A plug-in approach to sparse and robust principal component analysis

We propose a method for sparse and robust principal component analysis. The methodology is structured in two steps: first, a robust estimate of the covariance matrix is obtained, then this estimate is plugged-in into an elastic-net regression which enforces sparseness. Our approach provides an intuitive, general and flexible extension of sparse principal component analysis to the robust setting. We also show how to implement the algorithm when the dimensionality exceeds the number of observations by adapting the approach to the use of robust loadings from ROBPCA. The proposed technique is seen to compare well for simulated and real datasets.