Ant colony optimization for variable selection in discriminant linear analysis

Abstract

A new algorithm using ant colony optimization (ACO) for selection of variables in linear discriminant analysis (LDA) is presented. The role of ACO is explored in the context of LDA classification in which spectral variable multicollinearity is a known cause of generalization problems. The proposed ACO-LDA presents a metaheuristic that mimics the ant's cooperative behavior, randomly depositing pheromones at vector elements corresponding to the most relevant variables. Such cooperative ant-like behavior, which is absent in the genetic algorithm, increases the probability of discarding noninformative variables, favoring construction of more parsimonious models than genetic algorithm–linear discriminate analysis (GA-LDA). The classification performance of ACO-LDA is assessed in two case studies: (i) classification of edible vegetable oils (with respect to base oil) via ultraviolet–visible (UV-Vis) spectrometry and (ii) simultaneous classification of tea samples with respect to type and geographic origin via near-infrared (NIR) spectrometry. In the first study, ACO-LDA was tested in a data set involving wide absorption bands in the UV region with low-resolution and strong spectral overlapping. In the second study, its capacity to manage a data matrix with high dimensionality was evaluated. In both studies, ACO-LDA selected a small subset of variables, which led to correct classifications for almost all of the samples, achieving a performance level similar to the well-established partial least squares–discriminant analysis (PLS-DA), and considerably better than GA-LDA. The use of ACO to select LDA classification variables can minimize generalization problems commonly associated with multicollinearity.