LEAST-SQUARES JOINT DIAGONALIZATION OF A MATRIX SET BY A CONGRUENCE TRANSFORMATION
This Research has been partially funded by the French National Research Agency (ANR) within the National Network for Software Technologies (RNTL), project Open-ViBE (Open Platform for Virtual Brain Environments).
The approximate joint diagonalization (AJD) is an important analytic tool at the base of numerous independent component analysis (ICA) and other blind source separation (BSS) methods, thus finding more and more applications in medical imaging analysis. In this work we present a new AJD algorithm named SDIAG (Spheric Diagonalization). It imposes no constraint either on the input matrices or on the joint diagonalizer to be estimated, thus it is very general. Whereas it is well grounded on the classical least-squares criterion, a new normalization reveals a very simple form of the solution matrix. Numerical simulations shown that the algorithm, named SDIAG (spheric diagonalization), behaves well as compared to state-of-the art AJD algorithms.
