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In this paper we investigate the convergence of iterative stationary and Krylov subspace methods for the PageRank linear system, including the convergence dependency on tele-portation. We demonstrate that linear system iterations converge faster than the simple power method and are less sensitive to the changes in teleportation. In order to perform this… (More)

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)

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)

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)

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 factorization. It… (More)

Numerous algorithms are used for nonnegative matrix fac-torization under the assumption that the matrix is nearly separable. In this paper, we show how to make these algorithms efficient for data matrices that have many more rows than columns, so-called " tall-and-skinny matrices ". One key component to these improved methods is an orthogonal matrix… (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, which 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 this NP-hard combinatorial optimization problem. We show that… (More)

We first explore methods for approximating the commute time and Katz score between a pair of nodes. These methods are based on the approach of matrices, moments , and quadrature developed in the numerical linear algebra community. They rely on the Lanczos process and provide upper and lower bounds on an estimate of the pair-wise scores. We also explore… (More)