SIMPCA: a framework for rotating and sparsifying principal components

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.