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- Austin R. Benson, David F. Gleich, Jure Leskovec
- Science
- 2016

Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be captured at the level of individual nodes and edges. However, higher-order organization of complex networks--at the level of… (More)

- Austin R. Benson, Grey Ballard
- PPOPP
- 2015

Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and Strassen's fast algorithm on modest problem sizes and shapes. Furthermore, we show that the best choice of fast… (More)

- Austin R. Benson, David F. Gleich, James Demmel
- 2013 IEEE International Conference on Big Data
- 2013

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)

- Austin R. Benson, Sven Schmit, Robert Schreiber
- IJHPCA
- 2015

Errors due to hardware or low level software problems, if detected, can be fixed by various schemes, such as recomputation from a checkpoint. Silent errors are errors in application state that have escaped low-level error detection. At extreme scale, where machines can perform astronomically many operations per second, silent errors threaten the validity of… (More)

- Austin R. Benson, David F. Gleich, Jure Leskovec
- SDM
- 2015

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we… (More)

- Austin R. Benson, Jason D. Lee, Bartek Rajwa, David F. Gleich
- NIPS
- 2014

Introduction to (near-separable) NMF • NMF Problem: X ∈ Rm×n + is a matrix with nonnegative entries, and we want to compute a nonnegative matrix factorization (NMF) X = WH, where W ∈ Rm×r + and H ∈ Rr×n + . When r < m, this problem is NP-hard. • A separable matrix is one that admits a nonnegative factorization where W = X(:,K), i.e. W is just consists of… (More)

- Grey Ballard, Austin R. Benson, Alex Druinsky, Benjamin Lipshitz, Oded Schwartz
- SIAM J. Matrix Analysis Applications
- 2016

Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen’s original algorithm, few fast algorithms have been efficiently implemented or used in practical applications. However, there exist many… (More)

- Austin R. Benson, David F. Gleich, Lek-Heng Lim
- SIAM Review
- 2017

Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic process. A standard way to compute this distribution for a random walk on a finite set of states is to compute the… (More)

- Tao Wu, Austin R. Benson, David F. Gleich
- NIPS
- 2016

Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral co-clustering method that simultaneously clusters the rows, columns, and slices of a nonnegative three-mode tensor and… (More)

- Austin R. Benson, Carlos Riquelme, Sven Schmit
- KDD
- 2014

Using random graphs to model networks has a rich history. In this paper, we analyze and improve the multifractal network generators (MFNG) introduced by Palla <i>et al</i>. We provide a new result on the probability of subgraphs existing in graphs generated with MFNG. This allows us to quickly compute moments of an important set of graph properties, such as… (More)