Abstract

In many real-world datasets, associations between features are often non-linear, rendering traditional methods of linear association evaluation insufficient. To address this, the Kernel Association Coefficient (KAC) is introduced as a novel metric based on a standardised second-degree polynomial kernel function. KAC effectively detects both linear and non-linear associations between features, producing accurate results regardless of data distribution or sample size, with no inherent bias towards either type of association. Building upon the foundation of KAC, this study introduces the Kernel Association Rotation Analysis (KARA), an innovative unsupervised methodology designed to project high-dimensional data into a newly defined low-dimensional space. The primary objective of KARA is to establish new axes that retain the majority of the original variance, thereby facilitating dimensionality reduction while preserving critical data structures. This innovative methodology proves especially valuable in scenarios where linear and non-linear associations coexist, providing a unique advantage over conventional techniques that solely capture linear associations. Our comparative analysis with Gaussian Process Regression (GPR) underscores KARA’s proficiency in revealing complex patterns that may be neglected by conventional linear regression methods. Our investigation demonstrates KARA’s efficiency in modelling responses compared to other similar dimensionality reduction techniques.