An improved optimization algorithm and a Bayes factor termination criterion for sequential projection pursuit

Abstract

A fundamental problem in analysis of highly multivariate spectral or chromatographic data is the reduction of dimensionality. Principal components analysis (PCA), concerned with explaining the variance–covariance structure of the data, is a commonly used approach to dimension reduction. Recently, an attractive alternative to PCA, sequential projection pursuit (SPP), has been introduced. Designed to elicit clustering tendencies in the data, SPP may be more appropriate when performing clustering or classification analysis. However, the existing genetic algorithm (GA) implementation of SPP has two shortcomings, computation time and inability to determine the number of factors necessary to explain the majority of the structure in the data. We address both these shortcomings. First, we introduce a new SPP algorithm, a random scan sampling algorithm (RSSA), that significantly reduces computation time. We compare the computational burden of the RSSA and GA implementation for SPP on a data set containing Raman spectra of 12 organic compounds. Second, we propose a Bayes factor criterion, BFC, as an effective measure for selecting the number of factors needed to explain the majority of the structure in the data. We compare SPP to PCA on two data sets varying in type, size, and difficulty; in both cases, SPP achieves a higher accuracy with a lower number of latent variables.