The following are Matlab codes for some algorithms.

Gradient-based kernel dimension reduction

Reference: K. Fukumizu and C.Leng (2013) Gradient-based kernel dimension reduction for regression.
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


  • Fukumizu, K. Francis R. Bach and M. Jordan. Kernel dimension reduction in regression.
    The Annals of Statistics. 37(4), pp.1871-1905 (2009) pdf file

  • Fukumizu, K., Bach, F.R., and Jordan, M.I. "Dimensionality reduction for supervised learning with reproducing kernel Hilbert spaces",
    Journal of Machine Learning Research. 5(Jan):73-99, 2004. pdf

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