An Optimization View on Multi-Matching and Orthogonal Matrix Synchronization

Summary: Connected dynamical systems may exhibit interesting collective behavior such as synchronization, where the different entities or parts operate in unison. When designing such systems, we may choose the protocols as (local) optimization algorithms. Such algorithms may be used to improve performance in various applications including matching of shapes or feature points. We show how a simple algorithm may be used for local optimization of a quadratic function. We apply this algorithm to matrix synchronization and machine learning problems and identify how the structure of the system's interconnection graph affects properties such as optimality and convergence.