Principal Discriminant Variate Method for Classification of Multicollinear Data: Applications to Near-Infrared Spectra of Cow Blood Samples

Abstract

A new regularized discriminant analysis technique, the principal discriminant variate (PDV) method, has been developed for effectively handling multicollinear data commonly encountered in multivariate spectroscopy-based classification. The motivation behind this method is to seek a sequence of discriminant directions that not only optimize the separability between different classes, but also account for a maximized variation present in the data. This motivation furnishes the PDV method with improved stability in prediction without significant loss of separability. Different formulations for the PDV methods are suggested, and an effective computing procedure is proposed for a PDV method. Two sets of near-infrared (NIR) spectra data, one corresponding to the blood plasma samples from two cows and the other associated with the whole blood samples from mastitic and healthy cows, have been used to evaluate the behavior of the PDV method in comparison with principal component analysis (PCA), discriminant partial least-squares (DPLS), soft independent modeling of class analogies (SIMCA), and Fisher linear discriminant analysis (FLDA). Results obtained demonstrate that the NIR spectra of blood plasma samples from different classes are clearly discriminated by the PDV method, and the proposed method provides superior performance to PCA, DPLS, SIMCA, and FLDA, indicating that PDV is a promising tool in discriminant analysis of spectra-characterized samples with only small compositional differences.