# Austin R. Benson

• 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)
• 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&#039;s fast algorithm on modest problem sizes and shapes. Furthermore, we show that the best choice of fast(More)
• 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 &#x201C;tall-and-skinny matrices,&#x201D; there is a numerically stable, efficient, communication-avoiding algorithm for computing the QR factorization. It(More)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)