A method for sparse and robust independent component analysis

This work presents sparse invariant coordinate analysis, SICS, a new method for sparse and robust independent component analysis. SICS is based on classical invariant coordinate analysis, which is presented in such a form that a LASSO-type penalty can be applied to promote sparsity. Robustness is achieved by using robust scatter matrices. In the first part of the paper, the background and building blocks: scatter matrices, measures of robustness, ICS and independent component analysis, are carefully introduced. Then the proposed new method and its algorithm are derived and presented. This part also includes a consistency result for a general case of sparse ICS-like methods. The performance of SICS in identifying sparse independent component loadings is investigated with simulations. The method is also illustrated with example in constructing sparse causal graphs.