Publications

Results 76–100 of 199
Skip to search filters

Wedge sampling for computing clustering coefficients and triangle counts on large graphs

Statistical Analysis and Data Mining

Comandur, Seshadhri C.; Pinar, Ali P.; Kolda, Tamara G.

Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of such graphs. Some of the most useful graph metrics are based on triangles, such as those measuring social cohesion. Algorithms to compute them can be extremely expensive, even for moderately sized graphs with only millions of edges. Previous work has considered node and edge sampling; in contrast, we consider wedge sampling, which provides faster and more accurate approximations than competing techniques. Additionally, wedge sampling enables estimating local clustering coefficients, degree-wise clustering coefficients, uniform triangle sampling, and directed triangle counts. Our methods come with provable and practical probabilistic error estimates for all computations. We provide extensive results that show our methods are both more accurate and faster than state-of-the-art alternatives. © 2014 Wiley Periodicals, Inc.

More Details
TYPE Journal Article YEAR 2014
ScopusOSTIDOI

A scalable generative graph model with community structure

SIAM Journal on Scientific Computing

Kolda, Tamara G.; Pinar, Ali; Plantenga, Todd P.; Comandur, Seshadhri C.

Network data is ubiquitous and growing, yet we lack realistic generative network models that can be calibrated to match real-world data. The recently proposed block two-level Erd?os- Rényi (BTER) model can be tuned to capture two fundamental properties: degree distribution and clustering coefficients. The latter is particularly important for reproducing graphs with community structure, such as social networks. In this paper, we compare BTER to other scalable models and show that it gives a better fit to real data. We provide a scalable implementation that requires only O(dmax) storage, where dmax is the maximum number of neighbors for a single node. The generator is trivially parallelizable, and we show results for a Hadoop MapReduce implementation for modeling a real-worldWeb graph with over 4.6 billion edges. We propose that the BTER model can be used as a graph generator for benchmarking purposes and provide idealized degree distributions and clustering coefficient profiles that can be tuned for user specifications.

More Details
TYPE Journal Article YEAR 2014
ScopusOSTI

An adaptive shifted power method for computing generalized tensor eigenpairs

SIAM Journal on Matrix Analysis and Applications

Kolda, Tamara G.; Mayo, Jackson M.

Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson, and Zhang [J. Math. Anal. Appl., 350 (2009), pp. 416-422]. Given mth-order, n-dimensional realvalued symmetric tensors A and B, the goal is to find λ ε ℝ and x ε ℝn, x ≠= 0 such that Axm-1 = λBxm-1. Different choices for B yield different versions of the tensor eigenvalue problem. We present our generalized eigenproblem adaptive power (GEAP) method for solving the problem, which is an extension of the shifted symmetric higher-order power method (SS-HOPM) for finding Z-eigenpairs. A major drawback of SS-HOPM is that its performance depended on choosing an appropriate shift, but our GEAP method also includes an adaptive method for choosing the shift automatically.

More Details
TYPE Journal Article YEAR 2014
ScopusOSTIDOI
Results 76–100 of 199
Results 76–100 of 199