Reference: K. Fukumizu and C.Leng (2013) Gradient-based kernel dimension reduction for
Journal of the American Statistical Association, to appear. paper
Comment: This algorithm gKDR is much faster than KDR (below). It does not need numerical optimization but only eigendecomposition, and thus covers high-dimensional data. The previous KDR (kernel dimension reduction) needs non-convex optimization, but provides very accurate results for small data sets.
Kernel dimension reduction for regression