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 variance maximising transformation may be obtained through the minimisation of a loss function measuring departure from homogeneity. An alternating least squares algorithm is given. This is used as the basis of a cross-validation routine for model selection.
nonlinear principal components analysis dimension reduction principal curves nonlinear feature extraction radial basis functions homogeneity analysis