Approximate minimum enclosing balls in high dimensions using core-sets
Journal of Experimental Algorithmics (JEA)
Core Vector Machines: Fast SVM Training on Very Large Data Sets
The Journal of Machine Learning Research
Core Vector Regression for very large regression problems
ICML '05 Proceedings of the 22nd international conference on Machine learning
Training linear SVMs in linear time
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Cluster Based Core Vector Machine
ICDM '06 Proceedings of the Sixth International Conference on Data Mining
Minimum Enclosing Spheres Formulations for Support Vector Ordinal Regression
ICDM '06 Proceedings of the Sixth International Conference on Data Mining
Fast Kernel Classifiers with Online and Active Learning
The Journal of Machine Learning Research
Training a Support Vector Machine in the Primal
Neural Computation
Online Passive-Aggressive Algorithms
The Journal of Machine Learning Research
Large Scale Multiple Kernel Learning
The Journal of Machine Learning Research
Maximum margin coresets for active and noise tolerant learning
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Fitting the smallest enclosing bregman ball
ECML'05 Proceedings of the 16th European conference on Machine Learning
Structural Support Vector Machine
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
Coresets for polytope distance
Proceedings of the twenty-fifth annual symposium on Computational geometry
Criteria Ensembles in Feature Selection
MCS '09 Proceedings of the 8th International Workshop on Multiple Classifier Systems
Sparse kernel SVMs via cutting-plane training
Machine Learning
From minimum enclosing ball to fast fuzzy inference system training on large datasets
IEEE Transactions on Fuzzy Systems
Streamed learning: one-pass SVMs
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
A Fast BMU Search for Support Vector Machine
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part I
Addressing the problems of data-centric physiology-affect relations modeling
Proceedings of the 15th international conference on Intelligent user interfaces
Fast and Scalable Local Kernel Machines
The Journal of Machine Learning Research
What is the complexity of a network? the heat flow-thermodynamic depth approach
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
An online incremental learning support vector machine for large-scale data
ICANN'10 Proceedings of the 20th international conference on Artificial neural networks: Part II
Ordinal-class core vector machine
Journal of Computer Science and Technology
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
Two one-pass algorithms for data stream classification using approximate MEBs
ICANNGA'11 Proceedings of the 10th international conference on Adaptive and natural computing algorithms - Volume Part II
INFORMS Journal on Computing
New approximation algorithms for minimum enclosing convex shapes
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Rough margin based core vector machine
PAKDD'10 Proceedings of the 14th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part I
Computer Methods and Programs in Biomedicine
Ball ranking machines for content-based multimedia retrieval
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
On approximating the Riemannian 1-center
Computational Geometry: Theory and Applications
Reduced universal background model for speech recognition and identification system
MCPR'12 Proceedings of the 4th Mexican conference on Pattern Recognition
The bitvector machine: a fast and robust machine learning algorithm for non-linear problems
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Heat flow-thermodynamic depth complexity in directed networks
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Anomaly intrusion detection based on PLS feature extraction and core vector machine
Knowledge-Based Systems
The Journal of Machine Learning Research
Data analysis of (non-)metric proximities at linear costs
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
Training sparse SVM on the core sets of fitting-planes
Neurocomputing
Fast and robust approximation of smallest enclosing balls in arbitrary dimensions
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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The core vector machine (CVM) is a recent approach for scaling up kernel methods based on the notion of minimum enclosing ball (MEB). Though conceptually simple, an efficient implementation still requires a sophisticated numerical solver. In this paper, we introduce the enclosing ball (EB) problem where the ball's radius is fixed and thus does not have to be minimized. We develop efficient (1 + e)-approximation algorithms that are simple to implement and do not require any numerical solver. For the Gaussian kernel in particular, a suitable choice of this (fixed) radius is easy to determine, and the center obtained from the (1 + e)-approximation of this EB problem is close to the center of the corresponding MEB. Experimental results show that the proposed algorithm has accuracies comparable to the other large-scale SVM implementations, but can handle very large data sets and is even faster than the CVM in general.