247 research outputs found
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
Mining a medieval social network by kernel SOM and related methods
This paper briefly presents several ways to understand the organization of a
large social network (several hundreds of persons). We compare approaches
coming from data mining for clustering the vertices of a graph (spectral
clustering, self-organizing algorithms. . .) and provide methods for
representing the graph from these analysis. All these methods are illustrated
on a medieval social network and the way they can help to understand its
organization is underlined
Optimizing an Organized Modularity Measure for Topographic Graph Clustering: a Deterministic Annealing Approach
This paper proposes an organized generalization of Newman and Girvan's
modularity measure for graph clustering. Optimized via a deterministic
annealing scheme, this measure produces topologically ordered graph clusterings
that lead to faithful and readable graph representations based on clustering
induced graphs. Topographic graph clustering provides an alternative to more
classical solutions in which a standard graph clustering method is applied to
build a simpler graph that is then represented with a graph layout algorithm. A
comparative study on four real world graphs ranging from 34 to 1 133 vertices
shows the interest of the proposed approach with respect to classical solutions
and to self-organizing maps for graphs
Neural Networks for Complex Data
Artificial neural networks are simple and efficient machine learning tools.
Defined originally in the traditional setting of simple vector data, neural
network models have evolved to address more and more difficulties of complex
real world problems, ranging from time evolving data to sophisticated data
structures such as graphs and functions. This paper summarizes advances on
those themes from the last decade, with a focus on results obtained by members
of the SAMM team of Universit\'e Paris
How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?
In numerous applicative contexts, data are too rich and too complex to be
represented by numerical vectors. A general approach to extend machine learning
and data mining techniques to such data is to really on a dissimilarity or on a
kernel that measures how different or similar two objects are. This approach
has been used to define several variants of the Self Organizing Map (SOM). This
paper reviews those variants in using a common set of notations in order to
outline differences and similarities between them. It discusses the advantages
and drawbacks of the variants, as well as the actual relevance of the
dissimilarity/kernel SOM for practical applications
Utiliser SOMbrero pour la classification et la visualisation de graphes
International audienceGraphs have attracted a burst of attention in the last years, with applications to social science, biology, computer science... In the present paper, we illustrate how self-organizing maps (SOM) can be used to enlighten the structure of the graph, performing clustering of the graph together with visualization of a simplified graph. In particular, we present the R package SOMbrero which implements a stochastic version of the so-called relational algorithm: the method is able to process any dissimilarity data and several dissimilarities adapted to graphs are described and compared. The use of the package is illustrated on two real-world datasets: one, included in the package itself, is small enough to allow for a full investigation of the influence of the choice of a dissimilarity to measure the proximity between the vertices on the results. The other example comes from an application in biology and is based on a large bipartite graph of chemical reactions with several thousands vertices.L'analyse de graphes a connu un intĂ©rĂȘt croissant dans les derniĂšres annĂ©es, avec des applications en sciences sociales, biologie, informatique, ... Dans cet article, nous illustrons comment les cartes auto-organisatrices (SOM) peuvent ĂȘtre utilisĂ©es pour mettre en lumiĂšre la structure d'un graphe en combinant la classification de ses sommets avec une visualisation simplifiĂ©e de celui-ci. En particulier, nous prĂ©sentons le package R SOMbrero dans lequel est implĂ©mentĂ©e une version stochastique de l'approche dite « relationnelle » de l'algorithme de cartes auto-organisatrices. Cette mĂ©thode permet d'utiliser les cartes auto-organisatrices avec des donnĂ©es dĂ©crites par des mesures de dissimilaritĂ© et nous discutons et comparons ici plusieurs types de dissimilaritĂ©s adaptĂ©es aux graphes. L'utilisation du package est illustrĂ©e sur deux jeux de donnĂ©es rĂ©elles : le premier, inclus dans le package lui-mĂȘme, est suffisamment petit pour permettre l'analyse complĂšte de l'influence du choix de la mesure de dissimilaritĂ© sur les rĂ©sultats. Le second exemple provient d'une application en biologie et est basĂ© sur un graphe biparti de grande taille, issu de rĂ©actions chimiques et qui contient plusieurs milliers de noeuds
Clustering a medieval social network by SOM using a kernel based distance measure
6 pagesInternational audienceIn order to explore the social organization of a medieval peasant community before the Hundred Years' War, we propose the use of an adaptation of the well-known Kohonen Self Organizing Map to dissimilarity data. In this paper, the algorithm is used with a distance based on a kernel which allows the choice of a smoothing parameter to control the importance of local or global proximities
On-line relational and multiple relational SOM
International audienceIn some applications and in order to address real-world situations better, data may be more complex than simple numerical vectors. In some examples, data can be known only through their pairwise dissimilarities or through multiple dissimilarities, each of them describing a particular feature of the data set. Several variants of the Self Organizing Map (SOM) algorithm were introduced to generalize the original algorithm to the framework of dissimilarity data. Whereas median SOM is based on a rough representation of the prototypes, relational SOM allows representing these prototypes by a virtual linear combination of all elements in the data set, referring to a pseudo-euclidean framework. In the present article, an on-line version of relational SOM is introduced and studied. Similarly to the situation in the Euclidean framework, this on-line algorithm provides a better organization and is much less sensible to prototype initialization than standard (batch) relational SOM. In a more general case, this stochastic version allows us to integrate an additional stochastic gradient descent step in the algorithm which can tune the respective weights of several dissimilarities in an optimal way: the resulting \emph{multiple relational SOM} thus has the ability to integrate several sources of data of different types, or to make a consensus between several dissimilarities describing the same data. The algorithms introduced in this manuscript are tested on several data sets, including categorical data and graphs. On-line relational SOM is currently available in the R package SOMbrero that can be downloaded at http://sombrero.r-forge.r-project.org or directly tested on its Web User Interface at http://shiny.nathalievilla.org/sombrero
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