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1.
Numerical Algorithms - In this paper, we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II that reconstructs the vector $mathbf {x}in mathbb... 相似文献
2.
In this paper we consider the special case where a signal x\({\in }\,\mathbb {C}^{N}\) is known to vanish outside a support interval of length m < N. If the support length m of x or a good bound of it is a-priori known we derive a sublinear deterministic algorithm to compute x from its discrete Fourier transform \(\widehat {\mathbf x}\,{\in }\,\mathbb {C}^{N}\). In case of exact Fourier measurements we require only \({\mathcal O}\)(m\(\log \)m) arithmetical operations. For noisy measurements, we propose a stable \({\mathcal O}\)(m\(\log \)N) algorithm. 相似文献
3.
Refinable function vectors with arbitrary support are considered. In particular, necessary conditions for stability are given and a characterization of the symbol associated with a stable refinable function vector in terms of the transfer operator is provided: this is a generalization of Gundy’s theorem to the vector case. The proof adapts the tools provided in [S. Saliani, On stability and orthogonality of refinable functions, Appl. Comput. Harmon. Anal. 21 (2006) 254–261]. Though complications arise from noncommuting matrix products, the fundamental ideas are the same. 相似文献
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5.
《European Journal of Operational Research》2001,130(2):402-413
Classification is one of the most extensively studied problems in the fields of multivariate statistical analysis, operations research and artificial intelligence. Decisions involving a classification of the alternative solutions are of major interest in finance, since several financial decision problems are best studied by classifying a set of alternative solutions (firms, loan applications, investment projects, etc.) in predefined classes. This paper proposes an alternative approach to the classical statistical methodologies that have been extensively used for the study of financial classification problems. The proposed methodology combines the preference disaggregation approach (a multicriteria decision aid method) with decision support systems. More specifically, the FINancial CLASsification (FINCLAS) multicriteria decision support system is presented. The system incorporates a plethora of financial modeling tools, along with powerful preference disaggregation methods that lead to the development of additive utility models for the classification of the considered alternatives into predefined classes. An application in credit granting is used to illustrate the capabilities of the system. 相似文献
6.
We consider the problem of deleting bad influential observations (outliers) in linear regression models. The problem is formulated
as a Quadratic Mixed Integer Programming (QMIP) problem, where penalty costs for discarding outliers are used into the objective
function. The optimum solution defines a robust regression estimator called penalized trimmed squares (PTS). Due to the high
computational complexity of the resulting QMIP problem, the proposed robust procedure is computationally suitable for small
sample data. The computational performance and the effectiveness of the new procedure are improved significantly by using
the idea of ε-Insensitive loss function from support vectors machine regression. Small errors are ignored, and the mathematical formula
gains the sparseness property. The good performance of the ε-Insensitive PTS (IPTS) estimator allows identification of multiple outliers avoiding masking or swamping effects. The computational
effectiveness and successful outlier detection of the proposed method is demonstrated via simulated experiments.
This research has been partially funded by the Greek Ministry of Education under the program Pythagoras II. 相似文献
7.
Ioannis K. Argyros 《Journal of Applied Mathematics and Computing》2006,21(1-2):119-126
Local as well as semilocal convergence theorems for Newton-like methods have been given by us and other authors [1]—[8] using various Lipschitz type conditions on the operators involved. Here we relax these conditions by introducing weaker center-Lipschitz type conditions. This way we can cover a wider range of problems than before in the semilocal case, where as in the local case a larger convergence radius can be obtained in some cases. 相似文献
8.
Discrete support vector machines (DSVM), originally proposed for binary classification problems, have been shown to outperform
other competing approaches on well-known benchmark datasets. Here we address their extension to multicategory classification,
by developing three different methods. Two of them are based respectively on one-against-all and round-robin classification schemes, in which a number of binary discrimination problems are solved by means of a variant of DSVM. The
third method directly addresses the multicategory classification task, by building a decision tree in which an optimal split
to separate classes is derived at each node by a new extended formulation of DSVM. Computational tests on publicly available
datasets are then conducted to compare the three multicategory classifiers based on DSVM with other methods, indicating that
the proposed techniques achieve significantly higher accuracies.
This research was partially supported by PRIN grant 2004132117. 相似文献
9.
Bing Zheng Li 《数学学报(英文版)》2008,24(3):511-528
The purpose of this paper is to provide an error analysis for the multicategory support vector machine (MSVM) classificaton problems. We establish the uniform convergency approach for MSVMs and estimate the misclassification error. The main difficulty we overcome here is to bound the offset vector. As a result, we confirm that the MSVM classification algorithm with polynomial kernels is always efficient when the degree of the kernel polynomial is large enough. Finally the rate of convergence and examples are given to demonstrate the main results. 相似文献
10.
Theodore B. Trafalis Olutayo O. Oladunni Michael B. Richman 《Computational Management Science》2011,8(3):281-297
A knowledge-based linear Tihkonov regularization classification model for tornado discrimination is presented. Twenty-three
attributes, based on the National Severe Storms Laboratory’s Mesoscale Detection Algorithm, are used as prior knowledge. Threshold
values for these attributes are employed to discriminate the data into two classes (tornado, non-tornado). The Weather Surveillance
Radar 1998 Doppler is used as a source of data streaming every 6 min. The combination of data and prior knowledge is used
in the development of a least squares problem that can be solved using matrix or iterative methods. Advantages of this formulation
include explicit expressions for the classification weights of the classifier and its ability to incorporate and handle prior
knowledge directly to the classifiers. Comparison of the present approach to that of Fung et al. [in Proceedings neural information
processing systems (NIPS 2002), Vancouver, BC, December 10–12, 2002], over a suite of forecast evaluation indices, demonstrates
that the Tikhonov regularization model is superior for discriminating tornadic from non-tornadic storms. 相似文献
11.
《Journal of Computational and Applied Mathematics》1997,83(1):131-135
We consider an inverse-free Jarratt-type approximation of order four in a Banach space (Argyros et al., 1996). We establish a convergence theorem by using recurrence relations. The purpose of this note is to relax convergence conditions and give an example where our convergence theorem can be applied but not the other ones. 相似文献
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S. S. Marchenkov 《Mathematical Notes》1997,61(3):295-300
Dually discriminator algebras are considered up to clones generated by the algebra operations. In terms of binary relations,
all clones of the operators on a finite set that contain the Pixley dual discriminator are efficiently described. As a consequence,
a similar clone classification of quasi-primal algebras with finite support is determined.
Translated fromMatematicheskie Zametki, Vol. 61, No. 3, pp. 359–366, March, 1997.
Translated by A. I. Shtern 相似文献
14.
Takeshi Asada Yeboon Yun Hirotaka Nakayama Tetsuzo Tanino 《Computational Management Science》2004,1(3-4):211-230
Support Vector Machines (SVMs) are now very popular as a powerful method in pattern classification problems. One of main features of SVMs is to produce a separating hyperplane which maximizes the margin in feature space induced by nonlinear mapping using kernel function. As a result, SVMs can treat not only linear separation but also nonlinear separation. While the soft margin method of SVMs considers only the distance between separating hyperplane and misclassified data, we propose in this paper multi-objective programming formulation considering surplus variables. A similar formulation was extensively researched in linear discriminant analysis mostly in 1980s by using Goal Programming(GP). This paper compares these conventional methods such as SVMs and GP with our proposed formulation through several examples.Received: September 2003, Revised: December 2003, 相似文献
15.
Theoretical and Mathematical Physics - We use the Riemann problem on a torus to obtain and analyze new analytic solutions of the Landau–Lifshitz model that describe the nonlinear dynamics of... 相似文献
16.
Yu. V. Goncharov I. B. Muchnik L. V. Shvartser 《Computational Mathematics and Mathematical Physics》2008,48(7):1243-1260
An algorithm for selecting features in the classification learning problem is considered. The algorithm is based on a modification
of the standard criterion used in the support vector machine method. The new criterion adds to the standard criterion a penalty
function that depends on the selected features. The solution of the problem is reduced to finding the minimax of a convex-concave
function. As a result, the initial set of features is decomposed into three classes—unconditionally selected, weighted selected,
and eliminated features.
Original Russian Text Yu.V. Goncharov, I.B. Muchnik, L.V. Shvartser @, 2008, published in Zhurnal Vychislitel’noi Matematiki
i Matematicheskoi Fiziki, 2008, Vol. 48, No. 7, pp. 1318–1336. 相似文献
17.
D. Han D. Larson Z. Pan W. Wogen 《Proceedings of the American Mathematical Society》2007,135(3):713-723
It is an open problem whether every one-dimensional extension of a triangular operator admits a separating vector. We prove that the answer is positive for many triangular Hilbert space operators, and in particular, for strictly triangular operators. This is revealing, because two-dimensional extensions of such operators can fail to have separating vectors.
18.
Akihiro Nishi 《Annals of the Institute of Statistical Mathematics》1977,29(1):433-444
Summary This paper is concerned with probabilities (error probabilities), caused by misclassification, of linear classification procedures
(linear procedures) between two categories, whose mean vectors and covariance matrices are assumed to be known, while the
distribution of each category may well be continuous or discrete. The tightest upper bounds on the largest of two kinds of
error probability of each linear procedure and on the expected error probability for any apriori probabilities are obtained.
Moreover in some cases of interest, theoptimal linear procedure (in the sense of attaining the infimum out of all the upper bounds) is given. 相似文献
19.
The Courant-Friedrichs-Lewy (CFL) condition guarantees the stability of the popular explicit leapfrog method for the wave equation. However, it limits the choice of the time step size to be bounded by the minimal mesh size in the spatial finite element mesh. This essentially prohibits any sort of adaptive mesh refinement that would be required to reveal optimal convergence rates on domains with re-entrant corners. A simple subspace projection step inspired by numerical homogenisation can remove the critical time step restriction so that the CFL condition and approximation properties are balanced in an optimal way, even in the presence of spatial singularities. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
We present semidefinite relaxations of nonconvex, box-constrained quadratic programming, which incorporate the first- and
second-order necessary optimality conditions, and establish theoretical relationships between the new relaxations and a basic
semidefinite relaxation due to Shor. We compare these relaxations in the context of branch-and-bound to determine a global
optimal solution, where it is shown empirically that the new relaxations are significantly stronger than Shor’s. An effective
branching strategy is also developed. 相似文献