Learning averages over the lie group of unitary matrices

In the present paper, we treat the problem of learning averages out of a set of unitary matrices. We discuss a possible learning technique based on the differential geometrical properties of the Lie group of unitary matrices. We first recall some relevant notions from differential geometry, mainly related to Lie group theory, and then we propose a scheme for learning averages. Some numerical experiments will illustrate the features of the learnt averages.