报告主题：黎曼优化及其在社区发明中的利用( Riemannian Optimization with its Application to Community Detection)
报 告 人：黄文 传授（厦门大学）
报告择要：Optimization on Riemannian manifolds, also called Riemannian optimization, considers finding an optimum of a real-valued function defined on a Riemannian manifold. Riemannian optimization has been a topic of much interest over the past few years due to many important applications, e.g., blind source separation, computations on symmetric positive matrices, low-rank learning, graph similarity, community detection, and elastic shape analysis. In this presentation, the framework of Riemannian optimization is introduced, and the current state of Riemannian optimization algorithms are briefly reviewed. To show the application of Riemannian optimization algorithms, we reformulate the community detection problem as an optimization on a subset of a Euclidean space. The subset is proven to be a Riemannian manifold and its manifold geometry structure is also derived. A Riemannian proximal gradient method is used and preliminary numerical experiments are used to show its performance.