Graph Helmholtzian and rank learning

author: Lek-Heng Lim, UC Berkeley
published: Dec. 20, 2008,   recorded: December 2008,   views: 4630


Related Open Educational Resources

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.


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.

See Also:

Download slides icon Download slides: aml08_lim_ghrl_01.pdf (628.7┬áKB)

Help icon Streaming Video Help

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Write your own review or comment:

make sure you have javascript enabled or clear this field: