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Rank aggregation via nuclear norm minimization

Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Gleich, David F.; Lim, Lek H.

The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas produces a new method for ranking a set of items. The essence of our idea is that a rank aggregation describes a partially filled skew-symmetric matrix. We extend an algorithm for matrix completion to handle skew-symmetric data and use that to extract ranks for each item. Our algorithm applies to both pairwise comparison and rating data. Because it is based on matrix completion, it is robust to both noise and incomplete data. We show a formal recovery result for the noiseless case and present a detailed study of the algorithm on synthetic data and Netix ratings. Copyright 2011 ACM.

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TYPE Conference YEAR 2011
ScopusOSTI

Fast Katz and commuters : efficient estimation of social relatedness

Gleich, David F.

Motivated by social network data mining problems such as link prediction and collaborative filtering, significant research effort has been devoted to computing topological measures including the Katz score and the commute time. Existing approaches typically approximate all pairwise relationships simultaneously. In this paper, we are interested in computing: the score for a single pair of nodes, and the top-k nodes with the best scores from a given source node. For the pairwise problem, we apply an iterative algorithm that computes upper and lower bounds for the measures we seek. This algorithm exploits a relationship between the Lanczos process and a quadrature rule. For the top-k problem, we propose an algorithm that only accesses a small portion of the graph and is related to techniques used in personalized PageRank computing. To test the scalability and accuracy of our algorithms we experiment with three real-world networks and find that these algorithms run in milliseconds to seconds without any preprocessing.

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TYPE Conference YEAR 2010
OSTI

Fast Katz and commuters: Efficient estimation of social relatedness in large networks

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Esfandiar, Pooya; Bonchi, Francesco; Gleich, David F.; Greif, Chen; Lakshmanan, Laks V.S.; On, Byung W.

Motivated by social network data mining problems such as link prediction and collaborative filtering, significant research effort has been devoted to computing topological measures including the Katz score and the commute time. Existing approaches typically approximate all pairwise relationships simultaneously. In this paper, we are interested in computing: the score for a single pair of nodes, and the top-k nodes with the best scores from a given source node. For the pairwise problem, we apply an iterative algorithm that computes upper and lower bounds for the measures we seek. This algorithm exploits a relationship between the Lanczos process and a quadrature rule. For the top-k problem, we propose an algorithm that only accesses a small portion of the graph and is related to techniques used in personalized PageRank computing. To test the scalability and accuracy of our algorithms we experiment with three real-world networks and find that these algorithms run in milliseconds to seconds without any preprocessing. © 2010 Springer-Verlag.

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TYPE Conference YEAR 2010
ScopusOSTI

Overlapping clusters for distributed computation

Gleich, David F.

Scalable, distributed algorithms must address communication problems. We investigate overlapping clusters, or vertex partitions that intersect, for graph computations. This setup stores more of the graph than required but then affords the ease of implementation of vertex partitioned algorithms. Our hope is that this technique allows us to reduce communication in a computation on a distributed graph. The motivation above draws on recent work in communication avoiding algorithms. Mohiyuddin et al. (SC09) design a matrix-powers kernel that gives rise to an overlapping partition. Fritzsche et al. (CSC2009) develop an overlapping clustering for a Schwarz method. Both techniques extend an initial partitioning with overlap. Our procedure generates overlap directly. Indeed, Schwarz methods are commonly used to capitalize on overlap. Elsewhere, overlapping communities (Ahn et al, Nature 2009; Mishra et al. WAW2007) are now a popular model of structure in social networks. These have long been studied in statistics (Cole and Wishart, CompJ 1970). We present two types of results: (i) an estimated swapping probability {rho}{infinity}; and (ii) the communication volume of a parallel PageRank solution (link-following {alpha} = 0.85) using an additive Schwarz method. The volume ratio is the amount of extra storage for the overlap (2 means we store the graph twice). Below, as the ratio increases, the swapping probability and PageRank communication volume decreases.

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TYPE Conference YEAR 2010
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22 Results
22 Results