Problems of learning on manifolds
Problems of learning on manifolds
Model Selection for Regularized Least-Squares Algorithm in Learning Theory
Foundations of Computational Mathematics
Learning from Examples as an Inverse Problem
The Journal of Machine Learning Research
On regularization algorithms in learning theory
Journal of Complexity
Uniform convergence of adaptive graph-based regularization
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Ellipsoid approximation using random vectors
COLT'05 Proceedings of the 18th annual conference on Learning Theory
From graphs to manifolds – weak and strong pointwise consistency of graph laplacians
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Towards a theoretical foundation for laplacian-based manifold methods
COLT'05 Proceedings of the 18th annual conference on Learning Theory
On the eigenspectrum of the gram matrix and the generalization error of kernel-PCA
IEEE Transactions on Information Theory
Operator Norm Convergence of Spectral Clustering on Level Sets
The Journal of Machine Learning Research
Eigenvalues perturbation of integral operator for kernel selection
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Computers & Mathematics with Applications
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A large number of learning algorithms, for example, spectral clustering, kernel Principal Components Analysis and many manifold methods are based on estimating eigenvalues and eigenfunctions of operators defined by a similarity function or a kernel, given empirical data. Thus for the analysis of algorithms, it is an important problem to be able to assess the quality of such approximations. The contribution of our paper is two-fold: 1. We use a technique based on a concentration inequality for Hilbert spaces to provide new much simplified proofs for a number of results in spectral approximation. 2. Using these methods we provide several new results for estimating spectral properties of the graph Laplacian operator extending and strengthening results from von Luxburg et al. (2008).