Lagrangian Support Vector Machines

By Olvi L. Mangasarian, David R. Musicant. Journal of machine learning research, 2001

582 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/45204c008c8f3d9e9b66ea5623c032ce0b3089e7

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Citations in the corpus

Nonlinear optimization and support vector machines (2018, background): “Thus the requirements are well-defined from an optimization point of view, and this has motivated a wide research activity (even of the optimization community) to define efficient and convergent algorithms for SVM training (see, for instance, Astorino and Fuduli 2015; Boser et al. 1992; Byrd et al. ”
Genetic Programming with a Genetic Algorithm for Feature Construction and Selection (2005, methodology): “(‘Ordered Fuzzy ARTMAP’, a neural network algorithm) from [6], LSVM (Lagrangian Support Vector Machines) from [16] and Krawiec from [15].”
Training linear SVMs in linear time (2006, methodology): “Applying the LSVM to tasks with thousands of features is not tractable, since the algorithm requires storing and inverting an N × N matrix.”
Support vector machine-based expert system for reliable heartbeat recognition (2004, methodology): “For this type of optimization there exist many highly effective learning algorithms [14], [16], [17], leading in almost all cases to the global minimum of the cost function and to the best pos-”
Survey on SVM and their application in image classification (2018, methodology): “Over the past decades, various alterations to SVM appeared, such as Twin SVM [2], Lagrangian SVM [3], least square SVM [2], Decision tree SVM, DAG SVM, multi kernel classiﬁcation [4].”
QP Algorithms with Guaranteed Accuracy and Run Time for Support Vector Machines (2006, unknown): “…2005, 2006; Cristianini and Shawe-Taylor, 2000; Hsu and Lin, 2002; Hush and Scovel, 2003; Joachims, 1998; Keerthi et al., 2000, 2001; Laskov, 2002; Liao et al., 2002; List and Simon, 2004, 2 05; Mangasarian and Musicant, 1999, 2001; Osuna et al., 1997; Platt, 1998; Simon, 2004; Vapnik, 1998).”
Accurate fault location in the power transmission line using support vector machine approach (2004, methodology): “The learning process of the SVM networks has been performed by using Mangasarian algorithm [17].”
Core Vector Machines: Fast SVM Training on Very Large Data Sets (2005, methodology): “We first experiment on the 4× 4 checkerboard data (Figure 2) commonly used for evaluating large-scale SVM implementations (Lee and Mangasarian, 2001; Mangasarian and Musicant, 2001b; Schwaighofer and Tresp, 2001).”
Cutting-plane training of structural SVMs (2009, methodology): “While there are training algorithms for linear SVMs that scale linearly with n (e.g., Lagrangian SVM (Mangasarian and Musicant 2001) (using the (cid:4) ξ 2 i loss), Proximal SVM (Fung and Mangasarian 2001) (using an L 2 regression loss), and Interior Point Methods (Ferris and Munson 2003)), they use”
RSVM: Reduced Support Vector Machines (2001, methodology): “We interpret this as a possible instance-based learning [17, Chapter 8] where the small sample Ā is learning from the much larger training set A by forming the appropriate rectangular kernel relationship K(A, Ā′) between the i i i i i i i i 7 original and reduced sets.”
A Feature Selection Newton Method for Support Vector Machine Classification (2004, methodology): “Reported times for LSVM here differ from the ones reported in [19] because the calculation time for the matrix H of (2.”
Proximal support vector machine classifiers (2001, methodology): “In contrast, SVM l~gh~ [16] failed on this problem [ 24 ].”
An introduction to kernel-based learning algorithms (2001, unknown): “, [2], [63]).”