A method for sparse and robust independent component analysis – Lauri Heinonen (Department of Mathematics and Statistics)

Independent component analysis (ICA) is a popular family of methods for decomposing signal into independent sources. One group of ICA methods are those achieved by using symmetrized scatter matrices, or other scatter matrices with independence property, in invariant coordinate selection (ICS). Sparsity means that some, if not most, of the model parameters are estimated to be zero. Most well-known example of this is LASSO. This way the model is easier to interpret and the amount of noise or overfitting is decreased. Robustness means that the model is resistant to for example outliers.
Now, in this work, a sparse version of invariant coordinate selection (SICS) is presented to achieve sparse independent component analysis. The method is based on sparse PCA. The SICS method is formulated as a sequence of regression problems, and the LASSO penalty is used to achieve sparsity. The methods performance is illustrated with different simulations. Some theoretical results are also presented.