Weighted sparse principal component analysis

Sparse principal component analysis (SPCA) has been shown to be a fruitful method for the analysis of high-dimensional data. So far, however, no method has been proposed that allows to assign elementwise weights to the matrix of residuals, although this may have several useful applications. We propose a novel SPCA method that includes the flexibility to weight at the level of the elements of the data matrix. The superior performance of the weighted SPCA approach compared to unweighted SPCA is shown for data simulated according to the prevailing multiplicative-additive error model. In addition, applying weighted SPCA to genomewide transcription rates obtained soon after vaccination, resulted in a biologically meaningful selection of variables with components that are associated to the measured vaccine efficacy. The MATLAB implementation of the weighted sparse PCA method is freely available from https://github.com/katrijnvandeun/WSPCA.