Sparse Projection Pursuit Analysis: An Alternative for Exploring Multivariate Chemical Data

Abstract

Sparse projection pursuit analysis (SPPA), a new approach for the unsupervised exploration of highdimensional chemical data, is proposed as an alternative to traditional exploratory methods such as principal components analysis (PCA) and hierarchical cluster analysis (HCA). Where traditional methods use variance and distance metrics for data compression and visualization, the proposed method incorporates the fourth statistical moment (kurtosis) to access interesting subspaces that can clarify relationships within complex data sets. The quasi-power algorithm used for projection pursuit is coupled with a genetic algorithm for variable selection to efficiently generate sparse projection vectors that improve the chemical interpretability of the results while at the same time mitigating the problem of overmodeling. Several multivariate chemical data sets are employed to demonstrate that SPPA can reveal meaningful clusters in the data where other unsupervised methods cannot.

Complex Chemical Data Classification and Discrimination Using Locality Preserving Partial Least Squares Discriminant Analysis

“…Detailed information on the data sets is provided below as well as in Table . The Coffee data set contains 56 samples belonging to two different species: arabica and robusta species with 29 and 27 samples, respectively. The data was obtained by Fourier transform infrared spectroscopy with diffuse reflectance sampling, where each spectrum contains 286 variables in the range of 810–1910 cm –1 . The Pacific cod data set comes from a study of relative abundance of 47 fatty acids in Pacific cod sampled at two sites, Graves Harbor (site A) and Islas Bay (site B), in the Gulf of Alaska in 2011 and 2013. The data contains fatty acid profiles for 48 fishes with mean fatty acid proportions ranging from about 0.02 to 30%.…”

“…The data contains fatty acid profiles for 48 fishes with mean fatty acid proportions ranging from about 0.02 to 30%. As well, this data set contains balanced classes with 12 samples per class. The ink data set , contains infrared spectra of eight brands of pen ink obtained using Spectrum 400 (PerkinElmer) equipment with a universal attenuated total reflectance accessory in the range of 4000–650 cm –1 . The goal is to classify blue ink pens by brand.…”

“…The Pacific cod data set comes from a study of relative abundance of 47 fatty acids in Pacific cod sampled at two sites, Graves Harbor (site A) and Islas Bay (site B), in the Gulf of Alaska in 2011 and 2013. The data contains fatty acid profiles for 48 fishes with mean fatty acid proportions ranging from about 0.02 to 30%.…”

An efficient and accurate numerical determination of the cluster resolution metric in two dimensions

“…16,17 However for the technique to work, the number of variables in the data must be relatively low. 18 Driscoll et al 19 recently utilized variable selection by GA to minimize kurtosis in a dimensionality reduction step prior to analysis by sparse projection pursuit analysis (SPPA). Earlier, Lavine et al proposed a number of methods for complex classification problems using GAs, [20][21][22] of particular interest to chromatographic studies.…”

“…However for the technique to work, the number of variables in the data must be relatively low 18 . Driscoll et al 19 . recently utilized variable selection by GA to minimize kurtosis in a dimensionality reduction step prior to analysis by sparse projection pursuit analysis (SPPA).…”