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Large kinetic mechanisms are required in order to accurately model combustion systems. If no parameterization of the thermo-chemical state-space is used, solution of the species transport equations can become computationally prohibitive as the resulting system contains a wide range of time and length scales. Parameterization of the thermochemical state-space with an a priori prescription of the dimension of the underlying manifold would lead to a reduced yet accurate description. To this end, the potential oered by Principal Component Analysis (PCA) in identifying low-dimensional manifolds is very appealing. The present work seeks to advance the understanding and application of the PC-transport approach by analyzing the ability to parameterize the thermo-chemical state with the PCA basis using nonlinear regression. In order to demonstrate the accuracy of the method within a numerical solver, unsteady perfectly stirred reactor (PSR) calculations are shown using the PC-transport approach. The PSR analysis extends previous investigations by the authors to more complex fuels (methane and propane), showing the ability of the approach to deal with relatively large kinetic mechanisms. The ability to achieve highly accurate mapping through Gaussian Process based nonlinear regression is also shown. In addition, a novel method based on local regression of the PC source terms is also investigated which leads to improved results.