Unsupervised Bump Hunting Using Principal Components

TL;DR

This paper explores how principal component rotation can enhance mode detection in multivariate data, introducing a fast PRIM algorithm and demonstrating improved estimators through geometric insights and simulations.

Contribution

It develops a fast version of PRIM under normality and shows how PCA rotation improves mode estimation in response-predictor analysis.

Findings

PCA rotation can improve mode estimators.

A fast PRIM algorithm is introduced.

Simulation confirms theoretical advantages.

Abstract

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.