Joint Diagonalization of Several Scatter Matrices for ICA

Procedures such as FOBI that jointly diagonalize two matrices with the independence property have a long tradition in ICA. These procedures have well-known statistical properties, for example they are prone to failure if the sources have multiple identical values on the diagonal. In this paper we suggest to diagonalize jointly $k\ge 2$ scatter matrices havingthe independence property. For the joint diagonalization we suggest a novel algorithm which finds the correct direction in an deflation-based manner, one after another. The resulting algorithm can also handle degenerate signals and is robust against noise. This is demonstrated in a simulation study