Abstract
In recent years, discriminant analysis has been widely used in many fields. Usually, data involve multi-dimensional explanatory variables and one binary target response variable. When analysts encounter multi-dimensional data, they often have little information about the multivariate distribution, but they may have some knowledge about the form of the marginal densities, such as normality. In this thesis, we explore adopting kernel discriminant analysis (KDA) with marginal normality constraints, and propose a data-tilting approach for discriminant analysis. This new approach is called “Marginally Adjusted Kernel Discriminant Analysis (MAKDA).” We consider five MAKDA methods with different data tilting. In addition, in order to improve the discriminant results for boundary data, we propose a new discriminant rule call “normal weight prediction rule.” Extensive simulation studies are conducted to compare the proposed methods with conventional KDA in the following scenarios: bivariate normal distribution, bivariate dependent t-distribution, bivariate normal distribution plus one-dimensional discrete covariate, bivariate normal distribution plus three discrete covariates. The results show that three kinds of MAKDA have better performance than conventional KDA in different situations. Finally, the proposed methods are applied to analyze a real dataset in detecting malicious network activity.