SIMPCA: A framework for rotating and sparsifying principal components

TL;DR

SIMPCA is a new framework that computes genuinely sparse and interpretable principal components by projecting rotated components onto variable subsets, improving interpretability over traditional methods.

Contribution

The paper introduces SIMPCA, a novel algorithmic framework for generating sparse principal components through projection, enhancing interpretability and offering flexible simplification strategies.

Findings

Sparse components are highly correlated with original components.

Different simplification strategies yield diverse sparse solutions.

Effective sparse solutions demonstrated on public datasets.

Abstract

We propose an algorithmic framework for computing sparse components from rotated principal components. This methodology, called SIMPCA, is useful to replace the unreliable practice of ignoring small coefficients of rotated components when interpreting them. The algorithm computes genuinely sparse components by projecting rotated principal components onto subsets of variables. The so simplified components are highly correlated with the corresponding components. By choosing different simplification strategies different sparse solutions can be obtained which can be used to compare alternative interpretations of the principal components. We give some examples of how effective simplified solutions can be achieved with SIMPCA using some publicly available data sets.