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图Helmholtzian和等级学习Graph Helmholtzian and rank learning |
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| 课程网址: | http://videolectures.net/aml08_lim_ghrl/ |
| 主讲教师: | Lek-Heng Lim |
| 开课单位: | 加州大学伯克利分校 |
| 开课时间: | 2008-12-20 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | The graph Helmholtzian is the graph theoretic analogue of the Helmholtz operator or vector Laplacian, in much the same way the graph Laplacian is the analogue of the Laplace operator or scalar Laplacian. We will see that a decomposition associated with the graph Helmholtzian provides a way to learn ranking information from incomplete, imbalanced, and cardinal score-based data. In this framework, an edge flow representing pairwise ranking is orthogonally resolved into a gradient flow (acyclic) that represents the L2-optimal global ranking and a divergence-free flow (cyclic) that quantifies the inconsistencies. If the latter is large, then the data does not admit a statistically meaningful global ranking. A further decomposition of the inconsistent component into a curl flow (locally cyclic) and a harmonic flow (locally acyclic) provides information on the validity of small- and large-scale comparisons of alternatives. This is joint work with Xiaoye Jiang, Yuan Yao, and Yinyu Ye. |
| 关 键 词: | Helmholtzian图; 向量拉普拉斯算子; 和谐波流 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2021-01-28：nkq |
| 阅读次数: | 57 |