Proximal support vector machine classifiers

By glenn. fung, Olvi L. Mangasarian. Knowledge Discovery and Data Mining, 2001

918 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/f96a214a253aaab297a138405812c856945ed335

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Citations in the corpus

Nonlinear optimization and support vector machines (2018, background): “…1992; Byrd et al. 2011; Carrizosa and Romero Morales 2013; Cortes and 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…”
Multisurface proximal support vector machine classification via generalized eigenvalues (2006, background): “In another somewhat less standard approach, the proximal support vector classification [7], [25], [6], two parallel planes are generated such that each plane is closest to one of two data sets to be classified and such that the two planes are as far apart as possible.”
Privacy-preserving SVM classification (2008, positive): “Thus, from Eq. ( 6 ), to securely compute the dot products and thus the kernel functions between the support vectors and the testing data object, we need to run the secure addition of vectors, such that each element of the vector is a dot product between a partial support vector and the testing data”
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”
In Defense of One-Vs-All Classification (2004, background): “Fürnkranz (2002) reported that an AVA scheme substantially outperformed an OVA scheme over a wide variety of data sets; we decided to focus specifically on those data sets that Fürnkranz had found a large difference on.”
TSVR: An efficient Twin Support Vector Machine for regression (2010, methodology): “(42) In fact, for this nonlinear case we have to invert a matrix of order (l + 1), instead of order (n + 1) in the linear case, then if necessary, we can introduce the rectangular kernel technique (Fung & Mangasarian, 2001) to reduce the dimensionality of (39) and (40).”
Optimization method based extreme learning machine for classification (2010, methodology): “However, Liu et al. [14] and Frénay and Verleysen [15] have made a significant contribution showing that the ELM learning approach can be applied to SVMs directly by simply replacing SVM kernels with (random) ELM kernels and better generalization can be achieved.1 Random ELM kernels can be applied ”
Factors in automatic musical genre classification of audio signals (2003, background): “Figure 2 shows a BH for a piece of Rock music (notice the peaks at 80 BPM (main tempo) and 160 BPM).”
Regularized Extreme Learning Machine (2009, background): “|| || β which is derived from Maximizing the distance of the Margin separating classes [8][9][ 16 ].”
The Mathematics of Learning: Dealing with Data (2005, methodology): “This classification scheme was used at least as early as 1989 (for reviews see [7, 40] and then rediscovered again by many others (see [21, 49]), including Mangasarian (who refers to square loss regularization as “proximal vector machines”) and Suykens (who uses the name “least square SVMs”).”
A Modified Finite Newton Method for Fast Solution of Large Scale Linear SVMs (2005, methodology): “Similar observations hold for Mangasarian’s finite Newton method as well as our L2-SVMMFN.”