We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal action of the symmetric group on the sets of commuting and anticommuting variables. In this work, we present the superspace extension of the clas...

The spectral bundle method was introduced by Helmberg and Rendl [13] to solve a class of eigenvalue optimization problems that is equivalent to the class of semidefinite programs with the constant trace property. We investigate the feasibility and effectiveness of including full or partial second-order information in the spectral bundle method, building on work of Overton and Womersley [20, 23]...

An orthogonal forward selection (OFS) algorithm based on leave-one-out (LOO) misclassification rate is proposed for the construction of radial basis function (RBF) classifiers with tunable units. Each stage of the construction process determines a RBF unit, namely its centre vector and diagonal covariance matrix as well as weight, by minimising the LOO statistics. This OFS-LOO algorithm is comp...

In our previous work we have shown that Mahalanobis kernels are useful for support vector classifiers both from generalization ability and model selection speed. In this paper we propose using Mahalanobis kernels for function approximation. We determine the covariance matrix for the Mahalanobis kernel using all the training data. Model selection is done by line search. Namely, first the margin ...