DOE OSTI2019
Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. We consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal. In the probabilistic interpretation of low-rank PCA, the data has a normal multivariate distribution and, therefore, normal marginal distributions for each column. If some marginals are continuous but not normal, the semiparametric copula-based principal component analysis (COCA) method is an alternative to PCA that combines a Gaussian copula with nonparametric marginals. If some marginals are discrete or semi-continuous, we present a new extended PCA (XPCA) method that also uses a Gaussian copula and nonparametric marginals and accounts for discrete variables in the likelihood calculation by integrating over appropriate intervals. Like PCA, the factors produced by XPCA can be used to find latent structure in data, build predictive models, and perform dimensionality reduction. We implement the new model, XPCA, and its ancestors PCA and COCA in both R and Python. This software provides implementations of XPCA, COCA, and probabilistic PCA in both R and Python. XPCA is written in arXiv report https://arxiv.org/abs/1808.07510. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. SAND2019-10591 M