Estimation by Joint Diagonalization
Éric Moreau, Tülay Adalı · 2013
This chapter presents all the ingredients for the estimation of the mixing matrix or the separation matrix by using statistical information that can be found in a set of matrices. It begins by presenting a normalization of the problem possibly with a link to a dimension reduction and/or a whitening stage. Then, the chapter considers the important case of the joint diagonalization of two matrices with or without an explicit prewhitening stage. The chapter is devoted to the unitary approximate joint diagonalization that requires a prewhitening stage. It also considers both the case of a set of Hermitian matrices and a set of complex symmetric matrices. Finally, the chapter presents general approximate joint diagonalization case in terms of criteria and algorithms while pointing out a relative gradient case.