Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
The nature of statistical learning theory
The nature of statistical learning theory
International Journal of Computer Vision
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Level Set Model for Image Classification
International Journal of Computer Vision
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Complexity Measures of Supervised Classification Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation
International Journal of Computer Vision
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Reducing multiclass to binary: a unifying approach for margin classifiers
The Journal of Machine Learning Research
Rademacher and gaussian complexities: risk bounds and structural results
The Journal of Machine Learning Research
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
In Defense of One-Vs-All Classification
The Journal of Machine Learning Research
Distance--Based Classification with Lipschitz Functions
The Journal of Machine Learning Research
SVM that maximizes the margin in the input space
Systems and Computers in Japan
Active Hypercontours and Contextual Classification
ISDA '05 Proceedings of the 5th International Conference on Intelligent Systems Design and Applications
Dynamic Cluster Formation Using Level Set Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Machine Learning
Active contours as knowledge discovery methods
DS'07 Proceedings of the 10th international conference on Discovery science
Adaptive potential active hypercontours
ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
Rademacher penalties and structural risk minimization
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Consistency of support vector machines and other regularized kernel classifiers
IEEE Transactions on Information Theory
Minimax-optimal classification with dyadic decision trees
IEEE Transactions on Information Theory
IEEE Transactions on Image Processing
Minimax Optimal Level-Set Estimation
IEEE Transactions on Image Processing
A comparison of methods for multiclass support vector machines
IEEE Transactions on Neural Networks
Large margin nearest neighbor classifiers
IEEE Transactions on Neural Networks
Decision Manifolds—A Supervised Learning Algorithm Based on Self-Organization
IEEE Transactions on Neural Networks
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A variational level set method is developed for the supervised classification problem. Nonlinear classifier decision boundaries are obtained by minimizing an energy functional that is composed of an empirical risk term with a margin-based loss and a geometric regularization term new to machine learning: the surface area of the decision boundary. This geometric level set classifier is analyzed in terms of consistency and complexity through the calculation of its ε-entropy. For multicategory classification, an efficient scheme is developed using a logarithmic number of decision functions in the number of classes rather than the typical linear number of decision functions. Geometric level set classification yields performance results on benchmark data sets that are competitive with well-established methods.