  Conventional principal component analysis (PCA) finds a principal vector that
maximizes the sum of second powers of principal components. We consider a
generalized PCA that aims at maximizing the sum of an arbitrary convex function
of principal components. We present a gradient ascent algorithm to solve the
problem. For the kernel version of generalized PCA, we show that the solutions
can be obtained as fixed points of a simple single-layer recurrent neural
network. We also evaluate our algorithms on different datasets.
