2016/08/23 by Khaled Alyani, Alyani, Khaled, Marco Congedo +3
Mathematics · Computer Science · Engineering · #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1608.06613
In this paper, we introduce properly-invariant diagonality measures of\nHermitian positive-definite matrices. These diagonality measures are defined as\ndistances or divergences between a given positive-definite matrix and its\ndiagonal part. We then give closed-form expressions of these diagonality\nmeasures and discuss their invariance properties. The diagonality measure based\non the log-determinant \α-divergence is general enough as it includes a\ndiagonality criterion used by the signal processing community as a special\ncase. These diagonality measures are then used to formulate minimization\nproblems for finding the approximate joint diagonalizer of a given set of\nHermitian positive-definite matrices. Numerical computations based on a\nmodified Newton method are presented and commented.\n