Robust linear discriminant analysis for chemical pattern recognition

Abstract

Linear discriminant analysis (LDA) is an effective tool in multivariate multigroup data analysis. A standard technique for LDA is to project the data from a high-dimensional space onto a perceivable subspace such that the data can be separated by visual inspection. The criterion of LDA, unfortunately, is extremely susceptible to outliers which commonly occur because of instrument drift and gross errors. This paper proposes a robust discriminant criterion, and based on that criterion, a high-breakdown method for LDA is developed. In an effort to circumvent the local optima trapping, a real genetic algorithm (RGA) was used for the optimization of the criterion. The RGA is capable of locating the global optimal solution with high probability and acceptable computational burden. Classification of one simulated data set and two real chemical ones shows that the developed robust LDA (RLDA) method provides much superior performance to the standard method for outlier-contaminated data and behaves comparably well with the standard one for data without outliers. Copyright © 1999 John Wiley & Sons, Ltd.