Donniell E. Fishkind

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For random graphs distributed according to a stochastic block model, we consider the inferential task of partitioning vertices into blocks using spectral techniques. Spectral partitioning using the normalized Laplacian and the adjacency matrix have both been shown to be consistent as the number of vertices tend to infinity. Importantly, both procedures(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)
Suppose there is a need to swiftly navigate through a spatial arrangement of possibly forbidden regions, with each region marked with the probability that it is, indeed, forbidden. In close proximity to any of these regions, you have the dynamic capability of disambiguating the region and learning for certain whether or not the region is forbidden—only in(More)
We consider the problem of safely and swiftly navigating through a spatial arrangement of potential hazard detections in which each detection has associated with it a probability that the detection is indeed a true hazard. When in close proximity to a detection, we assume the ability—for a cost—to determine whether or not the hazard is real. Our approach to(More)
The human cerebral cortex is topologically equivalent to a sphere when it is viewed as closed at the brain stem. Due to noise and/or resolution issues, magnetic resonance imaging may see "handles" that need to be eliminated to reflect the true spherical topology. Shattuck and Leahy present an algorithm to correct such an image. The basis for their(More)
Suppose that a graph is realized from a stochastic block model where one of the blocks is of interest, but many or all of the vertices’ block labels are unobserved. The task is to order the vertices with unobserved block labels into a “nomination list” such that, with high probability, vertices from the interesting block are concentrated near the list’s(More)
The problem we consider is a stochastic shortest path problem in the presence of a dynamic learning capability. Specifically, a spatial arrangement of possible obstacles needs to be traversed as swiftly as possible, and the status of the obstacles may be disambiguated (at a cost) en route. No efficiently computable optimal policy is known, and many similar(More)
In this paper we exhibit, under suitable conditions, a neat relationship between the Moore–Penrose generalized inverse of a sum of two matrices and the Moore–Penrose generalized inverses of the individual terms. We include an application to the parallel sum of matrices. AMS 1991 subject classifications. Primary 15A09; secondary 15A18.
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)
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)