A new method for performing a nonlinear form of principal component an
alysis is proposed. By the use of integral operator kernel functions,
one can efficiently compute principal components in high-dimensional f
eature spaces, related to input space by some nonlinear map-for instan
ce, the space of all possible five-pixel products in 16 x 16 images. W
e give the derivation of the method and present experimental results o
n polynomial feature extraction for pattern recognition.