A Note on Automatic Data Transformation

TL;DR

This paper proposes an automatic data transformation method that enhances normality in variables with skewed distributions, improving the effectiveness of statistical analyses, especially in high-dimensional data like image features.

Contribution

It introduces a novel family of parametrized shifted logarithm transformations that automatically select optimal parameters to normalize data distributions.

Findings

Effective in reducing skewness and heteroscedasticity

Improves normality for high-dimensional data

Demonstrated utility on melanoma microscopy image features

Abstract

Modern data analysis frequently involves variables with highly non-Gaussian marginal distributions. However, commonly used analysis methods are most effective with roughly Gaussian data. This paper introduces an automatic transformation that improves the closeness of distributions to normality. For each variable, a new family of parametrizations of the shifted logarithm transformation is proposed, which is unique in treating the data as real-valued, and in allowing transformation for both left and right skewness within the single family. This also allows an automatic selection of the parameter value (which is crucial for high dimensional data with many variables to transform) by minimizing the Anderson-Darling test statistic of the transformed data. An application to image features extracted from melanoma microscopy slides demonstrate the utility of the proposed transformation in addressing data with excessive skewness, heteroscedasticity and influential observations.