Results 1  10
of
121
Authoritative Sources in a Hyperlinked Environment
 JOURNAL OF THE ACM
, 1999
"... The network structure of a hyperlinked environment can be a rich source of information about the content of the environment, provided we have effective means for understanding it. We develop a set of algorithmic tools for extracting information from the link structures of such environments, and repo ..."
Abstract

Cited by 2702 (10 self)
 Add to MetaCart
The network structure of a hyperlinked environment can be a rich source of information about the content of the environment, provided we have effective means for understanding it. We develop a set of algorithmic tools for extracting information from the link structures of such environments, and report on experiments that demonstrate their effectiveness in a variety of contexts on the World Wide Web. The central issue we address within our framework is the distillation of broad search topics, through the discovery of “authoritative ” information sources on such topics. We propose and test an algorithmic formulation of the notion of authority, based on the relationship between a set of relevant authoritative pages and the set of “hub pages ” that join them together in the link structure. Our formulation has connections to the eigenvectors of certain matrices associated with the link graph; these connections in turn motivate additional heuristics for linkbased analysis.
Normalized Cuts and Image Segmentation
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2000
"... ..."
Consistency of spectral clustering
, 2004
"... Consistency is a key property of statistical algorithms, when the data is drawn from some underlying probability distribution. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of a popular family of spe ..."
Abstract

Cited by 286 (15 self)
 Add to MetaCart
Consistency is a key property of statistical algorithms, when the data is drawn from some underlying probability distribution. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of a popular family of spectral clustering algorithms, which cluster the data with the help of eigenvectors of graph Laplacian matrices. We show that one of the two of major classes of spectral clustering (normalized clustering) converges under some very general conditions, while the other (unnormalized), is only consistent under strong additional assumptions, which, as we demonstrate, are not always satisfied in real data. We conclude that our analysis provides strong evidence for the superiority of normalized spectral clustering in practical applications. We believe that methods used in our analysis will provide a basis for future exploration of Laplacianbased methods in a statistical setting.
A Minmax Cut Algorithm for Graph Partitioning and Data Clustering
, 2001
"... An important application of graph partitioning is data clustering using a graph model  the pairwise similarities between all data objects form a weighted graph adjacency matrix that contains all necessary information for clustering. Here we propose a new algorithm for graph partition with an object ..."
Abstract

Cited by 150 (12 self)
 Add to MetaCart
An important application of graph partitioning is data clustering using a graph model  the pairwise similarities between all data objects form a weighted graph adjacency matrix that contains all necessary information for clustering. Here we propose a new algorithm for graph partition with an objective function that follows the minmax clustering principle. The relaxed version of the optimization of the minmax cut objective function leads to the Fiedler vector in spectral graph partition. Theoretical analyses of minmax cut indicate that it leads to balanced partitions, and lower bonds are derived. The minmax cut algorithm is tested on newsgroup datasets and is found to outperform other current popular partitioning/clustering methods. The linkagebased re nements in the algorithm further improve the quality of clustering substantially. We also demonstrate that the linearized search order based on linkage di erential is better than that based on the Fiedler vector, providing another e ective partition method.
Motion Segmentation and Tracking Using Normalized Cuts
, 1998
"... We propose a motion segmentation algorithm that aims to break a scene into its most prominent moving groups. A weighted graph is constructed on the ira. age sequence by connecting pixels that arc in the spatiotemporal neighborhood of each other. At each pizel, we define motion profile vectors which ..."
Abstract

Cited by 145 (5 self)
 Add to MetaCart
We propose a motion segmentation algorithm that aims to break a scene into its most prominent moving groups. A weighted graph is constructed on the ira. age sequence by connecting pixels that arc in the spatiotemporal neighborhood of each other. At each pizel, we define motion profile vectors which capture the probability distribution of the image veloczty. The distance between motion profiles is used to assign a weight on the graph edges. 5rsmg normalized cuts we find the most salient partitions of the spatiotemporaI graph formed by the image sequence. For swmenting long image sequences,' we have developed a recursire update procedure that incorporates knowledge of segmentation in previous frames for efficiently finding the group correspondence in the new frame.
Spectral Partitioning Works: Planar graphs and finite element meshes
 In IEEE Symposium on Foundations of Computer Science
, 1996
"... Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extr ..."
Abstract

Cited by 144 (8 self)
 Add to MetaCart
Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on boundeddegree planar graphs and finite element meshes the classes of graphs to which they are usually applied. While naive spectral bisection does not necessarily work, we prove that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is O( p n) for boundeddegree planar graphs and twodimensional meshes and O i n 1=d j for wellshaped ddimensional meshes. The heart of our analysis is an upper bound on the secondsmallest eigenvalues of the Laplacian matrices of these graphs. 1. Introduction Spectral partitioning has become one of the mos...
Nearlylinear time algorithms for graph partitioning, graph sparsification, and solving linear systems (Extended Abstract)
 STOC'04
, 2004
"... We present algorithms for solving symmetric, diagonallydominant linear systems to accuracy ɛ in time linear in their number of nonzeros and log(κf (A)/ɛ), where κf (A) isthe condition number of the matrix defining the linear system. Our algorithm applies the preconditioned Chebyshev iteration with ..."
Abstract

Cited by 136 (8 self)
 Add to MetaCart
We present algorithms for solving symmetric, diagonallydominant linear systems to accuracy ɛ in time linear in their number of nonzeros and log(κf (A)/ɛ), where κf (A) isthe condition number of the matrix defining the linear system. Our algorithm applies the preconditioned Chebyshev iteration with preconditioners designed using nearlylinear time algorithms for graph sparsification and graph partitioning.