Joint covariance estimation with mutual linear structure

We consider the joint estimation of structured covariance matrices. We assume the structure is unknown and perform the estimation using heterogeneous training sets. More precisely, we are given groups of measurements coming from centered normal populations with different covariance matrices. Assuming that all these covariance matrices span a low dimensional affine subspace in the space of symmetric matrices, our aim is to determine this structure. It is then utilized to improve the covariance estimation. We provide an algorithm discovering and exploring the underlying covariance structure and analyze its error bounds. Numerical simulations are presented to illustrate the performance benefits of the proposed algorithm.