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Efficient kernel clustering using random fourier features
 In Proceedings of ICDM’12
, 2012
"... Abstract—Kernel clustering algorithms have the ability to capture the nonlinear structure inherent in many real world data sets and thereby, achieve better clustering performance than Euclidean distance based clustering algorithms. However, their quadratic computational complexity renders them nons ..."
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Abstract—Kernel clustering algorithms have the ability to capture the nonlinear structure inherent in many real world data sets and thereby, achieve better clustering performance than Euclidean distance based clustering algorithms. However, their quadratic computational complexity renders them nonscalable to large data sets. In this paper, we employ random Fourier maps, originally proposed for large scale classification, to accelerate kernel clustering. The key idea behind the use of random Fourier maps for clustering is to project the data into a lowdimensional space where the inner product of the transformed data points approximates the kernel similarity between them. An efficient linear clustering algorithm can then be applied to the points in the transformed space. We also propose an improved scheme which uses the top singular vectors of the transformed data matrix to perform clustering, and yields a better approximation of kernel clustering under appropriate conditions. Our empirical studies demonstrate that the proposed schemes can be efficiently applied to large data sets containing millions of data points, while achieving accuracy similar to that achieved by stateoftheart kernel clustering algorithms. KeywordsKernel clustering, Kernel kmeans, Random Fourier features, Scalability
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J_ID: z8m Customer A_ID: 100145.R2 Cadmus Art: NAV21474 KGL ID: JWNAVT110078 — 2011/12/23 — page 1—#1 Rectangles Algorithm for Generating Normal Variates
, 2011
"... Abstract: We propose an algorithm for generating normal random variates that is based on the acceptance–rejection method and uses a piecewise majorizing function. The piecewise function has 2048 equalarea pieces, 2046 of which are constant, and the two extreme pieces are curves that majorize the ta ..."
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Abstract: We propose an algorithm for generating normal random variates that is based on the acceptance–rejection method and uses a piecewise majorizing function. The piecewise function has 2048 equalarea pieces, 2046 of which are constant, and the two extreme pieces are curves that majorize the tails. The proposed algorithm has not only good performance from correlation induction perspective, but also works well from a speed perspective. It is faster than the inversion method by Odeh and Evans and most other
a Two New RatioofUniforms Gamma Random Number Generators
"... Abstract: Two simple algorithms to generate gamma random numbers are proposed in this article. Both algorithms use the ratioofuniforms method and are based on logarithmic transformations of the gamma random variable. One algorithm applies to all positive shape parameter value without limitation. I ..."
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Abstract: Two simple algorithms to generate gamma random numbers are proposed in this article. Both algorithms use the ratioofuniforms method and are based on logarithmic transformations of the gamma random variable. One algorithm applies to all positive shape parameter value without limitation. It has good performance compared with other existing algorithms for both shape parameter values greater than 1 and smaller than 1. The other algorithm is limited to shape parameter smaller or equal to 1, but it has better performance compared with the first algorithm in that limited shape parameter range. Furthermore, the proposed methods will gain more efficiency if the logarithmic scale is used for the generated Gamma random numbers. Key words and phrases: Random Number Generation, RatioofUniforms, Simulation 1 1
Optimal Trading Strategies as Measures of Market Disequilibrium
"... For classification of the high frequency trading quantities, waiting times, price increments within and between sessions are referred to as the a, b, and cincrements. Statistics of the abcincrements are computed for the Time & Sales records posted by the Chicago Mercantile Exchange Group ..."
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For classification of the high frequency trading quantities, waiting times, price increments within and between sessions are referred to as the a, b, and cincrements. Statistics of the abcincrements are computed for the Time & Sales records posted by the Chicago Mercantile Exchange Group for the futures traded on Globex. The Weibull, Kumaraswamy, Riemann and Hurwitz Zeta, parabolic, ZipfMandelbrot distributions are tested for the a and bincrements. A discrete version of the FisherTippett distribution is suggested for approximating the extreme bincrements. Kolmogorov and Uspenskii classification of stochastic, typical, and chaotic random sequences is reviewed with regard to the futures price limits. Nonparametric L1 and loglikelihood tests are applied to check dependencies between the a and bincrements. The maximum profit strategies and optimal trading elements are suggested as measures of frequency and magnitude of the market offers and disequilibrium. Em