Simultaneous class-modelling in chemometrics: A generalization of Partial Least Squares class modelling for more than two classes by using error correcting output code matrices

Abstract

The paper presents a new methodology within the framework of the so-called compliant class-models, PLS2-CM, designed with the purpose of improving the performance of class-modelling in a setting with more than two classes. The improvement in the class-models is achieved through the use of multi-response PLS models with the classes encoded via Error-Correcting Output Codes (ECOC), instead of the traditional class indicator variables used in chemometrics. The proposed PLS2-CM entails a decomposition of a class-modelling problem into a series of binary learners, based on a family of code matrices with different code length, which are evaluated to obtain simultaneous compliant class-models with the best performance. The methodology develops both a new encoding system, based on multi-criteria optimization to search for optimal coding matrices, and a new decoding system, based on probability thresholds to assign objects to classmodels. The whole procedure implies that the characteristics of the dataset at hand affect the final selection of the coding matrix and therefore of built class-models, thus giving rise to a data-driven strategy. The application of PLS2-CM to a variety of cases (controlled data, experimental data and repository datasets) results in an enhanced class-modelling performance by means of the suggested procedure, as measured by the DMCEN (Diagonal Modified Confusion Entropy) index and by sensitivity-specificity matrices. The predictive ability of the compliant class-models has been evaluated.