Sparseness of Support Vector Machines---Some Asymptotically Sharp Bounds

By Ingo Steinwart. 2003

89 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Building Support Vector Machines with Reduced Classifier Complexity (2006, background): “A recent theoretical result by Steinwart (Steinwart, 2004) shows that nSV grows as a linear function of n.”
Multi-class Open Set Recognition Using Probability of Inclusion (2014, background): “Subsequently, Steinward [48] has developed asymptotic sharp upper and lower bounds on the number of support vectors.”
Training Invariant Support Vector Machines using Selective Sampling (2005, background): “The number s of support vectors asymptotically grows linearly with the number n of examples [38].”
Supervised classification and mathematical optimization (2013, background): “This number may be very large, since, as shown in [219], the number of support vectors may grow linearly in the number of data points.”
Classification using intersection kernel support vector machines is efficient (2008, background): “It has also been shown recently that the number of support vectors grow linearly with the number of training examples [23] so the complexity can only get worse with more training data are two general approaches to speeding up classification: reducing the number of support vectors by constructing spa”
Learning on the border: active learning in imbalanced data classification (2007, background): “• We know that the number of SVM support vectors scales linearly with the number of examples (Steinwart, 2004).”
Support Vector Machine Solvers (2007, methodology): “When the hyperparameter C follows the right scaling laws, Steinwart (2004) has shown that the total number of support vectors is asymptotically equivalent to 2Bn. Noisy problems do not lead to very sparse SVMs. Collobert et al. (2006) explore ways to improve sparsity in such cases.”
On Robustness Properties of Convex Risk Minimization Methods for Pattern Recognition (2004, unknown): “Upper bounds on the number of support vectors can be found in Steinwart (2004).”
An Equivalence between the Lasso and Support Vector Machines (2013, background): “In another way, sparsity has also been studied for SVMs in the literature, for example in the work of [39], which analyzes the asymptotic regime n → ∞.”
Fast Kernel Classifiers with Online and Active Learning (2005, background): “• We know that the number of SVM support vectors scales linearly with the number of examples (Steinwart, 2004).”