TY - CONF

T1 - Non-isometric manifold learning

T2 - 24th International Conference on Machine Learning, ICML 2007

AU - Dollár, Piotr

AU - Rabaud, Vincent

AU - Belongie, Serge

PY - 2007

Y1 - 2007

N2 - 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 corrupted by noise, generating novel points on a manifold, and more.

AB - 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 corrupted by noise, generating novel points on a manifold, and more.

UR - http://www.scopus.com/inward/record.url?scp=34547988139&partnerID=8YFLogxK

U2 - 10.1145/1273496.1273527

DO - 10.1145/1273496.1273527

M3 - Paper

AN - SCOPUS:34547988139

SP - 241

EP - 248

Y2 - 20 June 2007 through 24 June 2007

ER -