Un séminaire de l'équipe A3SI du LIGM (unité mixte de recherche de l'Université Paris Est) aura lieu le jeudi 18 mai de 13h00 à 14h00, salle 260 (ESIEE PARIS).
Abstract: Visualizing time-varying data defined on the nodes of a graph is a challenging problem that has been faced with different approaches. Although techniques based on aggregation, topology, and topic modeling have proven their usefulness, the visual analysis of smooth and/or abrupt data variations as well as the evolution of such variations over time are aspects not properly tackled by existing methods. In this work we propose a novel visualization methodology that relies on graph wavelet theory and stacked graph metaphor to enable the visual analysis of time-varying data defined on the nodes of a graph. The proposed method is able to identify regions where data presents abrupt and mild spacial and/or temporal variation while still been able to show how such changes evolve over time, making the identification of events an easier task. The usefulness of our approach is shown through a set of results using synthetic as well as a real data set involving taxi trips in downtown Manhattan. The methodology was able to reveal interesting phenomena and eve such as the identification of specific locations with abrupt variation in the number of taxi pickups.
Abstract: The problem of clustering is to partition the dataset into groups such that elements belonging to the same group are similar and elements belonging to the different groups are dissimilar. The unsupervised nature of the problem makes it widely applicable and also tough to solve objectively. Clustering in the context of image data is referred to as image segmentation. Distance based methods such as K-means fail to detect the non-globular clusters and hence spectral clustering was proposed to overcome this problem . This method detects the non globular structures by projecting the data set into a subspace, in which the usual clustering methods work well. Gamma convergence is the study of asymptotic behavior of minimizers of a family of minimization problems. Such a limit of minimizers is referred to as the gamma limit. Calculating the gamma limit for various variational problems have been proved useful - giving a different algorithm and insights into why existing methods work. In this article, we calculate the gamma limit of the spectral clustering methods, analyze its properties, and compare them with minimum spanning tree based clustering methods and spectral clustering methods.