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 | |
| Added by: | [ADM] |
| Total mark: | 0 |
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