| Suykens J.A.K., Vandewalle J., "Multiclass Least Squares Support Vector Machines," International Joint Conference on Neural Networks (IJCNN '99), Washington DC, July 1999. |
....Discriminant (b) Support Vector Machine Fig. 1. Comparison between KFD and SVM in a two class problem. Of course, that procedure represents a very complex algorithm in practice. Furthermore, the solution of multiclass SVM it has been already proposed using different and more efficient frameworks [14] [2] Then, the advantage of our approach lies on the fact that we can better understand the relation between KFD and SVM. As we have seen, the advantage of KFD is that its definition of the margin is statistically more precise than the one of SVM, and the advantage of SVM is that it only needs ....
Suykens J., and Vandewalle J., "Multiclass Least Square Support Vector Machine", Int. Joint Conf On Neural Networks IJCNN'99, Washington D.C., 1999.
....as we propose here, requires nolbhing more sophislbicalbed lbhan solving k syslbems of linear equalbions. EfIicienlb and faslb linear equalbion solvers are freely available [1] or are parlb of slbandard commercial packages such as MATLAB [18] and can solve very large syslbems. We nolbe lbhalb in [23], a mukiclass leaslb squares formulalbion is proposed lbhalb explicilbly requires Mercer s poskive definilbe heSS condilbion [25, 8] on lbhe kernels used which is nolb needed here. In addkion, lbhe problem in [23] is formulalbed as single large conslbrained oplbimizalbion problem in conlbraslb ....
....packages such as MATLAB [18] and can solve very large syslbems. We nolbe lbhalb in [23] a mukiclass leaslb squares formulalbion is proposed lbhalb explicilbly requires Mercer s poskive definilbe heSS condilbion [25, 8] on lbhe kernels used which is nolb needed here. In addkion, lbhe problem in [23] is formulalbed as single large conslbrained oplbimizalbion problem in conlbraslb lbo lbhe k smaller uncoupled and unconslbrained OFR approach used here. An inlbereslbing numerical comparison of mukiclass melbhods is given in [13] We summarize lbhe conlbenlbs of lbhe paper now. In Seclbion 2 we ....
J. A. K. Suykens and J. Vandewalle. Multiclass least squares support vector machines. In Proceedings of IJCNN'99, pages CD ROM, Washington, DC, 1999.
....seriously affected the progress rate 19 . 19 Many experiments had to be delayed because their parameter choices were to be based on experi Chapter 3. Experiments 55 To solve the restrictions on training set size, some variants of the SVM algorithm found in literature was examined ( 17] and [57]) These were designed to alleviate the problem, and claimed to function with extreme amounts of training data. However, these were found to return inferior results 20 . Regarding the bias, it was observed that the built in implicit bias in the large scale binary classifiers increased overall ....
J. A. K. Suykens and J. Vandewalle. Multiclass least squares support vector machines. In IJCNN'99 International Joint Conference on Neural Networks, Washington, DC, 1999.
.... account the fact that the computational complexity strongly increases with the number of training data least squares support vector machines (LS SVM s) can be efficiently estimated using iterative methods [4, 11] A straightforward extension of LS SVM s to the multiclass problem has been made in [12]. Related work on ridge regression type SVM s is [7] but without considering a bias term, which has serious implications concerning algorithms) 2] A drawback of LS SVM s on the other hand is that sparseness is lost due to the form of ridge regression. This is important in the context of an ....
Suykens J.A.K., Vandewalle J., "Multiclass Least Squares Support Vector Machines," Int. Joint Conference on Neural Networks IJCNN'99, Washington DC, July 1999.
.... In this paper we further investigate least squares support vector machines (LS SVM s) for function estimation, which is related to a ridge regression type of SVM [8] but with inclusion of an additional bias term in the model) LS SVM s were also proposed in the context of classification in [11, 12, 13]. Vapnik s SVM formulation is modified in the sense of ridge regression and taking equality instead of inequality constraints in the problem formulation. As a result one solves a linear system instead of a QP problem. An iterative method for solving large scale problems has been discussed in [12] ....
Suykens J.A.K., Vandewalle J., "Multiclass Least Squares Support Vector Machines," International Joint Conference on Neural Networks IJCNN'99, Washington DC, July 1999.
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Suykens J.A.K., Vandewalle J., "Multiclass Least Squares Support Vector Machines," International Joint Conference on Neural Networks (IJCNN '99), Washington DC, July 1999.
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