Sparsity Constraint Implementation for the Joint Eigenvalue Decomposition of Matrices

Joint eigenvalue decomposition consists in estimating a common basis of eigenvectors of a set of square matrices. Most joint eigenvalue decomposition algorithms are based on multiplicative updates and the sequential optimization of small subsets of variables through a sweeping procedure of all variables. Subset sizes are currently limited to one or two variables. In addition, the subset sequence is arbitrarily chosen and remains the same through the iterations. In this paper, we propose a more general algorithmic framework that allows to overcome these limitations. This framework is based on an automatic variable selection procedure by resorting to a sparsity constraint in the optimization step. Numerical simulations show that this strategy improves the estimation of the eigenvectors.