Spectral Clustering and Kernel PCA are Learning Eigenfunctions
msra(2003)
摘要
In this paper, we show a direct equivalence between spectral clustering and ker- nel 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 em- bedding, such as spectral clustering and Laplacian eigenmaps. The analysis hinges on a notion of generalization for embedding algorithms based on the estimation of under- lying eigenfunctions, and suggests ways to improve this generalization by smoothing the data empirical distribution.
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关键词
clustering,manifold learning,unsupervised learning,kernel pca,spectral clustering,inner product,eigenfunctions,hilbert space
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