Analyzing Gene Expression Time-Courses
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Beyond the point cloud: from transductive to semi-supervised learning
ICML '05 Proceedings of the 22nd international conference on Machine learning
Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples
The Journal of Machine Learning Research
A tutorial on spectral clustering
Statistics and Computing
Regularization on Graphs with Function-adapted Diffusion Processes
The Journal of Machine Learning Research
Modeling hidden topics on document manifold
Proceedings of the 17th ACM conference on Information and knowledge management
Towards a theoretical foundation for Laplacian-based manifold methods
Journal of Computer and System Sciences
Finding representative landmarks of data on manifolds
Pattern Recognition
On Learning with Integral Operators
The Journal of Machine Learning Research
Supervised neighborhood graph construction for semi-supervised classification
Pattern Recognition
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
Graph based semi-supervised human pose estimation: When the output space comes to help
Pattern Recognition Letters
Towards effective clustering techniques for the analysis of electric power grids
HiPCNA-PG '13 Proceedings of the 3rd International Workshop on High Performance Computing, Networking and Analytics for the Power Grid
Theoretical aspects of mapping to multidimensional optimal regions as a multi-classifier
Intelligent Data Analysis
Journal of Mathematical Imaging and Vision
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This thesis discusses the general problem of learning a function on a manifold given by data points. The space of functions on a Riemannian manifold has a family of smoothness functionals and a canonical basis associated to the Laplace-Beltrami operator. Moreover, the Laplace-Beltrami operator can be reconstructed with certain convergence guarantees when the manifold is only known through the sampled data points. This allows the techniques of regularization and Fourier analysis to be applied to functions defined on data. A convergence result is proved for the case when data is sampled from a compact submanifold of R∧k . Several applications are considered.