Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering
Abstract
Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low di(cid:173) mensional manifold embedded in a higher dimensional space. The algorithm provides a computationally efficient approach to non(cid:173) linear dimensionality reduction that has locality preserving prop(cid:173) erties and a natural connection to clustering. Several applications are considered.
Cite
Text
Belkin and Niyogi. "Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering." Neural Information Processing Systems, 2001.Markdown
[Belkin and Niyogi. "Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering." Neural Information Processing Systems, 2001.](https://mlanthology.org/neurips/2001/belkin2001neurips-laplacian/)BibTeX
@inproceedings{belkin2001neurips-laplacian,
title = {{Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering}},
author = {Belkin, Mikhail and Niyogi, Partha},
booktitle = {Neural Information Processing Systems},
year = {2001},
pages = {585-591},
url = {https://mlanthology.org/neurips/2001/belkin2001neurips-laplacian/}
}