Problems of learning on manifolds
Problems of learning on manifolds
Towards a theoretical foundation for laplacian-based manifold methods
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Intrinsic dimensionality estimation of submanifolds in Rd
ICML '05 Proceedings of the 22nd international conference on Machine learning
A Riemannian approach to graph embedding
Pattern Recognition
Transductive link spam detection
AIRWeb '07 Proceedings of the 3rd international workshop on Adversarial information retrieval on the web
Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples
The Journal of Machine Learning Research
Regularized clustering for documents
SIGIR '07 Proceedings of the 30th annual international ACM SIGIR conference on Research and development in information retrieval
A tutorial on spectral clustering
Statistics and Computing
Graph spectral image smoothing using the heat kernel
Pattern Recognition
Measuring Graph Similarity Using Spectral Geometry
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
Regularization on Graphs with Function-adapted Diffusion Processes
The Journal of Machine Learning Research
Manifold Learning: The Price of Normalization
The Journal of Machine Learning Research
Towards a theoretical foundation for Laplacian-based manifold methods
Journal of Computer and System Sciences
Graph characteristics from the heat kernel trace
Pattern Recognition
Clustering with local and global regularization
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Manifold denoising as preprocessing for finding natural representations of data
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Semi-supervised classification using local and global regularization
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
On Learning with Integral Operators
The Journal of Machine Learning Research
Cross system personalization and collaborative filtering by learning manifold alignments
KI'06 Proceedings of the 29th annual German conference on Artificial intelligence
An energy minimisation approach to attributed graph regularisation
EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
A general learning framework using local and global regularization
Pattern Recognition
Diffusion maps as a framework for shape modeling
Computer Vision and Image Understanding
iDVS: an interactive multi-document visual summarization system
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
A Topological View of Unsupervised Learning from Noisy Data
SIAM Journal on Computing
Hearing the clusters of a graph: A distributed algorithm
Automatica (Journal of IFAC)
Trace formula analysis of graphs
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Uniform convergence of adaptive graph-based regularization
COLT'06 Proceedings of the 19th 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
Web page and image semi-supervised classification with heterogeneous information fusion
Journal of Information Science
Manifold regularization and semi-supervised learning: some theoretical analyses
The Journal of Machine Learning Research
SMI 2013: Heat diffusion kernel and distance on surface meshes and point sets
Computers and Graphics
On the convergence of maximum variance unfolding
The Journal of Machine Learning Research
Parallel vector field embedding
The Journal of Machine Learning Research
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In the machine learning community it is generally believed that graph Laplacians corresponding to a finite sample of data points converge to a continuous Laplace operator if the sample size increases. Even though this assertion serves as a justification for many Laplacian-based algorithms, so far only some aspects of this claim have been rigorously proved. In this paper we close this gap by establishing the strong pointwise consistency of a family of graph Laplacians with data- dependent weights to some weighted Laplace operator. Our investigation also includes the important case where the data lies on a submanifold of ${\mathbb R}^{d}$.