New improved error bounds for the linear complementarity problem
Mathematical Programming: Series A and B
Nonlinear complementarity as unconstrained and constrained minimization
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
The nature of statistical learning theory
The nature of statistical learning theory
Matrix computations (3rd ed.)
Advances in kernel methods: support vector learning
Advances in kernel methods: support vector learning
Solving the quadratic programming problem arising in support vector classification
Advances in kernel methods
Making large-scale support vector machine learning practical
Advances in kernel methods
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Learning from Data: Concepts, Theory, and Methods
Learning from Data: Concepts, Theory, and Methods
Feature Selection via Concave Minimization and Support Vector Machines
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Successive overrelaxation for support vector machines
IEEE Transactions on Neural Networks
Proximal support vector machine classifiers
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Computing
Efficient computations for large least square support vector machine classifiers
Pattern Recognition Letters
Ho--Kashyap classifier with generalization control
Pattern Recognition Letters
The Journal of Machine Learning Research
The Journal of Machine Learning Research
Projection Support Vector Machine Generators
Machine Learning
A Feature Selection Newton Method for Support Vector Machine Classification
Computational Optimization and Applications
Seneschal: classification and analysis in supervised mixture-modelling
Design and application of hybrid intelligent systems
Decomposition methods for linear support vector machines
Neural Computation
Adapting two-class support vector classification methods to many class problems
ICML '05 Proceedings of the 22nd international conference on Machine learning
Core Vector Regression for very large regression problems
ICML '05 Proceedings of the 22nd international conference on Machine learning
Genetic Programming with a Genetic Algorithm for Feature Construction and Selection
Genetic Programming and Evolvable Machines
Convergence of the IRWLS Procedure to the Support Vector Machine Solution
Neural Computation
Ho-Kashyap classifier with early stopping for regularization
Pattern Recognition Letters
Training linear SVMs in linear time
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
QP Algorithms with Guaranteed Accuracy and Run Time for Support Vector Machines
The Journal of Machine Learning Research
General Polynomial Time Decomposition Algorithms
The Journal of Machine Learning Research
On the complexity of working set selection
Theoretical Computer Science
Semismooth Newton support vector machine
Pattern Recognition Letters
Classification with sparse grids using simplicial basis functions
Intelligent Data Analysis
A comparison of reduced support vector machines
International Journal of Intelligent Systems Technologies and Applications
Application of smoothing technique on twin support vector machines
Pattern Recognition Letters
Unsupervised and Semi-supervised Lagrangian Support Vector Machines
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part III: ICCS 2007
A Confident Majority Voting Strategy for Parallel and Modular Support Vector Machines
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks, Part III
Predicting Time Series Using Incremental Langrangian Support Vector Regression
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks, Part III
Speed Up SVM Algorithm for Massive Classification Tasks
ADMA '08 Proceedings of the 4th international conference on Advanced Data Mining and Applications
A Fast Method for Training Linear SVM in the Primal
ECML PKDD '08 Proceedings of the 2008 European Conference on Machine Learning and Knowledge Discovery in Databases - Part I
Nonlinear clustering-based support vector machine for large data sets
Optimization Methods & Software - Mathematical programming in data mining and machine learning
Least squares twin support vector machines for pattern classification
Expert Systems with Applications: An International Journal
Midpoint-Validation Method for Support Vector Machine Classification
IEICE - Transactions on Information and Systems
Smoothing Newton Method for L1 Soft Margin Data Classification Problem
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
Cutting-plane training of structural SVMs
Machine Learning
An incremental learning algorithm for Lagrangian support vector machines
Pattern Recognition Letters
A framework for kernel-based multi-category classification
Journal of Artificial Intelligence Research
Fast support vector machines for continuous data
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on cybernetics and cognitive informatics
Knowledge and Information Systems
Two Multi-class Lagrangian Support Vector Machine Algorithms
ICIC '07 Proceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
The multiple pairs SMO: a modified SMO algorithm for the acceleration of the SVM training
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Feature construction and selection using genetic programming and a genetic algorithm
EuroGP'03 Proceedings of the 6th European conference on Genetic programming
Feature selection by nonparametric Bayes error minimization
PAKDD'08 Proceedings of the 12th Pacific-Asia conference on Advances in knowledge discovery and data mining
Unsupervised and semi-supervised Lagrangian support vector machines with polyhedral perturbations
IITA'09 Proceedings of the 3rd international conference on Intelligent information technology application
Improvements to train support vector machines based on convex set conception
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 1
On Lagrangian support vector regression
Expert Systems with Applications: An International Journal
Spatial Point-Data Reduction Using Pulse Coupled Neural Network
Neural Processing Letters
Midpoint-validation algorithm for support vector machine classification
Artificial Life and Robotics
DC models for spherical separation
Journal of Global Optimization
Expert Systems with Applications: An International Journal
Using an iterative linear solver in an interior-point method for generating support vector machines
Computational Optimization and Applications
Error tolerance based support vector machine for regression
Neurocomputing
Realistic subsurface anomaly discrimination using electromagnetic induction and an SVM classifier
EURASIP Journal on Advances in Signal Processing - Special issue on advances in signal processing for maritime applications
The Journal of Machine Learning Research
Expert Systems with Applications: An International Journal
An Iterative Method for Deciding SVM and Single Layer Neural Network Structures
Neural Processing Letters
Support vector machine for recognition of bio-products in gasoline
ICANN'05 Proceedings of the 15th international conference on Artificial neural networks: formal models and their applications - Volume Part II
Journal of Intelligent and Robotic Systems
Computers in Biology and Medicine
Using the leader algorithm with support vector machines for large data sets
ICANN'11 Proceedings of the 21th international conference on Artificial neural networks - Volume Part I
Kernel machines for epilepsy diagnosis via EEG signal classification: A comparative study
Artificial Intelligence in Medicine
A simplified multi-class support vector machine with reduced dual optimization
Pattern Recognition Letters
A study of SVM using a combination of the online learning method and the midpoint-validation method
Artificial Life and Robotics
An evolutionary approach to automatic kernel construction
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part II
Online support vector machines with vectors sieving method
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Diversified SVM ensembles for large data sets
ECML'06 Proceedings of the 17th European conference on Machine Learning
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part I
An adaptive support vector machine learning algorithm for large classification problem
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
A new support vector machine for data mining
ADMA'05 Proceedings of the First international conference on Advanced Data Mining and Applications
General polynomial time decomposition algorithms
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Efficient detection of primary users in cognitive radio networks
International Journal of Communication Networks and Distributed Systems
Supervised subspace learning with multi-class lagrangian SVM on the grassmann manifold
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
Two-Step analysis of the fetal heart rate signal as a predictor of distress
ACIIDS'12 Proceedings of the 4th Asian conference on Intelligent Information and Database Systems - Volume Part II
Inverse matrix-free incremental proximal support vector machine
Decision Support Systems
Computerized analysis of fetal heart rate signals as the predictor of neonatal acidemia
Expert Systems with Applications: An International Journal
Hyperdisk based large margin classifier
Pattern Recognition
On proximal bilateral-weighted fuzzy support vector machine classifiers
International Journal of Advanced Intelligence Paradigms
Asymptotic error bounds for kernel-based Nyström low-rank approximation matrices
Journal of Multivariate Analysis
Finite Newton method for implicit Lagrangian support vector regression
International Journal of Knowledge-based and Intelligent Engineering Systems
Smooth Newton method for implicit Lagrangian twin support vector regression
International Journal of Knowledge-based and Intelligent Engineering Systems
Extending twin support vector machine classifier for multi-category classification problems
Intelligent Data Analysis
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An implicit Lagrangian for the dual of a simple reformulation of the standard quadratic program of a linear support vector machine is proposed. This leads to the minimization of an unconstrained differentiable convex function in a space of dimensionality equal to the number of classified points. This problem is solvable by an extremely simple linearly convergent Lagrangian support vector machine (LSVM) algorithm. LSVM requires the inversion at the outset of a single matrix of the order of the much smaller dimensionality of the original input space plus one. The full algorithm is given in this paper in 11 lines of MATLAB code without any special optimization tools such as linear or quadratic programming solvers. This LSVM code can be used "as is" to solve classification problems with millions of points. For example, 2 million points in 10 dimensional input space were classified by a linear surface in 82 minutes on a Pentium III 500 MHz notebook with 384 megabytes of memory (and additional swap space), and in 7 minutes on a 250 MHz UltraSPARC II processor with 2 gigabytes of memory. Other standard classification test problems were also solved. Nonlinear kernel classification can also be solved by LSVM. Although it does not scale up to very large problems, it can handle any positive semidefinite kernel and is guaranteed to converge. A short MATLAB code is also given for nonlinear kernels and tested on a number of problems.