A non-linear classification technique based on Fisher's discriminant is proposed. Main ingredient is the kernel trick which allows to efficiently compute the linear Fisher discriminant in feature space. The linear classification in feature space corresponds to a powerful non-linear decision function in input space. Large scale simulations demonstrate the competitiveness of our approach

Abstract-This paper provides an introduction to support vector machines (SVMs), kernel Fisher discriminant analysis, and kernel principal component analysis (PCA), as examples for successful kernel-based learning methods. We first give a short background about Vapnik-Chervonenkis (VC) theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations. We illustrate the usefulness of kernel algorithms by finally discussing applications such as optical character recognition (OCR) and DNA analysis.

This paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector (SV) kernel functions. We first discuss the geometry of feature space. In particular, we review what is known about the shape of the image of input space under the feature space map, and how this influences the capacity of SV methods. Following this, we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel, using the example of the class of inhomogeneous polynomial kernels, which are often used in SV pattern recognition. We then discuss the connection between feature space and input space by dealing with the question of how one can, given some vector in feature space, find a preimage (exact or approximate) in input space. We describe algorithms to tackle this issue, and show their utility in two applications of kernel methods. First, we use it to reduce the computational complexity of SV decision functions; second, we combine it with the Kernel PCA algorithm, thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real-world data.

kernel view of the dimensionality reduction of manifolds", . July 2004.

The task of finding TIS can be modeled as a classification problem. We demonstrate the applicability of support vector machines for this task, and show how to incorporate prior biological knowledge by engineering an appropriate kernel function. With the described techniques the recognition performance can be improved by 26% over leading existing approaches. We provide evidence that existing related methods (e.g. ESTScan) could profit from advanced TIS recognition.