Kurtosis removal for data pre-processing

Abstract

Mesokurtic projections are linear projections with null fourth cumulants. They might be useful data pre-processing tools when nonnormality, as measured by the fourth cumulants, is either an opportunity or a challenge. Nonnull fourth cumulants are opportunities when projections with extreme kurtosis are used to identify interesting nonnormal features, as for example clusters and outliers. Unfortunately, this approach suffers from the curse of dimensionality, which may be addressed by projecting the data onto the subspace orthogonal to mesokurtic projections. Nonnull fourth cumulants are challenges when using statistical methods whose sampling properties heavily depend on the fourth cumulant themselves. Mesokurtic projections ease the problem by allowing to use the inferential properties of the same methods under normality. The paper shows necessary and sufficient conditions for the existence of mesokurtic projections and compares them with other gaussianization methods. Theoretical and empirical results suggest that mesokurtic transformations are particularly useful when sampling from finite normal mixtures. The practical use of mesokurtic projections is illustrated with the AIS and the RANDU datasets.