A tutorial on spectral clustering
Statistics and Computing
Exact and interpolatory quadratures for curvature tensor estimation
Computer Aided Geometric Design
Kernels, regularization and differential equations
Pattern Recognition
Local and Nonlocal Discrete Regularization on Weighted Graphs for Image and Mesh Processing
International Journal of Computer Vision
Spectral clustering based on the graph p-Laplacian
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Learning Representation and Control in Markov Decision Processes: New Frontiers
Foundations and Trends® in Machine Learning
A regularized formulation for spectral clustering with pairwise constraints
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Interactive image segmentation using probabilistic hypergraphs
Pattern Recognition
International Journal of Computer Vision
Generalised Nonlocal Image Smoothing
International Journal of Computer Vision
Partial differences as tools for filtering data on graphs
Pattern Recognition Letters
Operator Norm Convergence of Spectral Clustering on Level Sets
The Journal of Machine Learning Research
Semi-supervised kernel canonical correlation analysis with application to human fMRI
Pattern Recognition Letters
An iterated graph laplacian approach for ranking on manifolds
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
A nonparametric classification method based on K-associated graphs
Information Sciences: an International Journal
On the relation of slow feature analysis and laplacian eigenmaps
Neural Computation
Tighter PAC-Bayes bounds through distribution-dependent priors
Theoretical Computer Science
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Given a sample from a probability measure with support on a submanifold in Euclidean space one can construct a neighborhood graph which can be seen as an approximation of the submanifold. The graph Laplacian of such a graph is used in several machine learning methods like semi-supervised learning, dimensionality reduction and clustering. In this paper we determine the pointwise limit of three different graph Laplacians used in the literature as the sample size increases and the neighborhood size approaches zero. We show that for a uniform measure on the submanifold all graph Laplacians have the same limit up to constants. However in the case of a non-uniform measure on the submanifold only the so called random walk graph Laplacian converges to the weighted Laplace-Beltrami operator.