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半定规划和机器学习中的弦稀疏

Chordal Sparsity in Semidefinite Programming and Machine Learning
课程网址: http://videolectures.net/nipsworkshops09_vandenberghe_css/  
主讲教师: Lieven Vandenberghe
开课单位: 加州大学
开课时间: 2010-01-19
课程语种: 英语
中文简介:
弦图在稀疏矩阵分解、图形模型和矩阵完成问题的算法中起着基本作用。在矩阵优化中,弦稀疏模式可以用快速算法来计算具有给定稀疏模式的正定矩阵和对应的双锥的锥的对数势垒函数。我们将对弦稀疏矩阵方法进行综述,并更详细地讨论两种应用:具有稀疏矩阵锥约束的线性优化和支持向量机训练中产生的稠密二次规划的近似解。
课程简介: Chordal graphs play a fundamental role in algorithms for sparse matrix factorization, graphical models, and matrix completion problems. In matrix optimization chordal sparsity patterns can be exploited in fast algorithms for evaluating the logarithmic barrier function of the cone of positive definite matrices with a given sparsity pattern and of the corresponding dual cone. We will give a survey of chordal sparse matrix methods and discuss two applications in more detail: linear optimization with sparse matrix cone constraints, and the approximate solution of dense quadratic programs arising in support vector machine training.
关 键 词: 稀疏矩阵; 分解算法; 圆锥对数障碍函数; 线性优化
课程来源: 视频讲座网
最后编审: 2020-06-06:zyk
阅读次数: 56