On Learning with Integral Operators

• DOI: 10.5555/1756006.1756036
• Publication Date: 2010-03-01
• Authors: Lorenzo Rosasco; Mikhail A. Belkin; Ernesto De Vito
• Keywords: Spectral Clustering; Eigenfunction; Kernel (algebra); Operator (biology); Spectral graph theory

A large number of learning algorithms, for example, spectral clustering, kernel Principal Components Analysis and many manifold methods are based on estimating eigenvalues eigenfunctions operators defined by a similarity function or kernel, given empirical data. Thus the analysis it is an important problem to be able assess quality such approximations. The contribution our paper two-fold: 1. We use technique concentration inequality Hilbert spaces provide new much simplified proofs results in approximation. 2. Using these we several properties graph Laplacian operator extending strengthening from von Luxburg et al. (2008).