svlab - A Kernel Methods Package
Abstractsvlab is an extensible, object oriented, package for kernel based learningin R. Its main objective is to provide a tool kit consisting of basic kernelfunctionality, optimizers and high level algorithms such as Support VectorMachines and Kernel Principal Component Analysis which can be extendedby the user in a very modular way. Based on this infrastructure kernel-basedmethods can be easily be constructed and developed. 1 Introduction It is often diﬃcult to solve problems like classiﬁcation, regression and clustering—ormore generally: supervised and unsupervised learning—in the space in which theunderlying observations have been made. One way out is to project the observationsinto a higher-dimensional feature space where these problems are easier to solve,e.g., by using simple linear methods. If the methods applied in the feature spaceare only based on dot or inner products the projection does not have to be carriedout explicitely but only implicitely using kernel functions. This is often referred toas the “kernel trick”. More precisely, if a projection Φ : X → H is used the dotproduct hΦ(x),Φ(y)i can be represented by a kernel function kk(x,y) = hΦ(x),Φ(y)i, (1)