学术报告|
当前位置:首页 > 科研 > 学术报告
发表时间:2019-01-04 阅读次数:152次
报告题目: Solving Inverse Problems on Networks: Graph Cuts, Optimization Landscape, Synchronization
报 告 人:凌舒扬
报告人所在单位:New York University
报告日期:2019-01-04 星期五
报告时间:14:00-15:00
报告地点:光华东主楼1801
  
报告摘要:

Information retrieval from graphs plays an increasingly important role in data science and machine learning. This talk focuses on two such examples. The first one concerns the graph cuts problem: how to find the optimal k-way graph cuts given an adjacency matrix. We present a convex relaxation of ratio cut and normalized cut, which gives rise to a rigorous theoretical analysis of graph cuts. We derive deterministic bounds of finding the optimal graph cuts via a spectral proximity condition which naturally depends on the intra-cluster and inter-cluster connectivity. Moreover, our theory provides theoretic guarantees for spectral clustering and community detection under stochastic block model.

The second example is about the landscape of a nonconvex cost function arising from group synchronization and matrix completion. This function also appears as the energy function of coupled oscillators on networks. We study how the landscape of this function is related to the underlying network topologies. We prove that the optimization landscape has no spurious local minima if the underlying network is a deterministic dense graph or an Erdos-Renyi random graph. The results find applications in signal processing and dynamical systems on networks.

海报

 

  
本年度学院报告总序号:12

Copyright © |2012 复旦大学数学科学学院版权所有 沪ICP备042465  

电话:+86(21)65642341 传真:+86(21)65646073