  Principal Components Analysis is a widely used technique for dimension
reduction and characterization of variability in multivariate populations. Our
interest lies in studying when and why the rotation to principal components can
be used effectively within a response-predictor set relationship in the context
of mode hunting. Specifically focusing on the Patient Rule Induction Method
(PRIM), we first develop a fast version of this algorithm (fastPRIM) under
normality which facilitates the theoretical studies to follow. Using basic
geometrical arguments, we then demonstrate how the PC rotation of the predictor
space alone can in fact generate improved mode estimators. Simulation results
are used to illustrate our findings.
