OPTIMIZATION ON LIE MANIFOLDS

摘要

A large class of pattern recognition problems can be formulated in a natural way as optimization over (Lie) transformation groups . While optimization on Lie manifolds provides a unifying framework for pattern recognition, the concerned optimization problems involve nonlinear equality constraints and are hence among the most difficult problems in optimization. This describes a new methodology for solving the optimization problems of interest to pattern recognition in a computationally efficient manner. The new method draws upon the differential geometry of Lie manifolds and the methodology has a widew range of applicability in pattern recognition and constitutes a powerful new tool. As an illustration, an application of the new method in the automated diagnosis of breast cancers is presented.