J. Suykens, J. Vandewalle, Least squares support vector machine classifiers, Neural Processing Letters 9 (3) (1999) 293--300. Home/Search Document Details and Download
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Nonlinear Modelling and Support Vector Machines - Suykens (2001) (Correct)
.... estimation) LS SVMs have been extended to recurrent models [31] and use in optimal control problems [32] The use of LS SVMs also has a number of computational advantages due to the availability of efficient iterative methods such as Krylov subspace methods (e.g. conjugate gradient methods) [29]. On the other hand, the use of a least squares cost function has potential drawbacks like the lack of sparseness in the solution vector and the condition for optimality under Gaussian assumptions. However, one can overcome these two problems [33] Because of the primal dual LS SVM formulation ....
Suykens J.A.K., Lukas L., Van Dooren P., De Moor B., Vandewalle J., "Least squares support vector machine classifiers: a large scale algorithm, " European Conference on Circuit Theory and Design, (ECCTD '99), pp.839-842, Stresa Italy, August 1999.
Nonlinear Modelling and Support Vector Machines - Suykens (2001) (Correct)
....support vector machines for classification and nonlinear function estimation, as originally introduced by Vapnik. Then we will focus on a least squares support vector machines version (LSSVM) which involves solving linear systems, for classification and nonlinear function estimation problems [28], 18] In primal weight space one formulates a constrained optimization problem which may take an infinite number of unknown parameters. However, one computes the solution of support values in the dual space instead of this primal weight space, after applying the Mercer condition. When no bias ....
....is decomposed into smaller subproblems. Platt s SMO (Sequential Minimal Optimization) is an extreme form of chunking. Another large scale method is successive overrelaxation (SOR) Mangasarian) which has been applied to huge data sets for SVMs. III. LEAST SQUARES SUPPORT VECTOR MACHINES In [28] we have modified Vapnik s SVM classifier formulation as follows: 1 subject to the equality constraints (x k ) b] 1 e k ; k = 1; N: 14) Feature space Input space x x x x x x x x x x x x x x x f (x) Fig. 4. In ....
Suykens J.A.K., Vandewalle J., "Least squares support vector machine classifiers," Neural Processing Letters, Vol.9, No.3, pp.293-300, 1999.
Regularized Least-Squares Classification - Rifkin, Yeo, Poggio (Correct)
....they penalize c c directly, which leads to a substantially more complicated algorithm. For linear RLSC where n #, they show how to use the Sherman Morrison Woodbury to solve the problem rapidly (see Section 7. 4) Suykens also uses the square loss in his Least Squares Support Vector Machines [16], but allows the unregularized free bias term b to remain, leading to a slightly di#erent optimization problem. We chose a new name for this old algorithm, Regularized Least Squares Classification, to emphasize both the key connection with regularization, and the fact RLSC is not a standard ....
J.A.K. Suykens and J. Vandewalle, Least squares support vector machine classifiers, Neural Processing Letters 9(3) (1999) 293--300.
Efficient Leave-One-Out Cross-Validation of Kernel Fisher.. - Cawley, Talbot (2003) (Correct)
....# # b# # # # # # # # # # # # 1# # # # # # where 1 is a column vector of # ones and y is a column vector with elements y i = # # j #i : x i j . This illustrates the similarities between the kernel Fisher discriminant and the least squares support vector machine (LS SVM) [21]. The kernel Fisher discriminant (KFD) classifier has been shown experimentally to demonstrate near state of the art performance on a range of artificial and real world benchmark datasets [1] and so is worthy of consideration for small to medium scale applications. 4 E#cient Leave One Out ....
J. A. K. Suykens and J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Letters, 9(3):293--300, June 1990.
A Study on Reduced Support Vector Machines - Kuan-Ming Lin And (2003) (3 citations) (Correct)
....theoretical analysis about the generalization error. This paper is organized as follows. In Section II, we outline the key modifications from standard SVM to RSVM. In Section III, we detail the Smooth SVM (SSVM) method used in [11] and apply three more techniques, the Least Square SVM (LS SVM) [23], the Lagrangian SVM (LSVM) 15] and the decomposition method to solve the RSVM problem. Issues related to practical implementations such as stopping criteria and approaches for solving multi class problems are in Section IV. Numerical experiments are in Section V which present that the accuracy ....
....Now we choose m l so we are safe to apply methods which were originally mainly suitable for linear SVM. In Section III A we will discuss the SSVM originally used in [10] while in Sections III B III D, we consider three methods which were suitable for linear SVM: Least Square SVM (LS SVM) [23], Lagrangian SVM (LSVM) 15] and the decomposition method for linear SVM. Before describing different implementations, for the sake of convenience, with following substitution Q = Q : R y b we consider a simpler form: #,# subject to #. 13) A. Using SSVM ....
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J. Suykens and J. Vandewalle. Least square support vector machine classifiers. Neural Processing Letters, 9(3):293--300, 1999.
Efficient Leave-One-Out Cross-Validation of Kernel Fisher.. - Cawley, Talbot (2003) (Correct)
....# b # # # # # # # # # # # # # # # # # # where 1 is a column vector of # ones and y is a column vector with elements y i = # # j #i : x i j . This illustrates the similarities between the kernel Fisher discriminant and the least squares support vector machine (LS SVM) [21]. The kernel Fisher discriminant (KFD) classifier has been shown experimentally to demonstrate near state of the art performance on a range of artificial and real world benchmark datasets [1] and so is worthy of consideration for small to medium scale applications. 4 E#cient Leave One Out ....
J. A. K. Suykens and J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Letters, 9(3):293--300, June 1990.
Faculteit Economie - En Bedrijfskunde Gent Self-citation (Suykens) (Correct)
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J. Suykens, J. Vandewalle, Least squares support vector machine classifiers, Neural Processing Letters 9 (3) (1999) 293--300.
Primal-Dual Monotone Kernel Regression - Pelckmans Espinoza De Self-citation (Suykens) (Correct)
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J.A.K. Suykens and J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Letters, 9(3):293--300, 1999.
Sparse LS-SVMs using Additive Regularization with a - Penalized Validation Criterion Self-citation (Suykens) (Correct)
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J.A.K. Suykens and J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Letters, 9(3):293--300, 1999.
and Stability for Additively Regularized LS-SVMs via - Convex Optimization Pelckmans (2004) Self-citation (Suykens) (Correct)
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J.A.K. Suykens and J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Letters, 9(3):293--300, 1999.
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J.A.K. Suykens and J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Letters, 9:293--300, 1999.
Partially Linear Models and Least Squares Support Vector.. - Espinoza, Suykens, De Moor (2004) Self-citation (Suykens) (Correct)
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J.A.K. Suykens and J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Letters, 9:293--300, 1999.
LS-SVM Regression Modelling and its Applications - De Brabanter (2004) Self-citation (Suykens Vandewalle) (Correct)
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Suykens, J.A.K., Vandewalle, J. (1999). Least squares support vector machine classifiers. Neural Processing Letters. Vol. 9(3), 293-300.
Regularization Constants in LS-SVMs: a Fast Estimate.. - Pelckmans, Suykens, De .. Self-citation (Suykens) (Correct)
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J. A. K. Suykens and J. Vandewalle, "Least squares support vector machine classifiers," Neural Processing Letters, vol. 9, no. 3, pp. 293-- 300, 1999.
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J. A. K. Suykens and J. Vandewalle, "Least squares support vector machine classifiers, " Neural Processing Letters, vol. 9, no. 3, pp. 293--300, june 1999.
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J.A.K. Suykens and J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Letters, 9:293-- 300, 1999.
Subspace Identification of Hammerstein Systems.. - Goethals.. Self-citation (Suykens) (Correct)
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J.A.K. Suykens, J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Letters, 9(3):293--300, 1999.
Departement Elektrotechniek ESAT-SISTA/TR 00-47 - Tom Schouten Suykens (2000) Self-citation (De moor) (Correct)
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Suykens J.A.K., Lukas L., Van Dooren P., De Moor B., Vandewalle J., "Least squares support vector machine classifiers: a large scale algorithm, " European Conference on Circuit Theory and Design, (ECCTD'99), pp.839-842, Stresa Italy, August 1999.
LS-SVMlab: a MATLAB/C toolbox for Least Squares.. - Pelckmans.. Self-citation (Vandewalle) (Correct)
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Suykens J.A.K., Vandewalle J., "Least squares support vector machine classifiers," Neural Processing Letters, 9(3), 293-300, 1999.
Predictive Low-Rank Decomposition for Kernel Methods - Francis Bach Francis (2005) (1 citation) (Correct)
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J. A. K. Suykens and J. Vandewalle. Least squares support vector machine classifiers. Neural Proc. Let., 9 (3):293--300, 1999.
Efficient Kernel Machines Using the Improved Fast Gauss.. - Yang, Duraiswami, Davis (2004) (Correct)
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J. A. K. Suykens and J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Letters, 9(3):293--300, 1999.
Reliable Spurious Mode Rejection Using Self Learning.. - Goethals, Vanluyten, De.. (2004) (Correct)
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J.A.K. Suykens, J. Vandewalle. "Least squares support vector machine classifiers," Neural Processing Letters, 9(3):293--300, 1999.
Sparseness of Support Vector Machines---Some - Asymptotically Sharp Bounds (2003) (Correct)
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J.A.K. Suykens and J. Vandewalle. Least squares support vector machine classifiers. Neural Processing Letters, 9:293--300, 1999.
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Suykens JAK, Vandewalle J. Least squares support vector machine classifiers, Neural Process Lett 1999;9(3):293-300.
Departement Elektrotechniek ESAT-SISTA/TR 00-47 - Tom Schouten Suykens (2000) (Correct)
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Suykens J.A.K., Vandewalle J., "Least squares support vector machine classifiers," Neural Processing Letters, Vol.9, No.3, pp.293-300, June 1999.
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