An Orthogonal Matrix Optimization by Dual Cayley Parametrization Technique

This paper addresses a mathematically sound technique for the orthogonal matrix optimization problem that has broad applications in recent signal processing problems including the independent component analysis. We propose Dual Cayley parametrization technique that can decompose a slightly restricted version of the original problem into a pair of simple constraint-free optimization problems. This decomposition frees us from using local parametrizations strongly dependent on the location of orthogonal matrices, and hence from numerical approximations of delicate computations, e.g., matrix exponential mappings or SVD.