ANOVA bootstrapped principal components analysis for logistic regression

Abstract

Principal components analysis (PCA) is often used as a dimensionality reduction technique. A small number of principal components is selected to be used in a classification or a regression model to boost accuracy. A central issue in the PCA is how to select the number of principal components. Existing algorithms often result in contradictions and the researcher needs to manually select the final number of principal components to be used. In this research the author proposes a novel algorithm that automatically selects the number of principal components. This is achieved based on a combination of ANOVA ranking of principal components, the bootstrap and classification models. Unlike the classical approach, the algorithm we propose improves the accuracy of the logistic regression and selects the best combination of principal components that may not necessarily be ordered. The ANOVA bootstrapped PCA classification we propose is novel as it automatically selects the number of principal components that would maximise the accuracy of the classification model.