Exploring Spectroscopic Regression Modelling Using Eureqa: Black-Box Chemometrics or a Useful Tool for Exploration and Learning?

Abstract

“Eureqa (pronounced ‘eureka’) is a software tool for detecting equations and hidden mathematical relationships in your data” made available by the Cornell Creative Machines Lab. ( http://creativemachines.cornell.edu/eureqfa ). Based on the use of evolutionary genetic programming, the program is capable of testing a wide variety of mathematical functions, and combinations thereof, to find relationships between data. Functions include the standard functions used in multi-linear regression (MLR; +, –, /, *, k) plus others, such as exponentials, roots, trigonometric etc. The objective of this investigation was to determine if this program might be useful in the investigation and development of spectroscopic calibrations. Two sets (173 or 241 samples) of forages (hays) and by-products (hulls, stalks etc.), some of which had been chemically treated with sodium chlorite to increase digestibility, were studied using Eureqa. Data for six analytes were available, but based on previous work using partial least squares regression, only crude protein, a well-determined analyte, and lignin, a much poorly determined analyte, were examined. Results indicated that standard spectral pre-treatments such as normalisation, mean centring, variance scaling, multiplicative scatter correction and derivatives might be beneficial in more rapidly obtaining the best calibrations, but were not necessary unless needed for data scaling. While overall results were comparable to those from partial least squares, but never as quite as good, several aspects of the program led to the conclusion that it is a wonderful exploration and learning tool for spectroscopy, even if one is not interested in developing MLR-based calibrations. As just one example, the results for all samples are displayed for each equation as developed and any of the best dozen or so can be displayed with a simple mouse click. Thus, it is easy to see how the developing equation effects the predicted versus actual fit, outliers etc. in nearly real time. Similarly, the many function fitting options (different error measures, both least- and non-least squares) allow one to explore and see how these affect both the final results and equation evolution. In conclusion, Eureqa is an exceedingly interesting and useful program, both for developing MLR-based calibrations and for studies of calibration development in general.