Ordered quantile normalization: a semiparametric transformation built for the cross-validation era

Normalization transformations have recently experienced a resurgence in popularity in the era of machine learning, particularly in data preprocessing. However, the classical methods that can be adapted to cross-validation are not always effective. We introduce Ordered Quantile (ORQ) normalization, a one-to-one transformation that is designed to consistently and effectively transform a vector of arbitrary distribution into a vector that follows a normal (Gaussian) distribution. In the absence of ties, ORQ normalization is guaranteed to produce normally distributed transformed data. Once trained, an ORQ transformation can be readily and effectively applied to new data. We compare the effectiveness of the ORQ technique with other popular normalization methods in a simulation study where the true data generating distributions are known. We find that ORQ normalization is the only method that works consistently and effectively, regardless of the underlying distribution. We also explore the use of repeated cross-validation to identify the best normalizing transformation when the true underlying distribution is unknown. We apply our technique and other normalization methods via the bestNormalize R package on a car pricing data set. We built bestNormalize to evaluate the normalization efficacy of many candidate transformations; the package is freely available via the Comprehensive R Archive Network.