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 dimensional manifold embedded in a higher dimensional space. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering. Several applications are considered.
Keywords
Spectral clusteringLaplace operatorEmbeddingCluster analysisArtificial intelligencePattern recognition (psychology)Computer scienceMathematicsGeographyMathematical analysis
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Publication Info
- Year
- 2002
- Type
- book-chapter
- Pages
- 585-592
- Citations
- 4494
- Access
- Closed
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Cite This
Mikhail Belkin,
Partha Niyogi
(2002).
Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering.
The MIT Press eBooks
, 585-592.
https://doi.org/10.7551/mitpress/1120.003.0080
Identifiers
- DOI
- 10.7551/mitpress/1120.003.0080