Group-wise Principal Component Analysis for Exploratory Data Analysis

In this paper, 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.