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Graph matching-aligning a pair of graphs to minimize their edge disagreements-has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have… (More)

We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures. We justify our approach by proving that modestly correlated, large stochastic block model random graphs are correctly… (More)

- Joshua T. Vogelstein, John M. Conroy, Vince Lyzinski, Louis J. Podrazik, Steven G. Kratzer, Eric T. Harley +3 others
- 2011

Graph matching (GM)—the process of finding an optimal permutation of the vertices of one graph to minimize adjacency disagreements with the vertices of another—is rapidly becoming an increasingly important computational problem, arising in fields ranging from machine vision to neuroscience. Because GM is N P-hard, exact algorithms are unsuitable for today's… (More)

Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of… (More)

- Vince Lyzinski, Daniel L Sussman, Minh Tang, Avanti Athreya, Carey E Priebe
- 2015

Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In this paper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering for the stochastic blockmodel and the degree-corrected stochastic blockmodel. We also show an analogous result for the… (More)

Unsupervised term discovery (UTD) is the task of automatically identifying the repeated words and phrases in a collection of speech audio without relying on any language-specific resources. While the solution space for the task is far from fully explored, the dominant approach to date decomposes the discovery problem into two steps, where (i) segmental… (More)

We develop a systematic matrix-analytic approach, based on intertwinings of Markov semigroups, for proving theorems about hitting-time distributions for finite-state Markov chains—an approach that (sometimes) deepens understanding of the theorems by providing corresponding sample-path-by-sample-path stochastic constructions. We employ our approach to give… (More)

We investigate joint graph inference for the chemical and electrical connectomes of the Caenorhabditis elegans roundworm. The C. elegans connectomes consist of [Formula: see text] non-isolated neurons with known functional attributes, and there are two types of synaptic connectomes, resulting in a pair of graphs. We formulate our joint graph inference from… (More)

Owing to random memory access patterns, sparse matrix multiplication is traditionally performed in memory and scales to large matrices using the distributed memory of multiple nodes. In contrast, we scale sparse matrix multiplication by utilizing commodity SSDs. We implement sparse matrix dense matrix multiplication (SpMM) in a semi-external memory (SEM)… (More)