Guided projections for analyzing the structure of high-dimensional data

Abstract

A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilizing projections onto a space spanned by a selection of a small number of observations allows measuring the similarity of other observations to the selection based on orthogonal and score distances. Observations are iteratively exchanged from the selection creating a non-random sequence of projections which we call guided projections. In contrast to conventional projection pursuit methods, which typically identify a low-dimensional projection revealing some interesting features contained in the data, guided projections generate a series of projections that serve as a basis not just for diagnostic plots but to directly investigate the group structure in data. Based on simulated data we identify the strengths and limitations of guided projections in comparison to commonly employed data transformation methods. We further show the relevance of the transformation by applying it to real-world data sets.