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Community detection in graphs

by Santo Fortunato , 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
Abstract - Cited by 801 (1 self) - Add to MetaCart
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices

Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering

by Mikhail Belkin, Partha Niyogi - Advances in Neural Information Processing Systems 14 , 2001
"... Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher ..."
Abstract - Cited by 664 (8 self) - Add to MetaCart
Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a

Reversible Markov chains and random walks on graphs

by David Aldous, James Allen Fill , 2002
"... ..."
Abstract - Cited by 549 (13 self) - Add to MetaCart
Abstract not found

Predicting Internet Network Distance with Coordinates-Based Approaches

by T. S. Eugene Ng, Hui Zhang - In INFOCOM , 2001
"... In this paper, we propose to use coordinates-based mechanisms in a peer-to-peer architecture to predict Internet network distance (i.e. round-trip propagation and transmission delay) . We study two mechanisms. The first is a previously proposed scheme, called the triangulated heuristic, which is bas ..."
Abstract - Cited by 633 (5 self) - Add to MetaCart
In this paper, we propose to use coordinates-based mechanisms in a peer-to-peer architecture to predict Internet network distance (i.e. round-trip propagation and transmission delay) . We study two mechanisms. The first is a previously proposed scheme, called the triangulated heuristic, which

A Framework for Dynamic Graph Drawing

by Robert F. Cohen, G. Di Battista, R. Tamassia, Ioannis G. Tollis - CONGRESSUS NUMERANTIUM , 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
Abstract - Cited by 627 (44 self) - Add to MetaCart
Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized

Convergent Tree-reweighted Message Passing for Energy Minimization

by Vladimir Kolmogorov - ACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI), 2006. ABSTRACTACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI) , 2006
"... Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33]- tree-reweighted max-product message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy ..."
Abstract - Cited by 491 (16 self) - Add to MetaCart
Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33]- tree-reweighted max-product message passing (TRW). It was inspired by the problem of maximizing a lower bound

Factor Graphs and the Sum-Product Algorithm

by Frank R. Kschischang, Brendan J. Frey, Hans-Andrea Loeliger - IEEE TRANSACTIONS ON INFORMATION THEORY , 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
Abstract - Cited by 1787 (72 self) - Add to MetaCart
A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple

Quantization Index Modulation: A Class of Provably Good Methods for Digital Watermarking and Information Embedding

by Brian Chen, Gregory W. Wornell - IEEE TRANS. ON INFORMATION THEORY , 1999
"... We consider the problem of embedding one signal (e.g., a digital watermark), within another "host" signal to form a third, "composite" signal. The embedding is designed to achieve efficient tradeoffs among the three conflicting goals of maximizing information-embedding rate, mini ..."
Abstract - Cited by 495 (15 self) - Add to MetaCart
, minimizing distortion between the host signal and composite signal, and maximizing the robustness of the embedding. We introduce new classes of embedding methods, termed quantization index modulation (QIM) and distortion-compensated QIM (DC-QIM), and develop convenient realizations in the form of what we

An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision

by Yuri Boykov, Vladimir Kolmogorov - IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE , 2001
"... After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time compl ..."
Abstract - Cited by 1311 (54 self) - Add to MetaCart
After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time

For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1-norm Solution is also the Sparsest Solution

by David L. Donoho - Comm. Pure Appl. Math , 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
Abstract - Cited by 560 (10 self) - Add to MetaCart
that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y having a representation y = Φα0 by a coefficient vector α0 ∈ R m with fewer than ρ · n nonzeros, the solution α1 of the ℓ 1 minimization problem min �x�1 subject to Φα = y is unique and equal to α0
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