Shrinkage heteroscedastic discriminant algorithms for classifying multi-class high-dimensional data: Insights from a national health survey

Abstract

In many practical data applications, there are often a large number of pre-processed heteroscedastic features. Discriminant analysis is a standard statistical learning method that is useful for classifying such multivariate features. It is well known in literature that the Linear Discriminant Analysis (LDA) is quite sub-optimal for the analysis of high-dimensional heteroscedastic data because of the inherent singularity and instability of the within-class variance. However, shrinkage discriminant analysis (SDA) and its variants often perform better due to its robustness against inherent multicollinearity and heteroscedasticity. In this article, we propose some newly modified discriminant classification algorithms based on the SDA and compare their sensitivities with those of other competing algorithms. The empirical application show that the proposed algorithms perform moderately well for datasets with high dimensions and unequal co-variance structures when applied to simulated and nutrition data with inherent heteroscedasticity and outliers. The sensitivity and precision of the algorithms for the target classes ranges from 70%–100%. The balanced accuracy of all the algorithms ranges from 50 to 75% for the three-class problem considered. Heteroscedastic discriminant algorithm performs moderately well with high sensitivity for classifying health data with high and low dimensions.