Estimation de Fermi | EPFL Graph Search

En physique et d'autres sciences, une estimation de Fermi ou problème de Fermi, encore appelée question de Fermi ou exercice de Fermi, est un problème d'estimation conçu pour enseigner la manière de faire des approximations correctes, sans données précises mais à partir d'hypothèses judicieusement choisies. Le nom de ce genre d'estimation vient du physicien du Enrico Fermi, qui aimait poser ce genre de questions à ses étudiants. En anglais, on appelle aussi ce genre d'estimation « back of the envelope calculation », calcul ou estimation « au dos de l'enveloppe » (expression traduite en français par « calcul de coin de table »), ceci faisant référence à la manière rapide d'effectuer un calcul grossier sur le premier bout de papier qui vous tombe sous la main en vue d'obtenir un résultat approximatif. Fermi était connu pour son habileté à faire de bons calculs d'approximation avec peu (ou aucune) données précises. Pendant l'essai atomique de Trinity, lors duquel la première bombe atom

Integration of scientific and social networks

Ehsaneddin Asgari

In this paper, we address the problem of scientific-social network integration to find a matching relationship between members of these networks (i.e. The DBLP publication network and the Twitter social network). This task is a crucial step toward building a multi environment expert finding system that has recently attracted much attention in Information Retrieval community. In this paper, the problem of social and scientific network integration is divided into two sub problems. The first problem concerns finding those profiles in one network, which presumably have a corresponding profile in the other network and the second problem concerns the name disambiguation to find true matching profiles among some candidate profiles for matching. Utilizing several name similarity patterns and contextual properties of these networks, we design a focused crawler to find high probable matching pairs, then the problem of name disambiguation is reduced to predict the label of each candidate pair as either true or false matching. Because the labels of these candidate pairs are not independent, state-of-the-art classification methods such as logistic regression and decision tree, which classify each instance separately, are unsuitable for this task. By defining matching dependency graph, we propose a joint label prediction model to determine the label of all candidate pairs simultaneously. Two main types of dependencies among candidate pairs are considered for designing the joint label prediction model which are quite intuitive and general. Using the discriminative approaches, we utilize various feature sets to train our proposed classifiers. An extensive set of experiments have been conducted on six test collection collected from the DBLP and the Twitter networks to show the effectiveness of the proposed joint label prediction model.

Springer2014

Graph Signal Processing

Ntorina Thanou

Over the past few decades we have been experiencing an explosion of information generated by large networks of sensors and other data sources. Much of this data is intrinsically structured, such as traffic evolution in a transportation network, temperature values in different geographical locations, information diffusion in social networks, functional activities in the brain, or 3D meshes in computer graphics. The representation, analysis, and compression of such data is a challenging task and requires the development of new tools that can identify and properly exploit the data structure. In this thesis, we formulate the processing and analysis of structured data using the emerging framework of graph signal processing. Graphs are generic data representation forms, suitable for modeling the geometric structure of signals that live on topologically complicated domains. The vertices of the graph represent the discrete data domain, and the edge weights capture the pairwise relationships between the vertices. A graph signal is then defined as a function that assigns a real value to each vertex. Graph signal processing is a useful framework for handling efficiently such data as it takes into consideration both the signal and the graph structure. In this work, we develop new methods and study several important problems related to the representation and structure-aware processing of graph signals in both centralized and distributed settings. We focus in particular in the theory of sparse graph signal representation and its applications and we bring some insights towards better understanding the interplay between graphs and signals on graphs. First, we study a novel yet natural application of the graph signal processing framework for the representation of 3D point cloud sequences. We exploit graph-based transform signal representations for addressing the challenging problem of compression of data that is characterized by dynamic 3D positions and color attributes. Next, we depart from graph-based transform signal representations to design new overcomplete representations, or dictionaries, which are adapted to specific classes of graph signals. In particular, we address the problem of sparse representation of graph signals residing on weighted graphs by learning graph structured dictionaries that incorporate the intrinsic geometric structure of the irregular data domain and are adapted to the characteristics of the signals. Then, we move to the efficient processing of graph signals in distributed scenarios, such as sensor or camera networks, which brings important constraints in terms of communication and computation in realistic settings. In particular, we study the effect of quantization in the distributed processing of graph signals that are represented by graph spectral dictionaries and we show that the impact of the quantization depends on the graph geometry and on the structure of the spectral dictionaries. Finally, we focus on a widely used graph process, the problem of distributed average consensus in a sensor network where sensors exchange quantized information with their neighbors. We propose a novel quantization scheme that depends on the graph topology and exploits the increasing correlation between the values exchanged by the sensors throughout the iterations of the consensus algorithm.

EPFL2016

Fair colorful k-center clustering

Xinrui Jia, Ola Nils Anders Svensson

An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius rho such that there exist balls of radius rho around k of the points that meet the coverage requirements. The motivation behind this problem is twofold. First, from fairness considerations: each color/group should receive a similar service guarantee, and second, from the algorithmic challenges it poses: this problem combines the difficulties of clustering along with the subset-sum problem. In particular, we show that this combination results in strong integrality gap lower bounds for several natural linear programming relaxations. Our main result is an efficient approximation algorithm that overcomes these difficulties to achieve an approximation guarantee of 3, nearly matching the tight approximation guarantee of 2 for the classical k-center problem which this problem generalizes. algorithms either opened more than k centers or only worked in the special case when the input points are in the plane.

SPRINGER HEIDELBERG2021

Graph Signal Processing

Ntorina Thanou

EPFL2016