STRATEGIC COMPARISON OF RIDGE REGRESSION AND PARTIAL LEAST SQUARES IN MODERN DATA ANALYSIS

Abstract

There has been a long-standing debate over the choice between Ridge Regression (RR) and Partial Least Squares (PLS) in the field of statistics and chemometrics. Statisticians argue that RR is firmly grounded in a wellestablished mathematical framework, making it a preferable choice. In contrast, chemometricians tend to favor PLS, which employs projection onto orthogonal vectors, akin to Canonical Correlation (CC). PLS maximizes the covariance between X- and Y-score vectors, while CC focuses on correlation. Both PLS and CC share a closely related theoretical foundation, making PLS an attractive option. One of the key advantages of PLS is its ability to handle datasets with more variables than samples, with validation techniques like cross-validation and test sets available for result validation. Additionally, graphical tools aid researchers in exploring the data. Previous studies, such as the work by Frank et al. (1993), have attempted to compare RR and PLS, with inconclusive results. The choice between the two methods remains contentious, with papers favoring RR, PLS, or showing mixed findings. This paper aims to contribute to this ongoing discussion and provide insights into the comparative performance of RR and PLS, specifically in the context of chemometrics.