1,367 research outputs found

    Analysis of approximate nearest neighbor searching with clustered point sets

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    We present an empirical analysis of data structures for approximate nearest neighbor searching. We compare the well-known optimized kd-tree splitting method against two alternative splitting methods. The first, called the sliding-midpoint method, which attempts to balance the goals of producing subdivision cells of bounded aspect ratio, while not producing any empty cells. The second, called the minimum-ambiguity method is a query-based approach. In addition to the data points, it is also given a training set of query points for preprocessing. It employs a simple greedy algorithm to select the splitting plane that minimizes the average amount of ambiguity in the choice of the nearest neighbor for the training points. We provide an empirical analysis comparing these two methods against the optimized kd-tree construction for a number of synthetically generated data and query sets. We demonstrate that for clustered data and query sets, these algorithms can provide significant improvements over the standard kd-tree construction for approximate nearest neighbor searching.Comment: 20 pages, 8 figures. Presented at ALENEX '99, Baltimore, MD, Jan 15-16, 199

    Efficient data structures for model-free data-driven computational mechanics

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    The data-driven computing paradigm initially introduced by Kirchdoerfer & Ortiz (2016) enables finite element computations in solid mechanics to be performed directly from material data sets, without an explicit material model. From a computational effort point of view, the most challenging task is the projection of admissible states at material points onto their closest states in the material data set. In this study, we compare and develop several possible data structures for solving the nearest-neighbor problem. We show that approximate nearest-neighbor (ANN) algorithms can accelerate material data searches by several orders of magnitude relative to exact searching algorithms. The approximations are suggested by—and adapted to—the structure of the data-driven iterative solver and result in no significant loss of solution accuracy. We assess the performance of the ANN algorithm with respect to material data set size with the aid of a 3D elasticity test case. We show that computations on a single processor with up to one billion material data points are feasible within a few seconds execution time with a speed up of more than 10⁶ with respect to exact k-d trees

    Searching for a trail of evidence in a maze

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    Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following hypothesis testing problem: under the null, the random variables have common distribution N(0,1) while under the alternative, there is an unknown path along which random variables have distribution N(μ,1)N(\mu,1), μ>0\mu> 0, and distribution N(0,1) away from it. For which values of the mean shift μ\mu can one reliably detect and for which values is this impossible? Consider, for example, the usual regular lattice with vertices of the form {(i,j):0i,ijiandjhastheparityofi}\{(i,j):0\le i,-i\le j\le i and j has the parity of i\} and oriented edges (i,j)(i+1,j+s)(i,j)\to (i+1,j+s), where s=±1s=\pm1. We show that for paths of length mm starting at the origin, the hypotheses become distinguishable (in a minimax sense) if μm1/logm\mu_m\gg1/\sqrt{\log m}, while they are not if μm1/logm\mu_m\ll1/\log m. We derive equivalent results in a Bayesian setting where one assumes that all paths are equally likely; there, the asymptotic threshold is μmm1/4\mu_m\approx m^{-1/4}. We obtain corresponding results for trees (where the threshold is of order 1 and independent of the size of the tree), for distributions other than the Gaussian and for other graphs. The concept of the predictability profile, first introduced by Benjamini, Pemantle and Peres, plays a crucial role in our analysis.Comment: Published in at http://dx.doi.org/10.1214/07-AOS526 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Spectral Approaches to Nearest Neighbor Search

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    We study spectral algorithms for the high-dimensional Nearest Neighbor Search problem (NNS). In particular, we consider a semi-random setting where a dataset PP in Rd\mathbb{R}^d is chosen arbitrarily from an unknown subspace of low dimension kdk\ll d, and then perturbed by fully dd-dimensional Gaussian noise. We design spectral NNS algorithms whose query time depends polynomially on dd and logn\log n (where n=Pn=|P|) for large ranges of kk, dd and nn. Our algorithms use a repeated computation of the top PCA vector/subspace, and are effective even when the random-noise magnitude is {\em much larger} than the interpoint distances in PP. Our motivation is that in practice, a number of spectral NNS algorithms outperform the random-projection methods that seem otherwise theoretically optimal on worst case datasets. In this paper we aim to provide theoretical justification for this disparity.Comment: Accepted in the proceedings of FOCS 2014. 30 pages and 4 figure

    Feature Match for Medical Images

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    This paper represents an algorithm for Feature Match, a summed up estimated approximate nearest neighbor field (ANNF) calculation system, between a source and target image. The proposed calculation can estimate ANNF maps between any image sets, not as a matter of course related. This generalization is accomplished through proper spatial-range changes. To register ANNF maps, worldwide shading adjustment is connected as a reach change on the source picture. Image patches from the pair of pictures are approximated utilizing low-dimensional elements, which are utilized alongside KD-tree to appraise the ANNF map. This ANNF guide is further enhanced in view of picture coherency and spatial changes. The proposed generalization, empowers to handle a more extensive scope of vision applications, which have not been handled utilizing the ANNF structure. Here one such application is outlined namely: optic plate discovery .This application manages restorative imaging, where optic circles are found in retinal pictures utilizing a sound optic circle picture as regular target picture. ANNF mappings is used in this application and is shown experimentally that the proposed approaches are faster and accurate, compared with the state-of the-art techniques
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