A Theoretic Note on Nonlinear Binary Separability in the Euclidean Feature Space of Arbitrary Dimension
The classical binary classification problem is considered in this paper. We show that every training set is nonlinearly separable in the Euclidean feature space, where the dimension of the Euclidean feature space can be arbitrarily pre-specified. This is done by explicitly constructing the required feature maps and the separating hyperplanes. Some comments on classical Cover's Theorem and the relation to support vector learning are also made. A numerical example is provided to illustrate our main results