A fast algorithm for the well-known Parzen window method to estimate density functions from the samples is described. The computational efforts required by the conventional and straightforward implementation of this e...
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A fast algorithm for the well-known Parzen window method to estimate density functions from the samples is described. The computational efforts required by the conventional and straightforward implementation of this estimation procedure limit its practical application to data of low dimensionality. The proposed algorithm makes the computation of the same density estimates with a substantial reduction of computer time possible, especially for data of high dimensionality. Some simulation experiments are presented which demonstrate the efficiency of the method. They indicate the computational savings that may be achieved through the use of this fast algorithm for artificially generated sets of data.","doi":"10.1109/TPAMI.1982.4767322","publicationTitle":"IEEE Transactions on Pattern Analysis and Machine Intelligence","startPage":"663","endPage":"666","rightsLink":"http://***/AppDispatchServlet?publisherName=ieee&publication=0162-8828&title=A+fast+algorithm+for+Nonparametric+Probability+Density+Estimation&isbn=&publicationDate=Nov.+1982&author=J.-G.+Postaire&ContentID=10.1109/TPAMI.1982.4767322&orderBeanReset=true&startPage=663&endPage=666&volumeNum=PAMI-4&issueNum=6","displayPublicationTitle":"IEEE Transactions on Pattern Analysis and Machine Intelligence","pdfPath":"/iel5/34/4767305/***","keywords":[{"type":"IEEE Keywords","kwd":["Kernel","Pattern recognition","Testing","Hypercubes","Density functional theory","Application software","Computational modeling","Probability density function","Random variables","Pattern analysis"]},{"type":"Author Keywords ","kwd":["pattern recognition","Density estimation","fast algorithm","Parzen window"]}],"allowComments":false,"pubLink":"/xpl/***?punumber=34","issueLink":"/xpl/***?isnumber=4767305","standardTitle":"A fast algorithm for Nonparametric Probability Density Estimation
Coherency measurements have proven to be an effective method for representing geological discontinuities such as faults and stradgraphic features in 3-D seismic data volumes. Unfortunately, application of the algorith...
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Coherency measurements have proven to be an effective method for representing geological discontinuities such as faults and stradgraphic features in 3-D seismic data volumes. Unfortunately, application of the algorithm suffers from the limitation of computation cost. This paper describes a new fast method for efficient and robust coherency estimation in 3-D seismic data. The method is characterized by greatly increasing the computational efficiency based on information divergence, which uses a recursion method and defines a new criterion by information divergence to calculate the coherency, to avoid directly computing the eigenvalues of the covariance matrix. In contrast to other algorithms, this method possesses higher computational efficiency and better anti-noise ability than commonly used methods. We demonstrate the advantage of this method using real seismic data examples. (C) 2015 Elsevier B.V. All rights reserved.
Motivated by the field experimental designs in agriculture, the theory of block designs has been applied to several areas such as statistics, combinatorics, communication networks, distributed systems, cryptography, e...
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Motivated by the field experimental designs in agriculture, the theory of block designs has been applied to several areas such as statistics, combinatorics, communication networks, distributed systems, cryptography, etc. An explicit formula and its fast computational algorithm for a class of symmetric balanced incomplete block designs are presented. Based on the formula and the careful investigation of the modulus multiplication table, the algorithm is developed. The computational costs of the algorithm is superior to those of the conventional ones.
In the past, prestack Gaussian beam migration adopted the steepest descent approximation to reduce the dimension of the integrals and speed up the computation. However, the simplified formula by the steepest descent a...
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In the past, prestack Gaussian beam migration adopted the steepest descent approximation to reduce the dimension of the integrals and speed up the computation. However, the simplified formula by the steepest descent approximation was still in the frequency domain, and it had to be evaluated at each frequency. To solve this problem, we present a fast algorithm by changing the order of the integrals. The innermost integral is regarded as a two-dimensional continuous function with respect to the real part and the imaginary part of the total traveltime. A lookup table corresponding to the value of the innermost integral is constructed at the sampling points. The value of the innermost integral at one imaging point can be obtained through interpolation in the constructed lookup table. The accuracy and efficiency of the fast algorithm are validated with the Marmousi dataset. The application to the Sigsbee2A dataset shows a good result.
A new fast algorithm for computing the two-dimensional discrete Hartley transform is presented. This algorithm requires the lowest number of multiplications compared with other related algorithms.
A new fast algorithm for computing the two-dimensional discrete Hartley transform is presented. This algorithm requires the lowest number of multiplications compared with other related algorithms.
Conditional Nonlinear Optimal Perturbation （CNOP） is a new method proposed by Mu et al. in 2003, which generalizes the linear singular vector （LSV） to include nonlinearity. It has become a powerful tool for studyi...
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Conditional Nonlinear Optimal Perturbation （CNOP） is a new method proposed by Mu et al. in 2003, which generalizes the linear singular vector （LSV） to include nonlinearity. It has become a powerful tool for studying predictability and sensitivity among other issues in nonlinear systems. This is because the CNOP is able to represent, while the LSV is unable to deal with, the fastest developing perturbation in a nonlinear system. The wide application of this new method, however, has been limited due to its large computational cost related to the use of an adjoint technique. In order to greatly reduce the computational cost, we hereby propose a fast algorithm for solving the CNOP based on the empirical orthogonal function （EOF）. The algorithm is tested in target observation experiments of Typhoon Matsa using the Global/Regional Assimilation and PrEdiction System （GRAPES）, an operational regional forecast model of China. The effectivity and feasibility of the algorithm to determine the sensitivity （target） area is evaluated through two observing system simulation experiments （OSSEs）. The results, as expected, show that the energy of the CNOP solved by the new algorithm develops quickly and nonlinearly. The sensitivity area is effectively identified with the CNOP from the new algorithm, using 24 h as the prediction time window. The 24-h accumulated rainfall prediction errors （ARPEs） in the verification region are reduced significantly compared with the ＂true state,＂ when the initial conditions （ICs） in the sensitivity area are replaced with the ＂observations.＂ The decrease of the ARPEs can be achieved for even longer prediction times （e.g., 72 h）. Further analyses reveal that the decrease of the 24-h ARPEs in the verification region is attributable to improved simulations of the typhoon＇s initial warm-core, upper level relative vorticity, water vapor conditions, etc., as a result of the updated ICs in the sensitivity area.
The subject of 2-D and higher dimensional object recognition finds widespread applications in areas such as image registration and pattern recognition. Radon transform is one technique used for efficient object matchi...
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The subject of 2-D and higher dimensional object recognition finds widespread applications in areas such as image registration and pattern recognition. Radon transform is one technique used for efficient object matching (e.g., and ). However, so far as we know, no results have been obtained that solves the recognition problem completely in the projection domain due to coupling of transform parameters. We develop a novel method for such parameter decoupling and an improved phase correlation method for accurate practical shift estimation, resulting in a fast matching algorithm based on projection data only. Simulation results show that the proposed algorithm is much faster than similar state-of-the-art approaches such as that in with comparable estimation accuracy.
The mathematical foundation of an algorithm for fast and accurate evaluation of singular integral transforms was given by Daripa [9,10,12]. By construction, the algorithm offers good parallelization opportunities and ...
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The mathematical foundation of an algorithm for fast and accurate evaluation of singular integral transforms was given by Daripa [9,10,12]. By construction, the algorithm offers good parallelization opportunities and a lower computational complexity when compared with methods based on quadrature rules. In this paper we develop a parallel version of the fast algorithm by redefining the inherently sequential recurrences present in the original sequential formulation. The parallel version only utilizes a linear neighbor-to-neighbor communication path, which makes the algorithm very suitable for any distributed memory architecture. Numerical results and theoretical estimates show good parallel scalability of the algorithm.
An algorithm for computing the normalized Hermite Functions, h(n)(x) in floating point arithmetic is presented. The algorithm is based on an efficient numerical evaluation of certain closed contour integrals in the co...
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An algorithm for computing the normalized Hermite Functions, h(n)(x) in floating point arithmetic is presented. The algorithm is based on an efficient numerical evaluation of certain closed contour integrals in the complex plane. For large degree n, the algorithm is significantly faster than the O(n) complexity of the well known three term recurrence relation. Comparable accuracy is achieved in no more than O(v n) operations, and for arguments bounded away from +/-root 2n, only O(root ln n) operations.
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