Asymptotic Behaviors of Support Vector Machines with Gaussian Kernel

By Peter L. Bartlett, S. Sathiya Keerthi, Chih-Jen Lin. 2003

1,770 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

How researchers see this paper

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

In Artificial Intelligence

1. Yoshua Bengio
2. Quoc V. Le
3. Mohit Bansal
4. Jason Aaron Edward Weston
5. Jianfeng Gao
6. Christopher D. Manning
7. Ruslan Salakhutdinov
8. Kai-Wei Chang

In Computational Mechanics

1. Emilio Carrizosa
2. Hsuan-Tien Lin
3. Dolores Romero Morales
4. L. Eon Bottou
5. Ronan Collobert
6. Jason Aaron Edward Weston
7. Veronica Piccialli
8. Marco Sciandrone

In Computer Vision and Pattern Recognition

1. Luc Van Gool
2. Trevor Darrell
3. Xiaogang Wang
4. Dacheng Tao
5. Jitendra Malik
6. Andrew Zisserman
7. Ming-Hsuan Yang
8. Chunhua Shen

Citations in the corpus

• Data Augmentation in Emotion Classification Using Generative Adversarial Networks (2017, methodology): “Support vector machines (SVM) with linear kernel function [14] is employed for classification task.”
• Volatility forecasting of crude oil market: A new hybrid method (2018, methodology): “This paper employs the radial basis function (RBF), which is a commonly used function regarding nonlinear regression problems (Keerthi & Lin, 2003; Schölkopf et al., 1997).”
• Combining meta-learning and search techniques to select parameters for support vector machines (2012, methodology): “In order to evaluate our proposal, we investigated the selection of two parameters for SVMs on regression problems (i.e. Support Vector Regressors): the parameter g of the RBF kernel and the regularization constant C , which may have a strong influence in SVM performance [9].”
• Using support vector machines for long-term discharge prediction (2006, background): “Furthermore, the linear kernel is a special case of RBF. Keerthi & Lin (2001) showed that the linear kernel with a penalty parameter C had the same performance as the RBF kernel with some parameters (C, σ).”
• Nonlinear optimization and support vector machines (2018, background): “…Vapnik 1995; Fan et al. 2008; Ferris and Munson 2004; Franc and Sonnenburg 2009; Fung and Mangasarian 2001; Gaudioso et al. 2017; Hsu and Lin 2002a; Keerthi and Lin 2003; Lee et al. 2015; Lee and Mangasarian 2001; Mangasarian and Musicant 2001; Mangasarian 2006; Mavroforakis and Theodoridis 2006;…”
• Supervised classification and mathematical optimization (2013, background): “[134], the asymptotic behavior of the SVM classifier for extreme values of C and γ is analyzed, characterizing cases for which the classifier underfits or overfits the data.”
• A methodological approach to the classification of dermoscopy images (2007, background): “Firstly, the linear kernel cannot handle nonlinearly separable classification tasks, and in any case, is a special case of the RBF kernel [ 40 ].”
• Deep Neural Networks Rival the Representation of Primate IT Cortex for Core Visual Object Recognition (2014, background): “By choosing a Gaussian kernel we can move between regression functions that are effectively linear, to functions that interpolate between the data points (a ‘‘complex’’ regression function) [40].”
• Classification of EMG signals using PSO optimized SVM for diagnosis of neuromuscular disorders (2013, background): “Improper parameter settings and feature-selection may lead to deprived classification results [12,13].”