(Note the unusual time: 4:30pm Shanghai, 10:30am Paris.)
The group synchronization problem calls for the estimation of a ground-truth vector from the noisy relative transforms of its elements, where the elements come from a group and the relative transforms are computed using the binary operation of the group. Such a problem provides an abstraction of a wide range of inverse problems that arise in practice. However, in many instances, one needs to tackle a non-convex optimization formulation. It turns out that for synchronization problems over certain subgroups of the orthogonal group, a simple projected gradient-type algorithm, often referred to as the generalized power method (GPM), is quite effective in finding the ground-truth when applied to their non-convex formulations. In this talk, we survey the related recent results in the literature and focus in particular on the techniques for analyzing the statistical and optimization performance of the GPM.
This talk covers joint works with Huikang Liu, Peng Wang, Man-Chung Yue, and Zirui Zhou.