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ICML
2007
IEEE

Non-isometric manifold learning: analysis and an algorithm

10 years 6 days ago
Non-isometric manifold learning: analysis and an algorithm
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 (LSML), and show it has good generalization properties. LSML 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 corru...
Piotr Dollár, Serge J. Belongie, Vincent Ra
Added 17 Nov 2009
Updated 17 Nov 2009
Type Conference
Year 2007
Where ICML
Authors Piotr Dollár, Serge J. Belongie, Vincent Rabaud
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