The Kernel Density Integral Transformation

TL;DR

This paper introduces the kernel density integral transformation as a versatile feature preprocessing method that generalizes and improves upon min-max scaling and quantile transformation, enhancing machine learning and statistical analysis.

Contribution

It presents a new transformation that subsumes existing methods and offers better performance with minimal tuning, applicable to various data analysis tasks.

Findings

Can replace min-max scaling and quantile transformation without tuning

Often outperforms traditional methods with hyperparameter tuning

Improves correlation analysis and univariate clustering

Abstract

Feature preprocessing continues to play a critical role when applying machine learning and statistical methods to tabular data. In this paper, we propose the use of the kernel density integral transformation as a feature preprocessing step. Our approach subsumes the two leading feature preprocessing methods as limiting cases: linear min-max scaling and quantile transformation. We demonstrate that, without hyperparameter tuning, the kernel density integral transformation can be used as a simple drop-in replacement for either method, offering protection from the weaknesses of each. Alternatively, with tuning of a single continuous hyperparameter, we frequently outperform both of these methods. Finally, we show that the kernel density transformation can be profitably applied to statistical data analysis, particularly in correlation analysis and univariate clustering.