Non-Isometric Manifold Learning: Analysis and an Algorithm

author: Piotr Dollár, University of California
published: June 23, 2007,   recorded: June 2007,   views: 10646


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.


In this work we take a novel view of nonlinear manifold learning. Usually, manifold learning is formulated in terms of finding an embedding or "unrolling" of a manifold into a lower dimensional space. Instead, we treat it as the problem of learning a representation of a nonlinear, possibly non-isometric manifold that allows for the manipulation of novel points. Central to this view of manifold learning is the concept of generalization beyond the training data. Drawing on concepts from supervised learning, we establish a framework for studying the problems of model assessment, model complexity, and model selection for manifold learning. We present an extension of a recent algorithm, Locally Smooth Manifold Learning (L S M L), and show it has good generalization properties. L S M L learns a representation of a manifold or family of related manifolds and can be used for computing geodesic distances, finding the projection of a point onto a manifold, recovering a manifold from points corrupted by noise, generating novel points on a manifold, and more.

See Also:

Download slides icon Download slides: icml07_corvallis_dollar_piotr.pdf (990.7 KB)

Download slides icon Download slides: icml07_corvallis_dollar_piotr.ppt (1.5 MB)

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: