize the original algorithm to this framework. Whereas median SOM is based on a rough representation of the prototypes, relational SOM allows representing these prototypes by a virtual combination of all elements in the data set. However, this latter approach suffers from two main drawbacks. First, its complexity can be large. Second, only a batch version of this algorithm has been studied so far and it often provides results having a bad topographic organization. In this article, an on-line version of relational SOM is described and justified. The algorithm is tested on several datasets, including categorical data and graphs, and compared with the batch version and with other SOM algorithms for non vector data

Self-Organizing Maps for clustering and visualization of bipartite graphs

National audienceGraphs (also frequently called networks) have attracted a burst of attention in the last years, with applications to social science, biology, computer science... The present paper proposes a data mining method for visualizing and clustering the nodes of a peculiar class of graphs: bipartite graphs. The method is based on a self-organizing map algorithm and relies on an extension of this approach to data described by a dissimilarity matrix

Algorithms for Hierarchical Clustering: An Overview, II

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm. This review adds to the earlier version, Murtagh and Contreras (2012)

Multiple kernel self-organizing maps

International audienceIn a number of real-life applications, the user is interested in analyzing several sources of information together: a graph combined with the additional information known on its nodes, numerical variables measured on individuals and factors describing these individuals... The combination of all sources of information can help him to understand the dataset in its whole better. The present article focuses on such an issue, by using self-organizing maps. The use a kernel version of the algorithm allows us to combine various types of information and automatically tune the data combination. This approach is illustrated on a simulated example