Understanding complex analytical data by a supervised correlation coefficient obtained from random forest

The analysis of complex analytical data, such as that obtained from mass spectrometry, nuclear magnetic resonance, or vibrational spectroscopic approaches, necessitates the employment of multivariate chemometric methods for the classification of biological samples or the quantification of individual components. In this context, accurate prediction of the samples is not the sole aim. The interpretation of the variables that contribute to this prediction is also of utmost importance. Consequently, a range of algorithms, e.g., based on partial least squares regression or random forest, have been developed for variable selection. One of these approaches, Surrogate Minimal Depth (SMD), utilizes surrogate variables, which are obtained in random forest, to incorporate variable relationships into the analysis of variable importance and to examine the mutual impact of variables on the model. The latter is expressed as a parameter that can be regarded as a supervised correlation coefficient. This paper aims to lucidly illustrate the selection of variables and the analysis of variable relationships with SMD. Furthermore, the method's potential for analyzing complex analytical data will be highlighted by demonstrating its application to various types of analytical data.