DATA-ADAPTIVE DISCRIMINANT ANALYSIS AND ITS DIAGNOSIS

Abstract

In the fields of physical, medical and social sciences, multivariate analysis of large scale data, especially discriminant analysis has been often applied. Ordinary discriminant analyses (such as, linear or quadratic discriminant analyses) are usually based on the multivariate normality of observations. However, the observations obtained in practice rarely satisfy this constrained assumption. Thus, in order to satisfy the multivariate normality of the observations, methods using multivariate normalizing transformation of the observations are presented. However, in the methods depending on the framework of such a "transformation" we cannot choose a suitable transformation when we discriminate the newly obtained observations. As a substitutional approach, we can consider this discriminant problem on the basis of the framework of "multivariate distribution" corresponding to the transformation. Then, we propose the methodology of the data-adaptive discriminant analysis (DDA), assuming the multivariate power-normal distribution as the underlying distribution of the observations, where the multivariate power-normal distribution is defined as the distribution specified before the multivariate power transformation. By DDA, we can assess the appropriateness of the linear or quadratic discriminant analyses since the multivariate power-normal distribution includes the multivariate normal distribution. Moreover, we present some diagnostic methods to DDA, and evaluate the performance of the data-adaptive discriminant analysis by certain literature examples and simulations. As a result, the data-adaptive discriminant analysis has better performance than other discrimination techniques based on multivariate normal distribution.