SSVM: A Smooth Support Vector Machine for Classification

By Yuh-Jye Lee, Olvi L. Mangasarian. Computational optimization and applications, 2001

598 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/b7a7e37b5cfae27dcd9d99765a36ff6fd30e730b

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Citations in the corpus

Proximal support vector machine classifiers (2001, methodology): “When using a rectangular kernel [18], the size of the problem can be reduced from m to k with k << m for the nonlinear case.”
Multicategory Support Vector Machines , Theory , and Application to the Classification of Microarray Data and Satellite Radiance Data (2004, methodology): “In the binary case, Lin (2002) adopted the approach of Cox and O’Sullivan (1990) to establish that the SVM directly targets the optimal classification rule, bypassing the estimation of a possibly more complex probability function.”
Nonlinear optimization and support vector machines (2018, methodology): “…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; Osuna et al. 1997; Glasmachers and…”
Training a Support Vector Machine in the Primal (2007, methodology): “If really one wants to approach the hinge loss solution, one can make h → 0 (similar to Lee & Mangasarian, 2001b).”
RSVM: Reduced Support Vector Machines (2001, methodology): “It was shown in [10] that the solution of problem (10) is obtained by solving problem (14) with α approaching infinity.”
Fast Optimization Methods for L1 Regularization: A Comparative Study and Two New Approaches (2007, methodology): “2, yielding a differentiable objective [12].”
Supervised classification and mathematical optimization (2013, methodology): “Smoothing techniques to replace the non-smooth operator (·) by a smooth proxy are discussed in [142], whereas [166] rewrites (16), for the `1 norm, as an equivalent unconstrained problem with smooth objective, solved via a Newton-type method.”
A Quasi-Newton Approach to Nonsmooth Convex Optimization Problems in Machine Learning (2008, background): “Some machine learning applications have also been pursued along these lines (Lee and Mangasarian, 2001; Zhang and Oles, 2001).”
A tutorial on support vector regression (2004, unknown): “If this is not the case, specialized methods can offer considerable computational savings (Lee and Mangasarian 2001).”
Lagrangian Support Vector Machines (2001, methodology): “Our results, shown in Figure 2, demonstrate that LSVM shows similar or better generalization capability on this dataset when compared to other methods [12, 18, 15].”
Deep Learning using Linear Support Vector Machines (2013, background): “A similar objective and its optimization are also discussed by (Lee & Mangasarian, 2001).”