  In climate studies, detecting spatial patterns that largely deviate from the
sample mean still remains a statistical challenge. Although a Principal
Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions
(EOF) decomposition, is often applied on this purpose, it can only provide
meaningful results if the underlying multivariate distribution is Gaussian.
Indeed, PCA is based on optimizing second order moments quantities and the
covariance matrix can only capture the full dependence structure for
multivariate Gaussian vectors. Whenever the application at hand can not satisfy
this normality hypothesis (e.g. precipitation data), alternatives and/or
improvements to PCA have to be developed and studied. To go beyond this second
order statistics constraint that limits the applicability of the PCA, we take
advantage of the cumulant function that can produce higher order moments
information. This cumulant function, well-known in the statistical literature,
allows us to propose a new, simple and fast procedure to identify spatial
patterns for non-Gaussian data. Our algorithm consists in maximizing the
cumulant function. To illustrate our approach, its implementation for which
explicit computations are obtained is performed on three family of of
multivariate random vectors. In addition, we show that our algorithm
corresponds to selecting the directions along which projected data display the
largest spread over the marginal probability density tails.
