Kurtosis-based projection pursuit analysis (PPA) was developed as an alternative exploratory data analysis algorithm. Instead of using variance and distance-based metrics to obtain, hopefully, informative projections of high-dimensional data (like PCA, HCA, and kNN), ordinary PPA searches for interesting projections by optimizing the kurtosis. However, if the sample-variable ratio is too low, it is possible for ordinary PPA to "overmodel" the data by finding spurious combinations of the original variables that give a low kurtosis value. To overcome this, one can compress their data with PCA prior to applying PCA (~10:1 sample-to-variable ratio). To make PPA independent of PCA, we have developed a sparse implementation of PPA (SPPA), where subsets of the original variables are selected using a genetic algorithm. This repository contains MATLAB code that can be used to apply SPPA to high-dimensional data, examples of SPPA in use, and the corresponding paper published on SPPA. Below is a figure from our recent paper that shows the basic approach of the algorithm.
SPPA.m is a MATLAB function to perform sparse kurtosis-based projection pursuit using a genetic algorithm.
Please cite Sparse Projection Pursuit Analysis: An Alternative for Exploring Multivariate Chemical Data (2020).
The master branch of this repository contains the original SPPA code (version 1.0) implemented for the work published in Sparse Projection Pursuit Analysis: An Alternative for Exploring Multivariate Chemical Data (2020). If available, enhancements to the original code can be found in additional branches named with a corresponding version number.
- Master - Original SPPA code (version 1.0)
- Version 1.1 - Improved selection of initial population to ensure maximum coverage of variables. If population size is sufficient, each variable is selected a minimum of n times. Residual individuals are selected at random without repetition. This is more equitable than the original version which might exclude some variables and over-represent others.
- Fast and simple methods for the optimization of kurtosis used as a projection pursuit index (2011)
- Re‐centered kurtosis as a projection pursuit index for multivariate data analysis (2013)
- Regularized projection pursuit for data with a small sample-to-variable ratio (2014)
- Procrustes rotation as a diagnostic tool for projection pursuit analysis (2015)
- Projection pursuit and PCA associated with near and middle infrared hyperspectral images to investigate forensic cases of fraudulent documents (2017)
To be completed. Please check demo.m for a quick demonstration showing the use of SPPA to explore a salmon plasma data set (Nuclear Magnetic Resonance (NMR) Spectroscopy).