A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
The nature of statistical learning theory
The nature of statistical learning theory
ACM Transactions on Mathematical Software (TOMS)
Matrix computations (3rd ed.)
Primal-dual interior-point methods
Primal-dual interior-point methods
Making large-scale support vector machine learning practical
Advances in kernel methods
Fast training of support vector machines using sequential minimal optimization
Advances in kernel methods
Exploiting generative models in discriminative classifiers
Proceedings of the 1998 conference on Advances in neural information processing systems II
The Kernel-Adatron Algorithm: A Fast and Simple Learning Procedure for Support Vector Machines
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Sparse Greedy Matrix Approximation for Machine Learning
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Kernel-based nonlinear blind source separation
Neural Computation
Kernel independent component analysis
The Journal of Machine Learning Research
Decomposition methods for linear support vector machines
Neural Computation
An efficient algorithm for damper optimization for linear vibrating systems using Lyapunov equation
Journal of Computational and Applied Mathematics
Exponential families for conditional random fields
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Predictive low-rank decomposition for kernel methods
ICML '05 Proceedings of the 22nd international conference on Machine learning
Heteroscedastic Gaussian process regression
ICML '05 Proceedings of the 22nd international conference on Machine learning
2005 Special Issue: Constructing Bayesian formulations of sparse kernel learning methods
Neural Networks - 2005 Special issue: IJCNN 2005
Neural Networks - 2005 Special issue: IJCNN 2005
Learning low-rank kernel matrices
ICML '06 Proceedings of the 23rd international conference on Machine learning
Concept boundary detection for speeding up SVMs
ICML '06 Proceedings of the 23rd international conference on Machine learning
Block-quantized kernel matrix for fast spectral embedding
ICML '06 Proceedings of the 23rd international conference on Machine learning
Incremental approximate matrix factorization for speeding up support vector machines
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Kernel Methods for Measuring Independence
The Journal of Machine Learning Research
On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning
The Journal of Machine Learning Research
Training a Support Vector Machine in the Primal
Neural Computation
An Efficient Implementation of an Active Set Method for SVMs
The Journal of Machine Learning Research
Large-scale RLSC learning without agony
Proceedings of the 24th international conference on Machine learning
Pegasos: Primal Estimated sub-GrAdient SOlver for SVM
Proceedings of the 24th international conference on Machine learning
A dependence maximization view of clustering
Proceedings of the 24th international conference on Machine learning
A kernel-based causal learning algorithm
Proceedings of the 24th international conference on Machine learning
A scalable modular convex solver for regularized risk minimization
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Optimally regularised kernel Fisher discriminant classification
Neural Networks
Semismooth Newton support vector machine
Pattern Recognition Letters
Improved Nyström low-rank approximation and error analysis
Proceedings of the 25th international conference on Machine learning
An efficient kernel matrix evaluation measure
Pattern Recognition
Training structural svms with kernels using sampled cuts
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Support Vector Machines, Data Reduction, and Approximate Kernel Matrices
ECML PKDD '08 Proceedings of the European conference on Machine Learning and Knowledge Discovery in Databases - Part II
Distribution-Free Learning of Bayesian Network Structure
ECML PKDD '08 Proceedings of the European conference on Machine Learning and Knowledge Discovery in Databases - Part II
Assessing Nonlinear Granger Causality from Multivariate Time Series
ECML PKDD '08 Proceedings of the European conference on Machine Learning and Knowledge Discovery in Databases - Part II
Nonlinear clustering-based support vector machine for large data sets
Optimization Methods & Software - Mathematical programming in data mining and machine learning
Graph nodes clustering with the sigmoid commute-time kernel: A comparative study
Data & Knowledge Engineering
Fast approximate spectral clustering
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Least Squares SVM for Least Squares TD Learning
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Sparse kernel SVMs via cutting-plane training
Machine Learning
Similarity and Kernel Matrix Evaluation Based on Spatial Autocorrelation Analysis
ISMIS '09 Proceedings of the 18th International Symposium on Foundations of Intelligent Systems
Improving k-NN for Human Cancer Classification Using the Gene Expression Profiles
IDA '09 Proceedings of the 8th International Symposium on Intelligent Data Analysis: Advances in Intelligent Data Analysis VIII
Feature Selection for Value Function Approximation Using Bayesian Model Selection
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part I
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Ensembles of partially trained SWMs with multiplicative updates
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Fast kernel-based independent component analysis
IEEE Transactions on Signal Processing
Fast support vector machines for continuous data
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on cybernetics and cognitive informatics
Maximum margin clustering made practical
IEEE Transactions on Neural Networks
Feature Extraction Using Linear and Non-linear Subspace Techniques
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
A fast SVM training method for very large datasets
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
On speeding up computation in information theoretic learning
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
On-line independent support vector machines
Pattern Recognition
Multi-Standard Quadratic Optimization: interior point methods and cone programming reformulation
Computational Optimization and Applications
Subset based least squares subspace regression in RKHS
Neurocomputing
Hybrid MPI/OpenMP Parallel Linear Support Vector Machine Training
The Journal of Machine Learning Research
Hash Kernels for Structured Data
The Journal of Machine Learning Research
Bundle Methods for Regularized Risk Minimization
The Journal of Machine Learning Research
Linear support vector machine based on variational inequality
ICNC'09 Proceedings of the 5th international conference on Natural computation
An effective method of pruning support vector machine classifiers
IEEE Transactions on Neural Networks
Sparse approximation through boosting for learning large scale kernel machines
IEEE Transactions on Neural Networks
Quadratic Programming Feature Selection
The Journal of Machine Learning Research
Computational Optimization and Applications
Large-scale support vector learning with structural kernels
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part III
Clustered Nyström method for large scale manifold learning and dimension reduction
IEEE Transactions on Neural Networks
Using an iterative linear solver in an interior-point method for generating support vector machines
Computational Optimization and Applications
Random Fourier approximations for skewed multiplicative histogram kernels
Proceedings of the 32nd DAGM conference on Pattern recognition
Mixing linear SVMs for nonlinear classification
IEEE Transactions on Neural Networks
A new algorithm for training SVMs using approximate minimal enclosing balls
CIARP'10 Proceedings of the 15th Iberoamerican congress conference on Progress in pattern recognition, image analysis, computer vision, and applications
Regression on Fixed-Rank Positive Semidefinite Matrices: A Riemannian Approach
The Journal of Machine Learning Research
LIBSVM: A library for support vector machines
ACM Transactions on Intelligent Systems and Technology (TIST)
Large-scale training of SVMs with automata kernels
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Exploiting separability in large-scale linear support vector machine training
Computational Optimization and Applications
Sequential learning with LS-SVM for large-scale data sets
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part II
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
Approximating a gram matrix for improved kernel-based learning
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Bayesian kernel learning methods for parametric accelerated life survival analysis
Proceedings of the First international conference on Deterministic and Statistical Methods in Machine Learning
Efficient semantic kernel-based text classification using matching pursuit KFDA
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part II
Expert Systems with Applications: An International Journal
The Journal of Machine Learning Research
Learning low-rank Mercer kernels with fast-decaying spectrum
Neurocomputing
Sampling methods for the Nyström method
The Journal of Machine Learning Research
Review: Supervised classification and mathematical optimization
Computers and Operations Research
Sparse spectral clustering method based on the incomplete Cholesky decomposition
Journal of Computational and Applied Mathematics
Separable approximate optimization of support vector machines for distributed sensing
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part II
Low-rank quadratic semidefinite programming
Neurocomputing
Fast and scalable polynomial kernels via explicit feature maps
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Regularized vector field learning with sparse approximation for mismatch removal
Pattern Recognition
Efficient kernel learning from side information using ADMM
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
The Journal of Machine Learning Research
Large-scale SVD and manifold learning
The Journal of Machine Learning Research
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SVM training is a convex optimization problem which scales with the training set size rather than the feature space dimension. While this is usually considered to be a desired quality, in large scale problems it may cause training to be impractical. The common techniques to handle this difficulty basically build a solution by solving a sequence of small scale subproblems. Our current effort is concentrated on the rank of the kernel matrix as a source for further enhancement of the training procedure. We first show that for a low rank kernel matrix it is possible to design a better interior point method (IPM) in terms of storage requirements as well as computational complexity. We then suggest an efficient use of a known factorization technique to approximate a given kernel matrix by a low rank matrix, which in turn will be used to feed the optimizer. Finally, we derive an upper bound on the change in the objective function value based on the approximation error and the number of active constraints (support vectors). This bound is general in the sense that it holds regardless of the approximation method.