Sparse variable reduced rank regression via Stiefel optimization

Reduced rank regression (RRR) has found application in various fields of signal processing. In this paper we propose a novel extension of the RRR model which we call sparse variable reduced rank regression (svRRR). By using a vector l1 penalty we remove variables completely from the RRR. The proposed estimation algorithm involves optimization on the Stiefel manifold and we illustrate it both on a simulated and a real functional magnetic resonance imaging (fMRI) data set.