Group-Wise Principal Component Analysis for Exploratory Data Analysis


In this article, we propose a new framework for matrix factorization based on principal component analysis (PCA) where sparsity is imposed. The structure to impose sparsity is defined in terms of groups of correlated variables found in correlation matrices or maps. The framework is based on three new contributions: an algorithm to identify the groups of variables in correlation maps, a visualization for the resulting groups, and a matrix factorization. Together with a method to compute correlation maps with minimum noise level, referred to as missing-data for exploratory data analysis (MEDA), these three contributions constitute a complete matrix factorization framework. Two real examples are used to illustrate the approach and compare it with PCA, sparse PCA, and structured sparse PCA. Supplementary materials for this article are available online.

Journal of Computational and Graphical Statistics
Rafael A. Rodríguez-Gómez
Rafael A. Rodríguez-Gómez
Associate Professor

My research interests include network security, the early detection of new threats and adversarial machine learning attacks-defense methods in the cybersecurity field.