Kernel principal component analysis (KPCA) as a nonlinear alternative to classical principal component analysis (PCA) of combustion composition space is investigated. With the proposed approach, thermochemical scalar's statistics are reconstructed from the KPCA derived moments. The tabulation of the scalars is then implemented using artificial neural networks (ANN). Excellent agreement with the original data is obtained with only 2 principal components (PCs) from numerical simulations of the Sandia Flame F flame for major species and temperature. A formulation for the source and diffusion coefficient matrix for the PCs is proposed. This formulation enables the tabulation of these key transport terms in terms of the PCs and their potential implementation for the numerical solution of the PCs' transport equations. (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.