[BibTeX] [RIS]
Spectral Clustering and Kernel {PCA} are Learning Eigenfunctions
Type of publication: Techreport
Citation: tr1239
Number: 1239
Year: 2003
Institution: Département d'informatique et recherche opérationnelle, Université de Montréal
URL: http://www.iro.umontreal.ca/~l...
Abstract: In this paper, we show a direct equivalence between spectral clustering and kernel PCA, and how both are special cases of a more general learning problem, that of learning the principal eigenfunctions of a kernel, when the functions are from a function space whose scalar product is defined with respect to a density model. This defines a natural mapping for new data points, for methods that only provided an embedding, such as spectral clustering and Laplacian eigenmaps. The analysis hinges on a notion of generalization for embedding algorithms based on the estimation of underlying eigenfunctions, and suggests ways to improve this generalization by smoothing the data empirical distribution.
Userfields: topics={HighDimensional,Kernel,Unsupervised},cat={T},
Keywords:
Authors Bengio, Yoshua
Vincent, Pascal
Paiement, Jean-François
Delalleau, Olivier
Ouimet, Marie
Le Roux, Nicolas
Added by: [ADM]
Total mark: 0
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