Unsupervised learning using radial kernels
Colin Fyfe, Donald MacDonald, Pierce Lai, Roman Rosipal, Darryl K. Charles · 2001
Introduction In this Chapter, we use radial kernels to learn mappings in an unsupervised manner. The use of radial kernels has been derived from the work of Vapnik [21], Burges [2] etc in the eld of Support Vectors Machines. Support Vector Machines for regression for example, perform a nonlinear mapping of the data set into some high dimensional feature space in which we may then perform linear operations. Since the original mapping was nonlinear, any linear operation in this feature space corresponds to a nonlinear operation in data space. We rst review recent work on Kernel Principal Component Analysis (KPCA) [19, 20, 16, 17, 14, 13, 18, 12, 15] which has been the most frequently reported linear operation involving unsupervised learning in feature space. We then extend the method to perform other Kernel-based operations: Kernel Principal Factor Analysis, Kernel Exploratory Projection Pursuit and Kernel Canonical Correlation Analysis. For each operation, we derive the appro