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15

JMLR
2008

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Manifold Learning: The Price of Normalization

13 years 4 months ago

Manifold Learning: The Price of Normalization

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We analyze the performance of a class of manifold-learning algorithms that find their output by minimizing a quadratic form under some normalization constraints. This class consists of Locally Linear Embedding (LLE), Laplacian Eigenmap, Local Tangent Space Alignment (LTSA), Hessian Eigenmaps (HLLE), and Diffusion maps. We present and prove conditions on the manifold that are necessary for the success of the algorithms. Both the finite sample case and the limit case are analyzed. We show that there are simple manifolds in which the necessary conditions are violated, and hence the algorithms cannot recover the underlying manifolds. Finally, we present numerical results that demonstrate our claims.

Yair Goldberg, Alon Zakai, Dan Kushnir, Yaacov Rit

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Added	13 Dec 2010
Updated	13 Dec 2010
Type	Journal
Year	2008
Where	JMLR
Authors	Yair Goldberg, Alon Zakai, Dan Kushnir, Yaacov Ritov

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