Machine Learning
Least Squares Support Vector Machine Classifiers
Neural Processing Letters
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
Ridge Regression Learning Algorithm in Dual Variables
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Duality and Geometry in SVM Classifiers
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Robust Real-Time Face Detection
International Journal of Computer Vision
A hierarchical method for multi-class support vector machines
ICML '04 Proceedings of the twenty-first international conference on Machine learning
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Training ν-Support Vector Classifiers: Theory and Algorithms
Neural Computation
Neural Computation
R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization
ICML '06 Proceedings of the 23rd international conference on Machine learning
Learning Nonlinear Image Manifolds by Global Alignment of Local Linear Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nearest hyperdisk methods for high-dimensional classification
Proceedings of the 25th international conference on Machine learning
Affine Subspace Nearest Points Classification Algorithm for Wavelet Face Recognition
CSIE '09 Proceedings of the 2009 WRI World Congress on Computer Science and Information Engineering - Volume 03
Video-based face recognition using probabilistic appearance manifolds
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Modeling the manifolds of images of handwritten digits
IEEE Transactions on Neural Networks
An improved conjugate gradient scheme to the solution of least squares SVM
IEEE Transactions on Neural Networks
Hyperdisk based large margin classifier
Pattern Recognition
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This paper introduces a geometrically inspired large margin classifier that can be a better alternative to the support vector machines (SVMs) for the classification problems with limited number of training samples. In contrast to the SVM classifier, we approximate classes with affine hulls of their class samples rather than convex hulls. For any pair of classes approximated with affine hulls, we introduce two solutions to find the best separating hyperplane between them. In the first proposed formulation, we compute the closest points on the affine hulls of classes and connect these two points with a line segment. The optimal separating hyperplane between the two classes is chosen to be the hyperplane that is orthogonal to the line segment and bisects the line. The second formulation is derived by modifying the @n-SVM formulation. Both formulations are extended to the nonlinear case by using the kernel trick. Based on our findings, we also develop a geometric interpretation of the least squares SVM classifier and show that it is a special case of the proposed method. Multi-class classification problems are dealt with constructing and combining several binary classifiers as in SVM. The experiments on several databases show that the proposed methods work as good as the SVM classifier if not any better.