Joint Diagonalization on the Oblique Manifold for Independent Component Analysis

Several blind source separation algorithms obtain a separating matrix by computing the congruence transformation that "best" diagonalizes a collection of covariance matrices. Recent methods avoid a pre-whitening phase and directly attempt to compute a non-orthogonal diagonalizing congruence. However, since the magnitude of the sources is unknown, there is a fundamental indeterminacy on the norm of the rows of the separating matrix. We show how this indeterminacy can be taken into account by restricting the separating matrix to the oblique manifold. The geometry of this manifold is developed and a trust-region-based algorithm for non-orthogonal joint diagonalization is proposed