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Community detection in graphs
, 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 ..."
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Cited by 801 (1 self)
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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
An open graph visualization system and its applications to software engineering
 SOFTWARE  PRACTICE AND EXPERIENCE
, 2000
"... We describe a package of practical tools and libraries for manipulating graphs and their drawings. Our design, which aimed at facilitating the combination of the package components with other tools, includes stream and event interfaces for graph operations, highquality static and dynamic layout alg ..."
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Cited by 452 (9 self)
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We describe a package of practical tools and libraries for manipulating graphs and their drawings. Our design, which aimed at facilitating the combination of the package components with other tools, includes stream and event interfaces for graph operations, highquality static and dynamic layout
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
Fusion, Propagation, and Structuring in Belief Networks
 ARTIFICIAL INTELLIGENCE
, 1986
"... Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used to repre ..."
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Cited by 482 (8 self)
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Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used
Efficiently mining long patterns from databases
, 1998
"... We present a patternmining algorithm that scales roughly linearly in the number of maximal patterns embedded in a database irrespective of the length of the longest pattern. In comparison, previous algorithms based on Apriori scale exponentially with longest pattern length. Experiments on real data ..."
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Cited by 465 (3 self)
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We present a patternmining algorithm that scales roughly linearly in the number of maximal patterns embedded in a database irrespective of the length of the longest pattern. In comparison, previous algorithms based on Apriori scale exponentially with longest pattern length. Experiments on real data show that when the patterns are long, our algorithm is more efficient by an order of magnimaximal frequent itemset, MaxMiner’s output implicitly and concisely represents all frequent itemsets. MaxMiner is shown to result in two or more orders of magnitude in performance improvements over Apriori on some datasets. On other datasets where the patterns are not so long, the gains are more modest. In practice, MaxMiner is demonstrated to run in time that is roughly linear in the number of maximal frequent itemsets and the size of the database, irrespective of the size of the longest frequent itemset. tude or more. 1.
Monochromatic Matchings in the Shadow Graph of Almost Complete Hypergraphs
 ANNALS OF COMBINATORICS
, 2010
"... Edge colorings of runiform hypergraphs naturally define a multicoloring on the 2shadow, i.e., on the pairs that are covered by hyperedges. We show that in any (r − 1)coloring of the edges of an runiform hypergraph with n vertices and at least (1 − ε) ( n) r edges, the 2shadow has a monochromat ..."
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Cited by 4 (2 self)
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monochromatic matching covering all but at most o(n) vertices. This result confirms an earlier conjecture and implies that for any fixed r and sufficiently large n, thereis a monochromatic Bergecycle of length (1 − o(1))n in every (r − 1)coloring of the edges of K (r) n, the complete runiform hypergraph on n
PROBLEMS AND RESULTS ON 3CHROMATIC HYPERGRAPHS AND SOME RELATED QUESTIONS
 COLLOQUIA MATHEMATICA SOCIETATIS JANOS BOLYAI 10. INFINITE AND FINITE SETS, KESZTHELY (HUNGARY)
, 1973
"... A hypergraph is a collection of sets. This paper deals with finite hypergraphs only. The sets in the hypergraph are called edges, the elements of these edges are points. The degree of a point is the number of edges containing it. The hypergraph is runiform if every edge has r points. A hypergraph i ..."
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Cited by 317 (0 self)
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is simple if any two edges have at most one common point, and it is called a clique if any two edges have at least one common point. The chromatic number of a hypergraph is the least number k such that the points can be kcolored so that no edge is monochromatic. As far as we know families of sets
ROCK: A Robust Clustering Algorithm for Categorical Attributes
 In Proc.ofthe15thInt.Conf.onDataEngineering
, 2000
"... Clustering, in data mining, is useful to discover distribution patterns in the underlying data. Clustering algorithms usually employ a distance metric based (e.g., euclidean) similarity measure in order to partition the database such that data points in the same partition are more similar than point ..."
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Cited by 430 (2 self)
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Clustering, in data mining, is useful to discover distribution patterns in the underlying data. Clustering algorithms usually employ a distance metric based (e.g., euclidean) similarity measure in order to partition the database such that data points in the same partition are more similar than
Results 1  10
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