Visually Mining the Datacube using a Pixel-Oriented Technique

International audienceThis paper introduces a new technique easing the navigation and interactive exploration of huge multidimensional datasets. Following the pixel-oriented paradigm, the key ingredients enabling the interactive navigation of extreme volumes of data rely on a set of functions bijectively mapping data elements to screen pixels. The use of the mapping from data elements to pixels constrain the computational complexity for the rendering process to be linear with respect to the number of rendered pixels on the screen as opposed to the dataset size. Our method furthermore allows the implementation of usual information visualization techniques such as zoom and pan, anamorphosis and texturing. As a proof-of-concept, we show how our technique can be adapted to interactively explore the Datacube, turning our approach into an efficient system for visual datamining. We report experiments conducted on a Datacube containing 50 millions of items. To our knowledge, our technique outperforms all existing ones and push the scalability limit close to the billion of elements. Supporting all basic navigation techniques, and being moreover flexible makes it easily reusable for a large number of applications

Visually Mining the Datacube using a Pixel-Oriented Technique

International audienceThis paper introduces a new technique easing the navigation and interactive exploration of huge multidimensional datasets. Following the pixel-oriented paradigm, the key ingredients enabling the interactive navigation of extreme volumes of data rely on a set of functions bijectively mapping data elements to screen pixels. The use of the mapping from data elements to pixels constrain the computational complexity for the rendering process to be linear with respect to the number of rendered pixels on the screen as opposed to the dataset size. Our method furthermore allows the implementation of usual information visualization techniques such as zoom and pan, anamorphosis and texturing. As a proof-of-concept, we show how our technique can be adapted to interactively explore the Datacube, turning our approach into an efficient system for visual datamining. We report experiments conducted on a Datacube containing 50 millions of items. To our knowledge, our technique outperforms all existing ones and push the scalability limit close to the billion of elements. Supporting all basic navigation techniques, and being moreover flexible makes it easily reusable for a large number of applications

PORGY: a Visual Analytics Platform for System Modelling and Analysis Based on Graph Rewriting

PORGY is a visual environment for rule-based modelling based on port graphs and port graph rewrite rules whose application is steered by rewriting strategies. The focus of this demonstration is the visual and interactive features offered by PORGY, which facilitate an exploratory approach to model, simu- late and analyse different ways of applying the rules while recording the model evolution, as well as tracking and plotting system parameters

Organization of Information for the Web using Hierarchical Fuzzy Clustering Algorithm based on Co-Occurrence Networks

International audienceIn this paper, we present a Hierarchical Fuzzy Clustering algorithm which uses domain knowledge to automatically determine the number of clusters and their initial values. The algorithm is applied on a collection of web pages and the results are compared with existing algorithms in the literature

Topological Decomposition and Heuristics for High Speed Clustering of Complex Networks

International audienceWith the exponential growth in the size of data and networks, development of new and fast techniques to analyze and explore these networks is becoming a necessity. Moreover the emergence of scale free and small world properties in real world networks has stimulated lots of activity in the field of network analysis and data mining. Clustering remains a fundamental technique to explore and organize these networks. A challenging problem is to find a clustering algorithm that works well in terms of clustering quality and is efficient in terms of time complexity. In this paper, we propose a fast clustering algorithm which combines some heuristics with a Topological Decomposition to obtain a clustering. The algorithm which we call Topological Decomposition and Heuristics for Clustering (TDHC) is highly efficient in terms of asymptotic time complexity as compared to other existing algorithms in the literature. We also introduce a number of Heuristics to complement the clustering algorithm which increases the speed of the clustering process maintaining the high quality of clustering. We show the effectiveness of the proposed clustering method on different real world data sets and compare its results with well known clustering algorithms

Lyndon factorization of the Thue-Morse word and its relatives

We compute the Lyndon factorization of the Thue-Morse word. We also compute the Lyndon factorization of two related sequences involving morphisms that give rise to new presentations of these sequences

Identifying the Presence of Communities in Complex Networks Through Topological Decomposition and Component Densities

International audienceThe exponential growth of data in various fields such as Social Networks and Internet has stimulated lots of activity in the field of network analysis and data mining. Identifying Communities remains a fundamental technique to explore and organize these networks. Few metrics are widely used to discover the presence of communities in a network. We argue that these metrics do not truly reflect the presence of communities by presenting counter examples. This is because these metrics concentrate on local cohesiveness among nodes where the goal is to judge whether two nodes belong to the same community or vise versa. Thus loosing the overall perspective of the presence of communities in the entire network. In this paper, we propose a new metric to identify the presence of communities in real world networks. This metric is based on the topological decomposition of networks taking into account two important ingredients of real world networks, the degree distribution and the density of nodes. We show the effectiveness of the proposed metric by testing it on various real world data sets

Evaluating the Quality of Clustering Algorithms using Cluster Path Lengths

International audienceMany real world systems can be modeled as networks or graphs. Clustering algorithms that help us to organize and understand these networks are usually referred to as, graph based clustering algo- rithms. Many algorithms exist in the literature for clustering network data. Evaluating the quality of these clustering algorithms is an impor- tant task addressed by different researchers. An important ingredient of evaluating these clustering techniques is the node-edge density of a clus- ter. In this paper, we argue that evaluation methods based on density are heavily biased to networks having dense components, such as social net- works, but are not well suited for data sets with other network topologies where the nodes are not densely connected. Example of such data sets are the transportation and Internet networks. We justify our hypothesis by presenting examples from real world data sets. We present a new metric to evaluate the quality of a clustering algorithm to overcome the limitations of existing cluster evaluation techniques. This new metric is based on the path length of the elements of a cluster and avoids judging the quality based on cluster density. We show the effectiveness of the proposed metric by comparing its results with other existing evaluation methods on artificially generated and real world data sets

PORGY : réécriture et visualisation de graphes dynamiques

International audienceCet article présente les premiers résultats sur la visualisation et la manipulation interactive d'un système de réécriture de graphes. Nous sommes amenés à nous pencher sur la visualisation de graphes dont la topologie évolue au cours du temps selon des modifications dictées par des règles de réécriture. Le système doit non seulement de montrer le graphe qui évolue au cours du temps, mais il apparaît ici comme un atelier complet permettant d'étudier le système de réécriture lui-même. Il s'agit d'amener la visualisation en appui à l'étude du système de réécriture pour permettre de comprendre son comportement et d'identifier ses propriétés comme par exemple la convergence des calculs ou les configurations bloquantes. Outre les questions relatives au dessin des graphes qui font encore l'objet de travaux, le système se penche sur les problèmes d'identification de motifs et d'historique des réécritures. Nous abordons aussi les questions plus techniques relatives à la structure interne du système