Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Digital Picture Processing
Diffusion Kernels on Graphs and Other Discrete Input Spaces
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Problems of learning on manifolds
Problems of learning on manifolds
On clusterings: Good, bad and spectral
Journal of the ACM (JACM)
Locality-sensitive hashing scheme based on p-stable distributions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Semi-Supervised Learning on Riemannian Manifolds
Machine Learning
A Unifying Approach to Hard and Probabilistic Clustering
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
The Journal of Machine Learning Research
Semi-Supervised Learning
Regularization on discrete spaces
PR'05 Proceedings of the 27th DAGM conference on 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
Learning Gradients: Predictive Models that Infer Geometry and Statistical Dependence
The Journal of Machine Learning Research
State-space dynamics distance for clustering sequential data
Pattern Recognition
Semi-supervised object recognition based on Connected Image Transformations
Expert Systems with Applications: An International Journal
Diffusion methods for wind power ramp detection
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advances in computational intelligence - Volume Part I
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Harmonic analysis and diffusion on discrete data has been shown to lead to state-of-the-art algorithms for machine learning tasks, especially in the context of semi-supervised and transductive learning. The success of these algorithms rests on the assumption that the function(s) to be studied (learned, interpolated, etc.) are smooth with respect to the geometry of the data. In this paper we present a method for modifying the given geometry so the function(s) to be studied are smoother with respect to the modified geometry, and thus more amenable to treatment using harmonic analysis methods. Among the many possible applications, we consider the problems of image denoising and transductive classification. In both settings, our approach improves on standard diffusion based methods.