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Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations

by Jure Leskovec, Jon Kleinberg, Christos Faloutsos , 2005
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
Abstract - Cited by 541 (48 self) - Add to MetaCart
increase slowly as a function of the number of nodes (like O(log n) orO(log(log n)). Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a “forest fire” spreading process, that has a simple, intuitive justification

Exploiting Generative Models in Discriminative Classifiers

by Tommi Jaakkola, David Haussler - In Advances in Neural Information Processing Systems 11 , 1998
"... Generative probability models such as hidden Markov models provide a principled way of treating missing information and dealing with variable length sequences. On the other hand, discriminative methods such as support vector machines enable us to construct flexible decision boundaries and often resu ..."
Abstract - Cited by 551 (9 self) - Add to MetaCart
Generative probability models such as hidden Markov models provide a principled way of treating missing information and dealing with variable length sequences. On the other hand, discriminative methods such as support vector machines enable us to construct flexible decision boundaries and often

Interprocedural Slicing Using Dependence Graphs

by Susan Horwitz, Thomas Reps, David Binkley - ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS , 1990
"... ... This paper concerns the problem of interprocedural slicing---generating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends previou ..."
Abstract - Cited by 837 (84 self) - Add to MetaCart
... This paper concerns the problem of interprocedural slicing---generating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends

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 628 (44 self) - Add to MetaCart
as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, series-parallel digraphs, planar st-digraphs, and planar

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 1791 (69 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

Three Generative, Lexicalised Models for Statistical Parsing

by Michael Collins , 1997
"... In this paper we first propose a new statistical parsing model, which is a generative model of lexicalised context-free gram- mar. We then extend the model to in- clude a probabilistic treatment of both subcategorisation and wh~movement. Results on Wall Street Journal text show that the parse ..."
Abstract - Cited by 570 (8 self) - Add to MetaCart
In this paper we first propose a new statistical parsing model, which is a generative model of lexicalised context-free gram- mar. We then extend the model to in- clude a probabilistic treatment of both subcategorisation and wh~movement. Results on Wall Street Journal text show

gSpan: Graph-Based Substructure Pattern Mining

by Xifeng Yan, Jiawei Han , 2002
"... We investigate new approaches for frequent graph-based pattern mining in graph datasets and propose a novel algorithm called gSpan (graph-based Substructure pattern mining) , which discovers frequent substructures without candidate generation. gSpan builds a new lexicographic order among graphs, and ..."
Abstract - Cited by 650 (34 self) - Add to MetaCart
We investigate new approaches for frequent graph-based pattern mining in graph datasets and propose a novel algorithm called gSpan (graph-based Substructure pattern mining) , which discovers frequent substructures without candidate generation. gSpan builds a new lexicographic order among graphs

Modeling Internet Topology

by Kenneth Calvert, Matthew B. Doar, Ellen W. Zegura - IEEE COMMUNICATIONS MAGAZINE , 1997
"... The topology of a network, or a group of networks such as the Internet, has a strong bearing on many management and performance issues. Good models of the topological structure of a network are essential for developing and analyzing internetworking technology. This article discusses how graph-based ..."
Abstract - Cited by 493 (21 self) - Add to MetaCart
The topology of a network, or a group of networks such as the Internet, has a strong bearing on many management and performance issues. Good models of the topological structure of a network are essential for developing and analyzing internetworking technology. This article discusses how graph

Fast approximate energy minimization via graph cuts

by Yuri Boykov, Olga Veksler, Ramin Zabih - IEEE Transactions on Pattern Analysis and Machine Intelligence , 2001
"... In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when v ..."
Abstract - Cited by 2120 (61 self) - Add to MetaCart
In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when

High dimensional graphs and variable selection with the Lasso

by Nicolai Meinshausen, Peter Bühlmann - ANNALS OF STATISTICS , 2006
"... The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a ..."
Abstract - Cited by 736 (22 self) - Add to MetaCart
is a computationally attractive alternative to standard covariance selection for sparse high-dimensional graphs. Neighborhood selection estimates the conditional independence restrictions separately for each node in the graph and is hence equivalent to variable selection for Gaussian linear models. We
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