Least-Squares Joint Diagonalization of a matrix set by a congruence transformation

Details Least-Squares Joint Diagonalization of a matrix set by a congruence transformation Least-Squares Joint Diagonalization of a matrix set by a congruence transformation

2009-04-05

arxiv.org/abs/0904.0779v1

Statistics

Computation

2nd Singaporean-French IPAL Symposium, Singapour : Singapour (2009)

Scientific paper

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 leastsquares 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.

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