Étude du petit monde | EPFL Graph Search

Le « phénomène du petit monde » (appelé aussi effet du petit monde également connu sous le vocable « paradoxe de Milgram » car ses résultats semblent contraires à l'intuition) est l'hypothèse que chacun puisse être relié à n'importe quel autre individu par une courte chaîne de relations sociales. Ce concept reprend, après l'expérience du petit monde, conduite en 1967 par le psychosociologue Stanley Milgram, le concept de « six degrés de séparation », formulé par le Hongrois Frigyes Karinthy en 1929. Celui-ci suggère que deux personnes, choisies au hasard parmi les citoyens américains, sont reliées en moyenne par une chaîne de six relations. En revanche, après plus de trente ans, le statut de cette idée comme description de réseaux sociaux hétérogènes reste une question ouverte. Des études sont encore menées actuellement sur le « petit monde », avec notamment le modèle mathématique de réseau « petit monde ». thumb|Les six degrés de séparation. Expérience menée par Milgram

Privacy and Dynamics of Social Networks (PhD Thesis: pre-print)

Pedram Pedarsani

Over the past decade, investigations in different fields have focused on studying and understanding real networks, ranging from biological to social to technological. These networks, called complex networks, exhibit common topological features, such as a heavy-tailed degree distribution and the small world effect. In this thesis we address two interesting aspects of complex, and more specifically, social networks: (1) users' privacy, and the vulnerability of a network to user identification, and (2) dynamics, or the evolution of the network over time. For this purpose, we base our contributions on a central tool in the study of graphs and complex networks: graph sampling. We conjecture that each network snapshot can be treated as a sample from an underlying network. Using this, a sampling process can be viewed as a way to observe dynamic networks, and to model the similarity of two correlated graphs by assuming that the graphs are samples from an underlying generator graph. We take the thesis in two directions. For the first, we focus on the privacy problem in social networks. There have been hot debates on the extent to which the release of anonymized information to the public can leak personally identifiable information (PII). Recent works have shown methods that are able to infer true user identities, under certain conditions and by relying on side information. Our approach to this problem relies on the graph structure, where we investigate the feasibility of de-anonymizing an unlabeled social network by using the structural similarity to an auxiliary network. We propose a model where the two partially overlapping networks of interest are considered samples of an underlying graph. Using such a model, first, we propose a theoretical framework for the de-anonymization problem, we obtain minimal conditions under which de-anonymization is feasible, and we establish a threshold on the similarity of the two networks above which anonymity could be lost. Then, we propose a novel algorithm based on a Bayesian framework, which is capable of matching two graphs of thousands of nodes - with no side information other than network structures. Our method has several potential applications, e.g., inferring user identities in an anonymized network by using a similar public network, cross-referencing dictionaries of different languages, correlating data from different domains, etc. We also introduce a novel privacy-preserving mechanism for social recommender systems, where users can receive accurate recommendations while hiding their profiles from an untrusted recommender server. For the second direction of this work, we focus on models for network growth, more specifically for network densification, by using a sampling process. The densification phenomenon has been recently observed in various real networks, and we argue that it can be explained simply through the way we observe (sample) the networks. We introduce a process of sampling the edges of a fixed graph, which results in the super-linear growth of edges versus nodes and the increase of the average degree as the network evolves.

2012

Privacy and Dynamics of Social Networks

Pedram Pedarsani

Over the past decade, investigations in different fields have focused on studying and understanding real networks, ranging from biological to social to technological. These networks, called complex networks, exhibit common topological features, such as a heavy-tailed degree distribution and the small world effect. In this thesis we address two interesting aspects of complex, and more specifically, social networks: (1) users’ privacy, and the vulnerability of a network to user identification, and (2) dynamics, or the evolution of the network over time. For this purpose, we base our contributions on a central tool in the study of graphs and complex networks: graph sampling. We conjecture that each observed network can be treated as a sample from an underlying network. Using this, a sampling process can be viewed as a way to observe dynamic networks, and to model the similarity of two correlated graphs by assuming that the graphs are samples from an underlying generator graph. We take the thesis in two directions. For the first, we focus on the privacy problem in social networks. There have been hot debates on the extent to which the release of anonymized information to the public can leak personally identifiable information (PII). Recent works have shown methods that are able to infer true user identities, under certain conditions and by relying on side information. Our approach to this problem relies on the graph structure, where we investigate the feasibility of de-anonymizing an unlabeled social network by using the structural similarity to an auxiliary network. We propose a model where the two partially overlapping networks of interest are considered samples of an underlying graph. Using such a model, first, we propose a theoretical framework for the de-anonymization problem, we obtain minimal conditions under which de-anonymization is feasible, and we establish a threshold on the similarity of the two networks above which anonymity could be lost. Then, we propose a novel algorithm based on a Bayesian framework, which is capable of matching two graphs of thousands of nodes - with no side information other than network structures. Our method has several potential applications, e.g., inferring user identities in an anonymized network by using a similar public network, cross-referencing dictionaries of different languages, correlating data from different domains, etc. We also introduce a novel privacy-preserving mechanism for social recommender systems, where users can receive accurate recommendations while hiding their profiles from an untrusted recommender server. For the second direction of this work, we focus on models for network growth, more specifically where the number of edges grows faster than the number of nodes, a property known as densification. The densification phenomenon has been recently observed in various real networks, and we argue that it can be explained simply through the way we observe (sample) networks. We introduce a process of sampling the edges of a fixed graph, which results in the super-linear growth of edges versus nodes, and show that densification arises if and only if the graph has a power-law degree distribution.

EPFL2013

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

Zvonimir Bujanovic, Daniel Kressner

The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil A - lambda B requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice for HT reduction relies entirely on Givens rotations regrouped and accumulated into small dense matrices which are subsequently applied using matrix multiplication routines. A nonvanishing fraction of the total flop-count must nevertheless still be performed as sequences of overlapping Givens rotations alternately applied from the left and from the right. The many data dependencies associated with this computational pattern leads to inefficient use of the processor and poor scalability. In this paper, we therefore introduce a fundamentally different approach that relies entirely on (large) Householder reflectors partially accumulated into block reflectors, by using (compact) WY representations. Even though the new algorithm requires more floating point operations than the state-of-the-art algorithm, extensive experiments on both real and synthetic data indicate that it is still competitive, even in a sequential setting. The new algorithm is conjectured to have better parallel scalability, an idea which is partially supported by early small-scale experiments using multithreaded BLAS. The design and evaluation of a parallel formulation is future work.

SIAM PUBLICATIONS2018

Privacy and Dynamics of Social Networks

Pedram Pedarsani

Over the past decade, investigations in different fields have focused on studying and understanding real networks, ranging from biological to social to technological. These networks, called complex networks, exhibit common topological features, such as a heavy-tailed degree distribution and the small world effect. In this thesis we address two interesting aspects of complex, and more specifically, social networks: (1) users’ privacy, and the vulnerability of a network to user identification, and (2) dynamics, or the evolution of the network over time. For this purpose, we base our contributions on a central tool in the study of graphs and complex networks: graph sampling. We conjecture that each observed network can be treated as a sample from an underlying network. Using this, a sampling process can be viewed as a way to observe dynamic networks, and to model the similarity of two correlated graphs by assuming that the graphs are samples from an underlying generator graph. We take the thesis in two directions. For the first, we focus on the privacy problem in social networks. There have been hot debates on the extent to which the release of anonymized information to the public can leak personally identifiable information (PII). Recent works have shown methods that are able to infer true user identities, under certain conditions and by relying on side information. Our approach to this problem relies on the graph structure, where we investigate the feasibility of de-anonymizing an unlabeled social network by using the structural similarity to an auxiliary network. We propose a model where the two partially overlapping networks of interest are considered samples of an underlying graph. Using such a model, first, we propose a theoretical framework for the de-anonymization problem, we obtain minimal conditions under which de-anonymization is feasible, and we establish a threshold on the similarity of the two networks above which anonymity could be lost. Then, we propose a novel algorithm based on a Bayesian framework, which is capable of matching two graphs of thousands of nodes - with no side information other than network structures. Our method has several potential applications, e.g., inferring user identities in an anonymized network by using a similar public network, cross-referencing dictionaries of different languages, correlating data from different domains, etc. We also introduce a novel privacy-preserving mechanism for social recommender systems, where users can receive accurate recommendations while hiding their profiles from an untrusted recommender server. For the second direction of this work, we focus on models for network growth, more specifically where the number of edges grows faster than the number of nodes, a property known as densification. The densification phenomenon has been recently observed in various real networks, and we argue that it can be explained simply through the way we observe (sample) networks. We introduce a process of sampling the edges of a fixed graph, which results in the super-linear growth of edges versus nodes, and show that densification arises if and only if the graph has a power-law degree distribution.

EPFL2013

Privacy and Dynamics of Social Networks (PhD Thesis: pre-print)

Pedram Pedarsani

2012