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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… (More)

The heat kernel is a type of graph diffusion that, like the much-used personalized PageRank diffusion, is useful in identifying a community nearby a starting seed node. We present the first deterministic, local algorithm to compute this diffusion and use that algorithm to study the communities that it produces. Our algorithm is formally a relaxation method… (More)

PageRank computes the importance of each node in a directed graph under a random surfer model governed by a teleportation parameter. Commonly denoted alpha, this parameter models the probability of following an edge inside the graph or, when the graph comes from a network of web pages and links, clicking a link on a web page. We empirically measure the… (More)

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will… (More)

Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to choose in specific applications. This article looks at method of moments estimators that are computationally much simpler… (More)

The communities of a social network are sets of vertices with more connections inside the set than outside. We theoretically demonstrate that two commonly observed properties of social networks, heavy-tailed degree distributions and large clustering coefficients, imply the existence of vertex neighborhoods (also known as egonets) that are themselves good… (More)

We propose a new distributed algorithm for sparse variants of the network alignment problem that occurs in a variety of data mining areas including systems biology, database matching, and computer vision. Our algorithm uses a belief propagation heuristic and provides near optimal solutions for an NP-hard combinatorial optimization problem. We show that our… (More)

Community detection is an important task in network analysis. A community (also referred to as a cluster) is a set of cohesive vertices that have more connections inside the set than outside. In many social and information networks, these communities naturally overlap. For instance, in a social network, each vertex in a graph corresponds to an individual… (More)

—The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called " tall-and-skinny matrices, " there is a numerically stable, efficient, communication-avoiding algorithm for computing the QR factoriza-tion. It has been… (More)

- Rajeev Motwani, David F. Gleich, Taher Haveliwala, Sepandar D. Kamvar, Dan Klein, Christopher Manning
- 2011