Abstract: Among neural models the Support Vector Machine
(SVM) solutions are attracting increasing attention, mostly because
they eliminate certain crucial questions involved by neural network
construction. The main drawback of standard SVM is its high
computational complexity, therefore recently a new technique, the
Least Squares SVM (LS–SVM) has been introduced. In this paper we
present an extended view of the Least Squares Support Vector
Regression (LS–SVR), which enables us to develop new
formulations and algorithms to this regression technique. Based on
manipulating the linear equation set -which embodies all information
about the regression in the learning process- some new methods are
introduced to simplify the formulations, speed up the calculations
and/or provide better results.
Abstract: In comparison to the original SVM, which involves a
quadratic programming task; LS–SVM simplifies the required
computation, but unfortunately the sparseness of standard SVM is
lost. Another problem is that LS-SVM is only optimal if the training
samples are corrupted by Gaussian noise. In Least Squares SVM
(LS–SVM), the nonlinear solution is obtained, by first mapping the
input vector to a high dimensional kernel space in a nonlinear
fashion, where the solution is calculated from a linear equation set. In
this paper a geometric view of the kernel space is introduced, which
enables us to develop a new formulation to achieve a sparse and
robust estimate.