Fetching the paper…

Reading the bibliography…

2013

Spectral Convergence of the connection Laplacian from random samples

Singer, Amit, Wu, Hau-tieng

Original
PDF
Post on X

Understand

Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction.

It was previously shown by Belkin and Niyogi \cite{belkin_niyogi:2007} that the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions and eigenvalues of the Laplace-Beltrami operator of the manifold in the limit of infinitely many data points sampled independently from the uniform distribution over the manifold.
Recently, we introduced Vector Diffusion Maps and showed that the connection Laplacian of the tangent bundle of the manifold can be approximated from random samples.
In this paper, we present a unified framework for approximating other connection Laplacians over the manifold by considering its principle bundle structure.

Spectral Convergence of the connection Laplacian from random samples · Around

Built on

Dunford, N. &
1958
Earlier work this paper cites.
Palais, R. S
1968
Earlier work this paper cites.
Gilkey, P
1974
Earlier work this paper cites.
Bérard, P., Besson, G. &
1994
Earlier work this paper cites.
van der Vaart, A. &
1996
Earlier work this paper cites.
Sternberg, S
1999
Earlier work this paper cites.
Bishop, R. L. &
2001
Earlier work this paper cites.
Belkin, M. &
2003
Earlier work this paper cites.
Berline, N., Getzler, E. &
2004
Earlier work this paper cites.
Hein, M., Audibert, J. &
2005
Earlier work this paper cites.
Coifman, R. R. &
2006
Earlier work this paper cites.

Similar

Frank, J
2006
Cited alongside, same era.
Giné, E. &
2006
Cited alongside, same era.
Singer, A
2006
Cited alongside, same era.
Arias-Castro, E., Lerman, G. &
Original
2007
Cited alongside, same era.
Huettel, S. A., Song, A. W. &
2008
Cited alongside, same era.
von Luxburg, U., Belkin, M. &
2008
Cited alongside, same era.
Little, A., Jung, Y.-M. &
2009
Cited alongside, same era.

Then

Singer, A., Zhao, Z., Shkolnisky, Y. &
2011
Later among the works it cites.
Wang, Y., Jiang, Y., Wu, Y. &
2011
Later among the works it cites.
Gong, D., Zhao, X. &
2012
Later among the works it cites.
Ovsjanikov, M., Ben-Chen, M., Solomon, J., Butscher, A. &
2012
Later among the works it cites.
Bandeira, A. S., Singer, A. &
2013
Closest in time.
Cheng, M.-Y. &
2013
Closest in time.
Wu, H.-T
Original
2013
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Niyogi, P., Smale, S. &

2009

Cited alongside, same era.

Chatelin, F

2011

Cited alongside, same era.

Hadani, R. &

2011

Cited alongside, same era.

Singer, A. &

2011

Cited alongside, same era.

Kaslovsky, D. &

2014

Closest in time.

Wang, X., Slavakis, K. &

2014

Closest in time.

2014

Closest in time.