A high-dimension two-sample test for the mean using cluster subspaces

Following the research of random subspaces, a modified test was proposed that might make more efficient use of covariance structure at high dimension. Hierarchical clustering is performed first such that highly correlated variables are clustered together. Next, Hotelling's statistics are computed for every cluster-subspace and summed as the new test statistic. High performance was demonstrated via simulations and real data analysis.