COVARIANCE-ADJUSTED SPATIAL DEPTH FUNCTIONS FOR CLASSIFICATION OF HIGH DIMENSIONAL DATA

Abstract

The process of scientific research and knowledge discovery has been revolutionized by technological innovations. The scourge of dimensionality arises when more variables are added to a multivariate model. An increase in the dimension of any data set makes it difficult to estimate certain quantities. In multivariate analysis, the performance of different depth functions for classification in low dimension has been investigated in the literature. One of the primary motivations for using spatial depth is its computational tractability, particularly when the dimension is high. However, spatial depth function does not account for correlation among variables. It has been proven that correlation values between variable in high dimensional data are very strong, therefore there is need for modification of spatial depth function which is implemented for three different known classification methods. This study presented three covariance-adjusted spatial depth functions for implementing maximum depth classification, depth-distribution classification and depth-depth classification. The performances of the classifiers were evaluated through the estimates of mean proportion of correct classification using simulation studies and analysis of real data. The result in this study showed that depth-depth classification method outperformed other methods in high dimensional data. However, this method can only be implemented in a two-class problem. Also, the diagonalized spatial depth function and regularized spatial depth function performed competitively well with the usual spatial depth function in maximum depth classification. The regularized spatial depth function performed optimally among others in depth-depth classification. However, its performance is suboptimal in depth distribution classification.