A loss function approach to model selection in nonlinear principal components

The nonlinear transformation of the input variables that characterises the first nonlinear principal component is modelled as a linear sum of radially -symmetric kernel functions. It is shown that the parameters of the varianc e maximising transformation may be obtained through the minimisation of a l oss function measuring departure from homogeneity. An alternating least squ ares algorithm is given. This is used as the basis of a cross-validation ro utine for model selection. Crown copyright (C) 1999 Published by Elsevier S cience Ltd. All rights reserved.