Effects of Correlation and Outliers on Data Reduction and Classification of High Dimensional Data

Abstract

In this study, Maximum depth and Depth distribution classification methods were considered for high dimensional data that are highly correlated in order to determine the effective method of classification in dimensional reduction using variable combinations and variable selection approaches with applications to some real life data and two different simulation studies. Four levels of correlation coefficients were considered in order to examine the degree of correlation that exits in the high dimensional data set.  The performances of depth functions in Maximum depth and depth distribution classifications were investigated for both the high dimensional dataset and the now reduced dataset when t and F tests were applied and the optimal depth function in Maximum depth classification and depth distribution classification was identified. The depth function with the highest mean proportion of correct classification was identified to be the optimal depth function. Moreover, the performances of this optimal depth function were evaluated for the two simulations and the real life dataset.