2017年11月20日 |  English version
网站首页 | 学院一览 | 学院新闻 | 科学研究 | 学科建设 | 师资队伍 | 人才培养 | 学生工作 | 下载专区 | 招考信息
 
A Fast Matrix Majorization-Projection Method for Constrained Stress Minimization in MDS

报告题目:A Fast Matrix Majorization-Projection Method for Constrained Stress Minimization in MDS

报告人:Houduo Qi, the University of Southampton

报告时间:2017年9月9日(周六)10:00

报告地点:行健楼学术报告室526

邀请人:韩德仁教授

摘要:Kruskal's stress minimization, though nonconvex and nonsmooth, has been a major computational model for dissimilarity data in multidimensional scaling. Semidefinite Programming (SDP) relaxation (by dropping the rank constraint) would lead to a high number of SDP cone constraints. This has rendered the SDP approach computationally challenging even for problems of small size. In this paper, we reformulate the stress as an Euclidean Distance Matrix (EDM) optimization with box constraints. A key element in our approach is the conditional positive semidefinite cone with rank cut. Although nonconvex, this geometric object allows a fast computation of the projection onto it and it naturally leads to a majorization-minimization algorithm with the minimization step having a closed-form solution. Moreover, we prove that our EDM optimization follows a continuously differentiable path, which greatly facilitated the analysis of the convergence to a stationary point. The superior performance of the proposed algorithm is demonstrated against some of the state-of-the-art solvers in the field of sensor network localization.

* This is a joint work with Xiu Naihua and Zhou Shenglong。

 返回
南京师范大学数学科学学院 版权所有 Copyright © 2009
通讯地址:南京市亚东新城区文苑路1号 南京师范大学数学科学学院 邮政编码:210023
联系电话:025-85898785