Applying stability selection to consistently estimate sparse principal components in high-dimensional molecular data

Principal component analysis (PCA) is a basic tool often used in bioinformatics for visualization and dimension reduction. However, it is known that PCA may not consistently estimate the true direction of maximal variability in high-dimensional, low sample size settings, which are typical for molecular data. Assuming that the underlying signal is sparse, i.e. that only a fraction of features contribute to a principal component (PC), this estimation consistency can be retained. Most existing sparse PCA methods use L1-penalization, i.e. the lasso, to perform feature selection. But, the lasso is known to lack variable selection consistency in high dimensions and therefore a subsequent interpretation of selected features can give misleading results.