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275
Random walks for image segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2006
"... Abstract—A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach on ..."
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Cited by 385 (21 self)
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Abstract—A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a highquality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs. Index Terms—Image segmentation, interactive segmentation, graph theory, random walks, combinatorial Dirichlet problem, harmonic functions, Laplace equation, graph cuts, boundary completion. Ç 1
Randomwalk computation of similarities between nodes of a graph, with application to collaborative recommendation
 IEEE Transactions on Knowledge and Data Engineering
, 2006
"... Abstract—This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted and undirected graph. It is based on a Markovchain model of random walk through the database. More precisely, we compute quantities (the average comm ..."
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Cited by 188 (19 self)
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Abstract—This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted and undirected graph. It is based on a Markovchain model of random walk through the database. More precisely, we compute quantities (the average commute time, the pseudoinverse of the Laplacian matrix of the graph, etc.) that provide similarities between any pair of nodes, having the nice property of increasing when the number of paths connecting those elements increases and when the “length ” of paths decreases. It turns out that the square root of the average commute time is a Euclidean distance and that the pseudoinverse of the Laplacian matrix is a kernel matrix (its elements are inner products closely related to commute times). A principal component analysis (PCA) of the graph is introduced for computing the subspace projection of the node vectors in a manner that preserves as much variance as possible in terms of the Euclidean commutetime distance. This graph PCA provides a nice interpretation to the “Fiedler vector, ” widely used for graph partitioning. The model is evaluated on a collaborativerecommendation task where suggestions are made about which movies people should watch based upon what they watched in the past. Experimental results on the MovieLens database show that the Laplacianbased similarities perform well in comparison with other methods. The model, which nicely fits into the socalled “statistical relational learning ” framework, could also be used to compute document or word similarities, and, more generally, it could be applied to machinelearning and patternrecognition tasks involving a relational database. Index Terms—Graph analysis, graph and database mining, collaborative recommendation, graph kernels, spectral clustering, Fiedler vector, proximity measures, statistical relational learning. 1
The slashdot zoo: Mining a social network with negative edges
 In WWW
, 2009
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Centrality estimation in large networks
 INTL. JOURNAL OF BIFURCATION AND CHAOS, SPECIAL ISSUE ON COMPLEX NETWORKS’ STRUCTURE AND DYNAMICS
, 2007
"... Centrality indices are an essential concept in network analysis. For those based on shortestpath distances the computation is at least quadratic in the number of nodes, since it usually involves solving the singlesource shortestpaths (SSSP) problem from every node. Therefore, exact computation is ..."
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Cited by 54 (0 self)
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Centrality indices are an essential concept in network analysis. For those based on shortestpath distances the computation is at least quadratic in the number of nodes, since it usually involves solving the singlesource shortestpaths (SSSP) problem from every node. Therefore, exact computation is infeasible for many large networks of interest today. Centrality scores can be estimated, however, from a limited number of SSSP computations. We present results from an experimental study of the quality of such estimates under various selection strategies for the source vertices.
Social Network Analysis for Information Flow in Disconnected DelayTolerant MANETs
"... Abstract—Message delivery in sparse mobile ad hoc networks (MANETs) is difficult due to the fact that the network graph is rarely (if ever) connected. A key challenge is to find a route that can provide good delivery performance and low endtoend delay in a disconnected network graph where nodes ma ..."
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Cited by 53 (0 self)
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Abstract—Message delivery in sparse mobile ad hoc networks (MANETs) is difficult due to the fact that the network graph is rarely (if ever) connected. A key challenge is to find a route that can provide good delivery performance and low endtoend delay in a disconnected network graph where nodes may move freely. We cast this challenge as an information flow problem in a social network. This paper presents social network analysis metrics that may be used to support a novel and practical forwarding solution to provide efficient message delivery in disconnected delaytolerant MANETs. These metrics are based on social analysis of a node’s past interactions and consists of three locally evaluated components: a node’s “betweenness ” centrality (calculated using ego networks), a node’s social “similarity ” to the destination node, and a node’s tie strength relationship with the destination node. We present simulations using three real trace data sets to demonstrate that by combining these metrics delivery performance may be achieved close to Epidemic Routing but with significantly reduced overhead. Additionally, we show improved performance when compared to PRoPHET Routing. Index Terms—Delay and disruptiontolerant networks, MANETs, sparse networks, ego networks, social network analysis.
Who's Who in Networks. Wanted: The Key Player
, 2005
"... Finite population noncooperative games with linearquadratic utilities, where each player decides how much action she exerts, can be interpreted as a network game with local payoff complementarities, together with a globally uniform payoff substitutability component and an ownconcavity effect. For ..."
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Cited by 52 (2 self)
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Finite population noncooperative games with linearquadratic utilities, where each player decides how much action she exerts, can be interpreted as a network game with local payoff complementarities, together with a globally uniform payoff substitutability component and an ownconcavity effect. For these games, the Nash equilibrium action of each player is proportional to her Bonacich centrality in the network of local complementarities, thus establishing a bridge with the sociology literature on social networks. We then analyze a policy that consists of targeting the key player, that is, the player who, once removed, leads to the optimal change in aggregate activity. We provide a geometric characterization of the key player identified with an intercentrality measure, which takes into account both a player’s centrality and her contribution to the centrality of the others.
A regularization framework for learning from graph data
 ICML Workshop on Statistical Relational Learning
, 2004
"... The data in many realworld problems can be thought of as a graph, such as the web, coauthor networks, and biological networks. We propose a general regularization framework on graphs, which is applicable to the classification, ranking, and link prediction problems. We also show that the method can ..."
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Cited by 52 (1 self)
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The data in many realworld problems can be thought of as a graph, such as the web, coauthor networks, and biological networks. We propose a general regularization framework on graphs, which is applicable to the classification, ranking, and link prediction problems. We also show that the method can be explained as lazy random walks. We evaluate the method on a number of experiments. 1.
Fast Approximation of Matrix Coherence and Statistical Leverage
"... The statistical leverage scores of a matrix A are the squared rownorms of the matrix containing its (top) left singular vectors and the coherence is the largest leverage score. These quantities are of interest in recentlypopular problems such as matrix completion and Nyströmbased lowrank matrix ..."
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Cited by 48 (11 self)
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The statistical leverage scores of a matrix A are the squared rownorms of the matrix containing its (top) left singular vectors and the coherence is the largest leverage score. These quantities are of interest in recentlypopular problems such as matrix completion and Nyströmbased lowrank matrix approximation as well as in largescale statistical data analysis applications more generally; moreover, they are of interest since they define the key structural nonuniformity that must be dealt with in developing fast randomized matrix algorithms. Our main result is a randomized algorithm that takes as input an arbitrary n×d matrix A, with n ≫ d, and that returns as output relativeerror approximations to all n of the statistical leverage scores. The proposed algorithm runs (under assumptions on the precise values of n and d) in O(nd logn) time, as opposed to the O(nd 2) time required by the naïve algorithm that involves computing an orthogonal basis for the range of A. Our analysis may be viewed in terms of computing a relativeerror approximation to an underconstrained leastsquares approximation problem, or, relatedly, it may be viewed as an application of JohnsonLindenstrauss type ideas. Several practicallyimportant extensions of our basic result are also described, including the approximation of socalled crossleverage scores, the extension of these ideas to matrices with n≈d, and the extension to streaming environments.
Graph theory and networks in biology
 IET Systems Biology, 1:89 – 119
, 2007
"... In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarch ..."
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Cited by 44 (0 self)
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In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation. 1