Kernel Principal Component Analysis Action Set

The pre-image map method was first proposed by Bakir, Weston, and Schölkopf (2003). The objective is to learn the pre-image map of the form

where is the KPCA projection operator with kernel function k, m is the number of features of the training data set, , n is the training data set size, and is a new kernel function different from k. Unlike the iterative pre-image method, the mapping method has no nonconvergence issues because it does not involve iteration. The mapping pre-image method is also faster than the iterative method, because once the mapping function is learned, you can score a batch of data all at the same time, instead of one observation at a time as in the iterative pre-image method.