Reproducing kernel Hilbert space

set of training data X = {(xi, yi)|xi ∈ Rd}ni=1, where xi is an obser- vation vector, yi ∈ {−1,1} is the class label of xi, and n is the size of X, we apply SVMs on X to train a binary classifier. SVMs aim to search a hyperplane in the Reproducing Kernel Hilbert Space (RKHS) that maximizes the margin between the two classes of data in X with the smallest train- ing error (Vapnik, 1995). This

three dimensions to represent can be difficult to interpret. One approach to simplification is to assume that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space. If the manifold is of low enough dimension, the data can be visualised in the low-dimensional space. Abstract— Dimensionality Reduction is a key issue in many scientific problems, in which data is originally given by high dimensional vectors, all of which lie however over a fewer dimensional manifold