On Rank-Rank Classification Method for High Dimensional Data

Source abstract

Advances in technology have made available several high-dimensional data, with dimension greater than sample size. In multivariate analysis, data depth was defined and well discussed in literature. Recently, the notion of rank-rank (RR) plot was introduced for classification in low dimension based on the notions of data depth. However, the performance of RR classification method needs to be investigated in high dimension especially when dimension is much greater than sample size. 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 variables 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. The performance of spatial depth function and modified depth function were compared in depth-depth classification method, depth-oriented classification method and rank-rank classification method. The performance of the classifiers was 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 rank-rank classification method outperformed other methods for high dimensional data.