Semi-supervised Learning by Higher Order Regularization
published: May 6, 2011, recorded: April 2011, views: 3705
Slides
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.
Description
In semi-supervised learning, at the limit of infinite unlabeled points while fixing labeled ones, the solutions of several graph Laplacian regularization based algorithms were shown by Nadler et al. (2009) to degenerate to constant functions with "spikes" at labeled points in Rd for d ¸ 2. These optimization problems all use the graph Laplacian regularizer as a common penalty term. In this paper, we address this problem by using regularization based on an iterated Laplacian, which is equivalent to a higher order Sobolev semi-norm. Alternatively, it can be viewed as a generalization of the thin plate spline to an unknown submanifold in high dimensions. We also discuss relationships between Reproducing Kernel Hilbert Spaces and Green's functions. Experimental results support our analysis by showing consistently improved results using iterated Laplacians.
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: