Liu, Xiaoke; (2020) Discriminative principal component analysis for high dimensional classification with applications in NIR spectroscopy. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Principal component analysis (PCA) has been widely applied in various fields such as bioscience, chemistry, computer science and social science as a signal processing, dimension reduction or feature extraction tool. Regardless of its popularity, when PCA is used as a preliminary dimension reduction step in developing classification rules with high-dimensional data it has a drawback that as an unsupervised method PCA fails to use the class labels when constructing the components. As a result, its maximization of the variance of the projected patterns is not necessarily in favour of discrimination among classes. To address this problem, in this thesis we propose five methods from three perspectives: 1) We propose two methods, reweighted PCA and between PCA, which combine supervised information in the feature generation step of PCA, so that more discriminating features are constructed within the classic PCA framework. 2) We propose two feature filtering methods, reordered PCA and stepwise-reordered PCA. In these methods, principal components are generated with the classic PCA framework, but re-ranked and selected according to their discriminating power with quadratic discriminant analysis (QDA). 3) We propose a penalised QDA based supervised feature extraction method to replace PCA, which can use the label information to generate more discriminating features. We use two near infrared (NIR) spectroscopic data sets, a wheat data set and a paddy rice data set to evaluate our methods in both binary and multi-class classification. We compare our methods with the classic principal component discriminant analysis (PCDA) and partial least squares discriminant analysis (PLS-DA). Enhancements in classification accuracy are witnessed for all our modified methods in all examples compared with the classic PCDA. Four simulations have been constructed to help understanding the mechanism and evaluating the performance of our penalised QDA based feature extraction method in Chapter 3.

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