Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel

European exchange trading funds trading with locally weighted support vector regression

In this paper, two different Locally Weighted Support Vector Regression (wSVR) algorithms are generated and applied to the task of forecasting and trading five European Exchange Traded Funds. The trading application covers the recent European Monetary Union debt crisis. The performance of the proposed models is benchmarked against traditional Support Vector Regression (SVR) models. The Radial Basis Function, the Wavelet and the Mahalanobis kernel are explored and tested as SVR kernels. Finally, a novel statistical SVR input selection procedure is introduced based on a principal component analysis and the Hansen, Lunde, and Nason (2011) model confidence test. The results demonstrate the superiority of the wSVR models over the traditional SVRs and of the v-SVR over the ε-SVR algorithms. We note that the performance of all models varies and considerably deteriorates in the peak of the debt crisis. In terms of the kernels, our results do not confirm the belief that the Radial Basis Function is the optimum choice for financial series

Sparse multinomial kernel discriminant analysis (sMKDA)

Dimensionality reduction via canonical variate analysis (CVA) is important for pattern recognition and has been extended variously to permit more flexibility, e.g. by "kernelizing" the formulation. This can lead to over-fitting, usually ameliorated by regularization. Here, a method for sparse, multinomial kernel discriminant analysis (sMKDA) is proposed, using a sparse basis to control complexity. It is based on the connection between CVA and least-squares, and uses forward selection via orthogonal least-squares to approximate a basis, generalizing a similar approach for binomial problems. Classification can be performed directly via minimum Mahalanobis distance in the canonical variates. sMKDA achieves state-of-the-art performance in terms of accuracy and sparseness on 11 benchmark datasets