Bernard Haasdonk

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In this contribution we describe a novel classification approach for on-line handwriting recognition. The technique combines dynamic time warping (DTW) and support vector machines (SVMs) by establishing a new SVM kernel. We call this kernel Gaussian DTW (GDTW) kernel. This kernel approach has a main advantage over common HMM techniques. It does not assume a(More)
Kernel methods are becoming increasingly popular for various kinds of machine learning tasks, the most famous being the support vector machine (SVM) for classification. The SVM is well understood when using conditionally positive definite (cpd) kernel functions. However, in practice, non-cpd kernels arise and demand application in SVM. The procedure of(More)
During recent years much effort has been spent in incorporating problem specific a-priori knowledge into kernel methods for machine learning. A common example is a-priori knowledge given by a distance measure between objects. A simple but effective approach for kernel construction consists of substituting the Euclidean distance in ordinary kernel functions(More)
The model order reduction methodology of reduced basis (RB) techniques offers efficient treatment of parametrized partial differential equations (PDEs) by providing both approximate solution procedures and efficient error estimates. RB-methods have so far mainly been applied to finite element schemes for elliptic and parabolic problems. In the current study(More)
Kernel methods are a class of well established and successful algorithms for pattern analysis thanks to their mathematical elegance and good performance. Numerous nonlinear extensions of pattern recognition techniques have been proposed so far based on the so-called kernel trick. The objective of this paper is twofold. First, we derive an additional kernel(More)
Modern techniques for data analysis and machine learning are so called kernel methods. The most famous and successful one is represented by the support vector machine (SVM) for classification or regression tasks. Further examples are kernel principal component analysis for feature extraction or other linear classifiers like the kernel perceptron. The(More)
We present a new approach to treat nonlinear operators in reduced basis approximations of parametrized evolution equations. Our approach is based on empirical interpolation of nonlinear differential operators and their Frechet derivatives. Efficient offline/online decomposition is obtained for discrete operators that allow an efficient evaluation for a(More)