Drawing Clustered Graphs as Topographic Maps

The visualization of clustered graphs is an essential tool for the analysis of networks, in particular, social networks, in which clustering techniques like community detection can reveal various structural properties. In this paper, we show how clustered graphs can be drawn as topographic maps, a type of map easily understandable by users not familiar with information visu- alization. Elevation levels of connected entities correspond to the nested structure of the cluster hierarchy. We present methods for initial node placement and describe a tree mapping based algorithm that produces an area efficient layout. Given this layout, a triangular ir- regular mesh is generated that is used to extract the elevation data for rendering the map. In addition, the mesh enables the routing of edges based on the topo- graphic features of the map

MolMap - Visualizing Molecule Libraries as Topographic Maps

We present a new application for graph drawing and visualization in the context of drug discovery. Combining the scaffold-based cluster hierarchy with molecular similarity graphs — both standard concepts in cheminfor- matics — allows one to get new insights for analyzing large molecule libraries. The derived clustered graphs represent different aspects of structural similarity. We suggest visualizing them as topographic maps. Since the cluster hierarchy does not reflect the underlying graph structure as in (Gronemann and Jünger, 2012), we suggest a new partitioning algorithm that takes the edges of the graph into account. Experiments show that the new algorithm leads to significant improvements in terms of the edge lengths in the obtained drawings

MolMap - Visualizing Molecule Libraries as Topographic Maps

We present a new application for graph drawing and visualization in the context of drug discovery. Combining the scaffold-based cluster hierarchy with molecular similarity graphs — both standard concepts in cheminfor- matics — allows one to get new insights for analyzing large molecule libraries. The derived clustered graphs represent different aspects of structural similarity. We suggest visualizing them as topographic maps. Since the cluster hierarchy does not reflect the underlying graph structure as in (Gronemann and Jünger, 2012), we suggest a new partitioning algorithm that takes the edges of the graph into account. Experiments show that the new algorithm leads to significant improvements in terms of the edge lengths in the obtained drawings

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

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

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 intérêt croissant dans les dernières années, avec des applications en sciences sociales, biologie, informatique, ... Dans cet article, nous illustrons comment les cartes auto-organisatrices (SOM) peuvent être utilisées pour mettre en lumière la structure d'un graphe en combinant la classification de ses sommets avec une visualisation simplifiée de celui-ci. En particulier, nous présentons le package R SOMbrero dans lequel est implémentée une version stochastique de l'approche dite « relationnelle » de l'algorithme de cartes auto-organisatrices. Cette méthode permet d'utiliser les cartes auto-organisatrices avec des données décrites par des mesures de dissimilarité et nous discutons et comparons ici plusieurs types de dissimilarités adaptées aux graphes. L'utilisation du package est illustrée sur deux jeux de données réelles : le premier, inclus dans le package lui-même, est suffisamment petit pour permettre l'analyse complète de l'influence du choix de la mesure de dissimilarité sur les résultats. Le second exemple provient d'une application en biologie et est basé sur un graphe biparti de grande taille, issu de réactions chimiques et qui contient plusieurs milliers de noeuds

A methodology for small scale rural land use mapping in semi-arid developing countries using orbital imagery. Part 6: A low-cost method for land use mapping using simple visual techniques of interpretation

The author has identified the following significant results. It was found that color composite transparencies and monocular magnification provided the best base for land use interpretation. New methods for determining optimum sample sizes and analyzing interpretation accuracy levels were developed. All stages of the methodology were assessed, in the operational sense, during the production of a 1:250,000 rural land use map of Murcia Province, Southeast Spain

Seeing is believing: the importance of visualization in real-world machine learning applications

The increasing availability of data sets with a huge amount of information, coded in many diff erent features, justifi es the research on new methods of knowledge extraction: the great challenge is the translation of the raw data into useful information that can be used to improve decisionmaking processes, detect relevant profi les, fi nd out relationships among features, etc. It is undoubtedly true that a picture is worth a thousand words, what makes visualization methods be likely the most appealing and one of the most relevant kinds of knowledge extration methods. At ESANN 2011, the special session "Seeing is believing: The importance of visualization in real-world machine learning applications" reflects some of the main emerging topics in the field. This tutorial prefaces the session, summarizing some of its contributions, while also providing some clues to the current state and the near future of visualization methods within the framework of Machine Learning.Postprint (published version

Self-Organizing Time Map: An Abstraction of Temporal Multivariate Patterns

This paper adopts and adapts Kohonen's standard Self-Organizing Map (SOM) for exploratory temporal structure analysis. The Self-Organizing Time Map (SOTM) implements SOM-type learning to one-dimensional arrays for individual time units, preserves the orientation with short-term memory and arranges the arrays in an ascending order of time. The two-dimensional representation of the SOTM attempts thus twofold topology preservation, where the horizontal direction preserves time topology and the vertical direction data topology. This enables discovering the occurrence and exploring the properties of temporal structural changes in data. For representing qualities and properties of SOTMs, we adapt measures and visualizations from the standard SOM paradigm, as well as introduce a measure of temporal structural changes. The functioning of the SOTM, and its visualizations and quality and property measures, are illustrated on artificial toy data. The usefulness of the SOTM in a real-world setting is shown on poverty, welfare and development indicators