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32
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 189 (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
"... christian.bauckhage ..."
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Learning Spectral Graph Transformations for Link Prediction
"... We present a unified framework for learning link prediction and edge weight prediction functions in large networks, based on the transformation of a graph’s algebraic spectrum. Our approach generalizes several graph kernels and dimensionality reduction methods and provides a method to estimate their ..."
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Cited by 47 (4 self)
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We present a unified framework for learning link prediction and edge weight prediction functions in large networks, based on the transformation of a graph’s algebraic spectrum. Our approach generalizes several graph kernels and dimensionality reduction methods and provides a method to estimate their parameters efficiently. We show how the parameters of these prediction functions can be learned by reducing the problem to a onedimensional regression problem whose runtime only depends on the method’s reduced rank and that can be inspected visually. We derive variants that apply to undirected, weighted, unweighted, unipartite and bipartite graphs. We evaluate our method experimentally using examples from social networks, collaborative filtering, trust networks, citation networks, authorship graphs and hyperlink networks. 1.
An experimental investigation of graph kernels on a collaborative recommendation task
 Proceedings of the 6th International Conference on Data Mining (ICDM 2006
, 2006
"... This paper presents a survey as well as a systematic empirical comparison of seven graph kernels and two related similarity matrices (simply referred to as graph kernels), namely the exponential diffusion kernel, the Laplacian exponential diffusion kernel, the von Neumann diffusion kernel, the regul ..."
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Cited by 27 (7 self)
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This paper presents a survey as well as a systematic empirical comparison of seven graph kernels and two related similarity matrices (simply referred to as graph kernels), namely the exponential diffusion kernel, the Laplacian exponential diffusion kernel, the von Neumann diffusion kernel, the regularized Laplacian kernel, the commutetime kernel, the randomwalkwithrestart similarity matrix, and finally, three graph kernels introduced in this paper: the regularized commutetime kernel, the Markov diffusion kernel, and the crossentropy diffusion matrix. The kernelonagraph approach is simple and intuitive. It is illustrated by applying the nine graph kernels to a collaborativerecommendation task and to a semisupervised classification task, both on several databases. The graph methods compute proximity measures between nodes that help study the structure of the graph. Our comparisons suggest that the regularized commutetime and the Markov diffusion kernels perform best, closely followed by the regularized Laplacian kernel. 1
Spectral Analysis of Signed Graphs for Clustering, Prediction and Visualization
"... We study the application of spectral clustering, prediction and visualization methods to graphs with negatively weighted edges. We show that several characteristic matrices of graphs can be extended to graphs with positively and negatively weighted edges, giving signed spectral clustering methods, s ..."
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Cited by 26 (0 self)
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We study the application of spectral clustering, prediction and visualization methods to graphs with negatively weighted edges. We show that several characteristic matrices of graphs can be extended to graphs with positively and negatively weighted edges, giving signed spectral clustering methods, signed graph kernels and network visualization methods that apply to signed graphs. In particular, we review a signed variant of the graph Laplacian. We derive our results by considering random walks, graph clustering, graph drawing and electrical networks, showing that they all result in the same formalism for handling negatively weighted edges. We illustrate our methods using examples from social networks with negative edges and bipartite rating graphs. 1
A family of dissimilarity measures between nodes generalizing both the shortestpath and the commutetime distances
 in Proceedings of the 14th SIGKDD International Conference on Knowledge Discovery and Data Mining
"... This work introduces a new family of linkbased dissimilarity measures between nodes of a weighted directed graph. This measure, called the randomized shortestpath (RSP) dissimilarity, depends on a parameter θ and has the interesting property of reducing, on one end, to the standard shortestpath d ..."
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Cited by 25 (11 self)
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This work introduces a new family of linkbased dissimilarity measures between nodes of a weighted directed graph. This measure, called the randomized shortestpath (RSP) dissimilarity, depends on a parameter θ and has the interesting property of reducing, on one end, to the standard shortestpath distance when θ is large and, on the other end, to the commutetime (or resistance) distance when θ is small (near zero). Intuitively, it corresponds to the expected cost incurred by a random walker in order to reach a destination node from a starting node while maintaining a constant entropy (related to θ) spread in the graph. The parameter θ is therefore biasing gradually the simple random walk on the graph towards the shortestpath policy. By adopting a statistical physics approach and computing a sum over all the possible paths (discrete path integral), it is shown that the RSP dissimilarity from every node to a particular node of interest can be computed efficiently by solving two linear systems of n equations, where n is the number of nodes. On the other hand, the dissimilarity between every couple of nodes is obtained by inverting an n × n matrix. The proposed measure can be used for various graph mining tasks such as computing betweenness centrality, finding dense communities, etc, as shown in the experimental section.
The sumoverpaths covariance kernel: A novel covariance measure between nodes of a directed graph
 IEEE Transactions on Pattern Analysis and Machine Intelligence
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An experimental investigation of kernels on graphs for collaborative . . .
 NEURAL NETWORKS
, 2012
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Predicting Positive and Negative Links in Signed Social Networks by Transfer Learning
"... Different from a large body of research on social networks that has focused almost exclusively on positive relationships, we study signed social networks with both positive and negative links. Specifically, we focus on how to reliably and effectively predict the signs of links in a newly formed sign ..."
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Cited by 10 (0 self)
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Different from a large body of research on social networks that has focused almost exclusively on positive relationships, we study signed social networks with both positive and negative links. Specifically, we focus on how to reliably and effectively predict the signs of links in a newly formed signed social network (called a target network). Since usually only a very small amount of edge sign information is available in such newly formed networks, this small quantity is not adequate to train a good classifier. To address this challenge, we need assistance from an existing, mature signed network (called a source network) which has abundant edge sign information. We adopt the transfer learning approach to leverage the edge sign information from the source network, which may have a different yet related joint distribution of the edge instances and their class labels. As there is no predefined feature vector for the edge instances in a signed network, we construct generalizable features that can transfer the topological knowledge from the source network to the target. With the extracted features, we adopt an AdaBoostlike transfer learning algorithm with instance weighting to utilize more useful training instances in the source network for model learning. Experimental results on three real large signed social networks demonstrate that our transfer learning algorithm can improve the prediction accuracy by 40 % over baseline methods.
prediction: the power of maximal entropy random walk
 In: Proceedings of the 20th ACM International Conference on Information and Knowledge Management
"... Link prediction is a fundamental problem in social network analysis. The key technique in unsupervised link prediction is to find an appropriate similarity measure between nodes of a network. A class of wildly used similarity measures are based on random walk on graph. The traditional random walk ( ..."
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Cited by 6 (1 self)
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Link prediction is a fundamental problem in social network analysis. The key technique in unsupervised link prediction is to find an appropriate similarity measure between nodes of a network. A class of wildly used similarity measures are based on random walk on graph. The traditional random walk (TRW) considers the link structures by treating all nodes in a network equivalently, and ignores the centrality of nodes of a network. However, in many real networks, nodes of a network not only prefer to link to the similar node, but also prefer to link to the central nodes of the network. To address this issue, we use maximal entropy random walk (MERW) for link prediction, which incorporates the centrality of nodes of the network. First, we study certain important properties of MERW on graph G by constructing an eigenweighted graph G. We show that the transition matrix and stationary distribution of MERW on G are identical to the ones of TRW on G. Based on G, we further give the maximal entropy graph Laplacians, and show how to fast compute the hitting time and commute time of MERW. Second, we propose four new graph kernels and two similarity measures based on MERW for link prediction. Finally, to exhibit the power of MERW in link prediction, we compare 27 various link prediction methods over 3 synthetic and 8 real networks. The results show that our newly proposed MERW based methods outperform the stateoftheart method on most datasets.