Higher order learning with graphs
ICML '06 Proceedings of the 23rd international conference on Machine learning
Graph regularization for color image processing
Computer Vision and Image Understanding
Regularization on Graphs with Function-adapted Diffusion Processes
The Journal of Machine Learning Research
Graph-based tools for microscopic cellular image segmentation
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
Diffusion Learning and Regularization
Proceedings of the 2009 conference on New Directions in Neural Networks: 18th Italian Workshop on Neural Networks: WIRN 2008
Graph Regularisation Using Gaussian Curvature
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Simulated Iterative Classification A New Learning Procedure for Graph Labeling
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part II
Graph-Based Discrete Differential Geometry for Critical Instance Filtering
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part II
Removing Multiplicative Noise by Douglas-Rachford Splitting Methods
Journal of Mathematical Imaging and Vision
Discrete regularization on weighted graphs for image and mesh filtering
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Generalised Nonlocal Image Smoothing
International Journal of Computer Vision
Partial differences as tools for filtering data on graphs
Pattern Recognition Letters
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
A Variational Framework for Exemplar-Based Image Inpainting
International Journal of Computer Vision
A framework for intrinsic image processing on surfaces
Computer Vision and Image Understanding
Image smoothing and segmentation by graph regularization
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
A Nonlocal Version of the Osher-Solé-Vese Model
Journal of Mathematical Imaging and Vision
Nonlinear Multilayered Representation of Graph-Signals
Journal of Mathematical Imaging and Vision
Dependence maps, a dimensionality reduction with dependence distance for high-dimensional data
Data Mining and Knowledge Discovery
Toward a cyber-physical topology language: applications to NERC CIP audit
Proceedings of the first ACM workshop on Smart energy grid security
A New Nonlocal H1 Model for Image Denoising
Journal of Mathematical Imaging and Vision
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We consider the classification problem on a finite set of objects. Some of them are labeled, and the task is to predict the labels of the remaining unlabeled ones. Such an estimation problem is generally referred to as transductive inference. It is well-known that many meaningful inductive or supervised methods can be derived from a regularization framework, which minimizes a loss function plus a regularization term. In the same spirit, we propose a general discrete regularization framework defined on finite object sets, which can be thought of as discrete analogue of classical regularization theory. A family of transductive inference schemes is then systemically derived from the framework, including our earlier algorithm for transductive inference, with which we obtained encouraging results on many practical classification problems. The discrete regularization framework is built on discrete analysis and geometry developed by ourselves, in which a number of discrete differential operators of various orders are constructed, which can be thought of as discrete analogues of their counterparts in the continuous case.