Recent developments in discriminant analysis on high dimensional spectral data

Abstract

There are basically two strategies which can be used to discriminate high dimensional spectral data. It is common practice to first reduce the dimensionality by some feature extraction preprocessing method, and then use an appropriate (low-dimensional) classifier. An alternative procedure is to use a (high-dimensional) classifier which is capable of handling a large number of variables. We introduce some novel dimension reducing techniques as well as low and high dimensional classifiers which have evolved only recently. The discrete wavelet transform is introduced as a method for extracting features. The Fourier transform, principal component analysis, stepwise strategies, and other variable selection methods for reducing the dimensionality are also discussed. The low dimensional classifier, flexible discriminant analysis is a new method which combines nonparametric regression with Fisher's linear discriminant analysis to achieve nonlinear decision boundaries. We also discuss some of the time honoured techniques such as Fisher's linear discriminant analysis, and the Bayesian linear and quadratic methods. The modern high dimensional classifiers which we report on are penalized discriminant analysis and regularized discriminant analysis. Each of the classifiers and a selection of dimensionality reducing techniques are applied to the discrimination of seagrass spectral data. Results indicate a promising future for wavelets in discriminant analysis, and the recently introduced flexible and penalized discriminant analysis. Regularized discriminant analysis also performs well.