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fast cross-validation of high-breakdown resampling methods for PCA

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2007年第10期51卷 5013-5024页

作者： Hubert, Mia Engelen, Sanne Katholieke Univ Leuven Dept Math B-3001 Louvain Belgium

Cross-validation (CV) is a very popular technique for model selection and model validation. The general procedure of leaveone-out CV (LOO-CV) is to exclude one observation from the data set, to construct the fit of the remaining observations and to evaluate that fit on the item that was left out. In classical procedures such as least-squares regression or kernel density estimation, easy formulas can be derived to compute this CV fit or the residuals of the removed observations. However, when high-breakdown resampling algorithms are used, it is no longer possible to derive such closed-form expressions. High-breakdown methods are developed to obtain estimates that can withstand the effects of outlying observations. fast algorithms are presented for LOO-CV when using a high-breakdown method based on resampling, in the context of robust covariance estimation by means of the MCD estimator and robust principal component analysis. A robust PRESS curve is introduced as an exploratory tool to select the number of principal components. Simulation results and applications on real data show the accuracy and the gain in computation time of these fast CV algorithms. (c) 2006 Elsevier B.V. All rights reserved.

关键词： cross-validation robustness MCD ROBPCA PRESS fast algorithms

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fast radiation pattern evaluation for lens and reflector antennas

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2003年第5期51卷 1063-1068页

作者： Boag, A Letrou, C Tel Aviv Univ Dept Elect Engn Phys Elect IL-69978 Tel Aviv Israel CNRS FRE 2310 GETINT Lab SAMOVAR F-91011 Evry France

A novel algorithm referred to as the fast physical optics (FPO) for computing the radiation patterns of nonplanar aperture antennas over a range of observation angles is presented. The computation is performed in the framework of the conventional physical optics approximation appropriate for the high frequency regime. The proposed algorithm is directly applicable to reflector and lens antennas as well as to radomes. The method comprises two steps. First, a decomposition of the aperture into subdomains and computation of the pertinent radiation pattern of each subdomain. Second, interpolation, phase-correction and aggregation of the radiation patterns into the final pattern of the whole aperture. A multilevel algorithm is formulated via a recursive application of the domain decomposition and aggregation steps. The computational structure of the multilevel algorithm resembles that of the FFT while avoiding its limitations.

关键词： computation time fast algorithms lens antennas physical optics radomes reflector antennas

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Singer product apertures-A coded aperture system with a fast decoding algorithm

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NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT 2017年 856卷 147-153页

作者： Byard, Kevin Shutler, Paul M. E. Auckland Univ Technol Fac Business Econ & Law Sch Econ Auckland 1142 New Zealand Nanyang Technol Univ Natl Inst Educ 1 Nanyang Walk Singapore 637616 Singapore

A new type of coded aperture configuration that enables fast decoding of the coded aperture shadowgram data is presented. Based on the products of incidence vectors generated from the Singer difference sets, we call these Singer product apertures. For a range of aperture dimensions, we compare experimentally the performance of three decoding methods: standard decoding, induction decoding and direct vector decoding. In all cases the induction and direct vector methods are several orders of magnitude faster than the standard method, with direct vector decoding being significantly faster than induction decoding. For apertures of the same dimensions the increase in speed offered by direct vector decoding over induction decoding is better for lower throughput apertures.

关键词： Coded aperture Singer sets Binary arrays fast algorithms

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ON fast ALGORITHM FOR TESTING THE STABILITY OF DISCRETE-TIME SYSTEMS

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SIGNAL PROCESSING 1989年第3期17卷 251-257页

作者： KRISHNA, H WANG, YB Department of Electrical and Computer Engineering Syracuse University Link Hall Syracuse NY 13244-1240 U.S.A.

In this work, we study the computational aspects of the algorithms for testing the strict sense and wide sense stability of discrete time systems. These algorithms are based on the computation of the reflection coefficients for a given real polynomial. The algorithms presented here require one-half the number of multiplications and the same number of additions as compared to the previously known similar algorithms. Zusammenfassung In dieser Arbeit werden Algorithmen untersucht, welche die Stabilität im weiteren und engeren Sinne für zeitdiskrete Systeme prüfen. Diese Algorithmen basieren auf der Bestimmung der Reflexionskoeffizienten für ein gegebenes reelles Polynom. Die hier vorgestellten Verfahren benötigen bei gleicher Anzahl von Additionen nur halb so viele Multiplikationen wie die bisher bekannten vergleichbaren Stabilitätstests.

关键词： fast algorithms discrete systems unit circle strict sense stability computational complexity multiplications and additions stepdown procedure

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A block splitting technique for fast 2D Walsh transform

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SIGNAL PROCESSING 2007年第5期87卷 1163-1168页

作者： Chen, Ningtao Shi, Baochang Wang, Nengchao Huazhong Univ Sci & Technol Sch Comp Sci & Technol Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Parallel Comp Inst Wuhan 430074 Peoples R China

A new two-dimensional (2D) Walsh transform scheme is presented based on a block splitting technique. The advantage of the proposed approach lies in the simple data flow architecture and the reduction in array accessing operations compared with the conventional row-column (RC) scheme. The new scheme exploits adequately two local accessing properties of the cache: the time local property and the space local property. The new 2D scheme is faster than the RC scheme when applying the same one-dimensional (ID) algorithm. (c) 2006 Elsevier B.V. All rights reserved.

关键词： fast algorithms 2D Walsh transforms Hadamard transform block splitting

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fast multi-order computation of system matrices in subspace-based system identification

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CONTROL ENGINEERING PRACTICE 2012年第9期20卷 882-894页

作者： Doehler, Michael Mevel, Laurent Ctr Rennes Bretagne Atlantique Inria F-35092 Rennes France

Subspace methods have proven to be efficient for the identification of linear time-invariant systems, especially applied to mechanical, civil or aeronautical structures in operation conditions. Therein, system identification results are needed at multiple (over-specified) model orders in order to distinguish the true structural modes from spurious modes using the so-called stabilization diagrams. In this paper, new efficient algorithms are derived for this multi-order system identification with subspace-based identification algorithms and the closely related Eigensystem Realization Algorithm. It is shown that the new algorithms are significantly faster than the conventional algorithms in use. They are demonstrated on the system identification of a large-scale civil structure. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： System identification Subspace methods Unknown model order fast algorithms Modal analysis Stabilization diagram

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A fast learning algorithm for time-delay neural networks

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INFORMATION SCIENCES 2002年第1-4期148卷 27-39页

作者： Jiang, MH Gielen, G Deng, BX Zhu, XY Tsing Hua Univ Dept Chinese Language Lab Computat Linguist Beijing 100084 Peoples R China Katholieke Univ Leuven Dept Elektrotech ESAT MICAS B-3001 Heverlee Belgium Tsing Hua Univ Dept Elect Engn Beijing 100084 Peoples R China Tsing Hua Univ State Key Lab Intelligent Tech & Syst Dept Comp Beijing 100084 Peoples R China

To solve the long training time in Waibel's time-delay neural networks (TDNNs) for phoneme recognition, several improved fast learning methods are put forward: (1) by a combination between the unsupervised Oja's rule learning method with the similar error backpropagation (BP) algorithm for initial weights training;(2) by improving of the error energy function with weights update according to the output error size;(3) by changing of BP error from along layers to frames and using the averaged overlapping part of frame-shift delta values in the weights of the bottom layer;(4) by training of the data from a small to large number of samples gradually;and (5) by using the optimal modular neural networks (OMNNs) with tree structure for multiple phonemes. Our experimental results indicate that the convergence speed is accelerated with orders of magnitude and in most cases the error function descends monotonically while the network complexity increases less and the recognition rates are almost the same among the different comparative experiments. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： phoneme recognition time-delay neural networks convergence speed fast algorithms

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Method of fast 1-D paired transforms for computing the 2-D discrete hadamard transform

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-ANALOG AND DIGITAL SIGNAL PROCESSING 2000年第10期47卷 1098-1104页

作者： Grigoryan, AM Agaian, SS Texas A&M Univ Dept Elect Engn College Stn TX 77843 USA Univ Texas Div Engn San Antonio TX 78249 USA

In this brief, two different approaches to compute the 2-D discrete Hadamard transform (DHAT) of sizes 2(r) x 2(r), r > 1 are presented. The both are based on the so-caned 1-D discrete paired transforms, which split the 2(r)-point DHAT into a set of smaller 2(r-z)-point transforms, i = 1 : r. The first approach is a column(rom)-wise algorithm which requires, on average, no more than 12 operations of additions per sample. The second approach is a splitting algorithm, in which the 2(r) x 2(r)-point DHAT is reduced to the computation of 2(r-1)3 1-D DHATs instead of 2(r+1) 1-D DHAT's in the column(rom)-wise algorithm, but requires more operations of additions. Examples and comparison of the proposed algorithms with the known algorithms are provided.

关键词： fast algorithms Hadamard transform paired functions

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fast fundamental frequency estimation: Making a statistically efficient estimator computationally efficient

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SIGNAL PROCESSING 2017年 135卷 188-197页

作者： Nielsen, Jesper Kjaer Jensen, Tobias Lindstrom Jensen, Jesper Rindom Christensen, Mads Graesboll Jensen, Soren Holdt Aalborg Univ Audio Anal Lab AD MT Rendsburggade 14 DK-9000 Aalborg Denmark Bang & Olufsen AS Acoust Res Peter Bangs Vej 15 DK-7600 Struer Denmark Aalborg Univ Dept Elect Syst Fredrik Bajers Vej 7B DK-9220 Aalborg Denmark

Modelling signals as being periodic is common in many applications. Such periodic signals can be represented by a weighted sum of sinusoids with frequencies being an integer multiple of the fundamental frequency. Due to its widespread use, numerous methods have been proposed to estimate the fundamental frequency, and the maximum likelihood (ML) estimator is the most accurate estimator in statistical terms. When the noise is assumed to be white and Gaussian, the ML estimator is identical to the non-linear least squares (NLS) estimator. Despite being optimal in a statistical sense, the NLS estimator has a high computational complexity. In this paper, we propose an algorithm for lowering this complexity significantly by showing that the NLS estimator can be computed efficiently by solving two Toeplitz-plus-Hankel systems of equations and by exploiting the recursive-in-order matrix structures of these systems. Specifically, the proposed algorithm reduces the time complexity to the same order as that of the popular harmonic summation method which is an approximate NLS estimator. The performance of the proposed algorithm is assessed via Monte Carlo and timing studies. These show that the proposed algorithm speeds up the evaluation of the NLS estimator by a factor of 50-100 for typical scenarios.

关键词： Fundamental frequency estimation Toeplitz Hankel fast algorithms Pitch

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fast Matrix-Vector Multiplication in the Sparse-Grid Galerkin Method

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JOURNAL OF SCIENTIFIC COMPUTING 2011年第3期47卷 328-346页

作者： Zeiser, Andreas TU Berlin Inst Math D-10623 Berlin Germany

Sparse grid discretization of higher dimensional partial differential equations is a means to break the curse of dimensionality. For classical sparse grids based on the one-dimensional hierarchical basis, a sophisticated algorithm has been devised to calculate the application of a vector to the Galerkin matrix in linear complexity, despite the fact that the matrix is not sparse. However more general sparse grid constructions have been recently introduced, e.g. based on multilevel finite elements, where the specified algorithms only have a log-linear scaling. This article extends the idea of the linear scaling algorithm to more general sparse grid spaces. This is achieved by abstracting the algorithm given in (Balder and Zenger, SIAM J. Sci. Comput. 17:631, 1996) from specific bases, thereby identifying the prerequisites for performing the algorithm. In this way one can easily adapt the algorithm to specific discretizations, leading for example to an optimal linear scaling algorithm in the case of multilevel finite element frames.

关键词： Sparse grid Unidirectional principle fast algorithms Linear scaling Multilevel methods

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