  Principal Component Analysis (PCA) is a dimensionality reduction technique
widely used to reduce the computational cost associated with numerical
simulations of combustion phenomena. However, PCA, which transforms the
thermo-chemical state space based on eigenvectors of co-variance of the data,
could fail to capture information regarding important localized chemical
dynamics, such as the formation of ignition kernels, appearing as
\rev{extreme-valued} samples in a dataset. In this paper, we propose an
alternate dimensionality reduction procedure, co-kurtosis PCA (CoK-PCA),
wherein the required principal vectors are computed from a high-order joint
statistical moment, namely the co-kurtosis tensor, which may better identify
directions in the state space that represent stiff dynamics. We first
demonstrate the potential of the proposed CoK-PCA method using a synthetically
generated dataset that is representative of typical combustion simulations.
Thereafter, we characterize and contrast the accuracy of CoK-PCA against PCA
for datasets representing spontaneous ignition of premixed ethylene-air in a
simple homogeneous reactor and ethanol-fueled homogeneous charged compression
ignition (HCCI) engine. Specifically, we compare the low-dimensional manifolds
in terms of reconstruction errors of the original thermo-chemical state, and
species production and heat release rates computed from the reconstructed
state. \rev{The latter -- a comparison of species production and heat release
rates -- is a more rigorous assessment of the accuracy of dimensionality
reduction.} We find that, even using a simplistic linear reconstruction, the
co-kurtosis based reduced manifold represents the original thermo-chemical
state more accurately than PCA, especially in the regions where chemical
reactions are important.
