Convergence of a Generalized SMO Algorithm for SVM Classifier Design

By S. Sathiya Keerthi, Elmer G. Gilbert. Machine-mediated learning, 2002

323 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/e62fb4d2027d46d8d39c4fbda74aff89dcf5574e

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Citations in the corpus

A Study on SMO-Type Decomposition Methods for Support Vector Machines (2006, unknown): “The first study on the stopping condition of SMO-type methods is [11].”
QP Algorithms with Guaranteed Accuracy and Run Time for Support Vector Machines (2006, background): “Instead however we setτ = 1/n since this value is also valid and it greatly simplifies the iteration bounds without changing their bas c n ture.”
Supervised Machine Learning: A Review of Classification Techniques (2007, unknown): “Keerthi and Gilbert (2002) suggested two modified versions of SMO that are significantly faster than the original SMO in most situations.”
Large Scale Machine Learning (2004, methodology): “Convergence Keerthi and Gilbert (2002) proved that the decomposition algorithm converges for a working set of size 2, if the shrinking is not used. Furthermore, Lin (2001) has shown the convergence of this algorithm for any value of working set size (but again without shrinking), under the following”
Supervised classification and mathematical optimization (2013, background): “SMO was subsequently improved in [135], and the convergence of this improvement was proved in [133].”
Training v-Support Vector Regression: Theory and Algorithms (2002, result): “Discussions for classiﬁcation are in (Keerthi and Gilbert 2002; Chang and Lin 2001b).”
Fast Kernel Classifiers with Online and Active Learning (2005, background): “We can also claim that (Keerthi and Gilbert, 2002; Takahashi and Nishi, 2003) have established proposition 16 with κ = 0 and τ > 0 for the specific case of SVMs.”
Support Vector Machine Solvers (2007, methodology): “• The asymptotic convergence and finite termination properties of this particular case of the decomposition method are very well understood (e.g. Keerthi and Gilbert, 2002; Takahashi and Nishi, 2005; Chen et al., 2006; Hush et al., 2006).”
A novel Frank-Wolfe algorithm. Analysis and applications to large-scale SVM training (2013, methodology): “Recently, in [40], the Mitchell-Demnyanov-Malozemov (MDM) algorithm [42], another classic geometric algorithm to solve MNPs and NPPs, was found to be essentially equivalent to the SMO algorithm [45, 16] devised specifically for SVMs and similar quadratic programs [37].”
Support Vector Ordinal Regression (2007, unknown): “However, since the most violating pair is always chosen, the ideas of Keerthi and Gilbert (2002) can be adapted to prove the convergence of the SMO algorithm.”
Machine learning: a review of classification and combining techniques (2006, background): “Keerthi and Gilbert (2002) suggested two modified versions of SMO that are significantly faster than the original SMO in most situations.”
Nonlinear optimization and support vector machines (2018, methodology): “SMO algorithms were the first methods proposed for SVM training and the related literature is wide (see, e.g., Joachims 1999; Keerthi and Gilbert 2002; Lin 2001b; Osuna et al. 1997; Platt 1999).”
Learning on the border: active learning in imbalanced data classification (2007, background): “Following Keerthi and Gilbert (2002), we bypass this technical difficulty by defining a notion of approximate optimum and proving convergence in finite time.”
LIBSVM: A library for support vector machines (2011, unknown): “This section describes LIBSVM ’s evaluation measures, shows some simple examples of running LIBSVM , and presents the code structure.”