Chapter 4 - Multivariate Classification for Qualitative Analysis

Abstract

Classification methods are fundamental chemometric techniques designed to find mathematical models able to recognize the membership of each object to its proper class on the basis of a set of measurements. Classification techniques can be probabilistic, if they are based on estimates of probability distributions. Among probabilistic techniques, parametric and nonparametric methods can be distinguished, when probability distributions are characterized by location, and dispersion parameters such as mean, variance, and covariance. Classification methods can also be defined as distance-based, if they require the calculation of distances between objects or between objects, and models. Several parameters can be used for the quality estimation of classification models, both for fitting and validation purposes. These parameters are related to the presence of errors in the results, even if errors can be considered with different weights on the basis of the classification aims. One of the simplest classification methods is nearest mean classifier (NMC) that is a parametric, unbiased, and probabilistic method. Among traditional classifiers, discriminant analysis is probably the most known method and can be considered the first multivariate classification technique. Artificial neural networks (ANNs) are increasing in uses related to several chemical applications and nowadays can be considered as one of the most important emerging tools in chemometrics.