New Support Vector Algorithms

By Bernhard Schölkopf, Alex Smola, Robert C. Williamson, Peter L. Bartlett. 2000

2,978 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

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Security Evaluation of Pattern Classifiers under Attack (2014, background): “In the above setting, it amounts to choosing the values of the n parameter of the learning algorithm (which is an upper bound on the false positive error rate on training data [50]), and the g value of the RBF kernel.”
A Survey on Neural Architecture Search (2019, background): “Empirically, they find that the ν-Support Vector Regression (Schölkopf et al., 2000) performs best among other alternatives such as random forest or Bayesian linear regression.”
Kernel methods in machine learning (2007, neutral): “[120]) by using as loss function the “pinball” loss, that is, ψ(ξ) = (1− τ)ψ if ψ < 0 and ψ(ξ) = τψ if ψ > 0.”
Sampling Matters in Deep Embedding Learning (2017, positive): “Note that the use of ν here is very similar to the ν-trick in ν-SVM [24].”
Pattern Recognition and Machine Learning (2006, neutral): “As with the classification case, there is an alternative formulation of the SVM for regression in which the parameter governing complexity has a more intuitive interpretation (Schölkopf et al., 2000).”
Duality and Geometry in SVM Classifiers (2000, methodology): “The reader should consult (Schölkopf et al., 2000) for a more formal derivation of these and additional properties for the ν-SVM formulation which also has been shown to solve the closest points between the reduced convex hulls problem (Crisp & Burges, 1999).”
Support Vector Machines as Probabilistic Models (2011, methodology): “This is analoguous to the ν-SVM reformulation of the standard SVM (Schölkopf et al., 2000), in which the rather unintuitive regularization parameter is replaced by a parameter controlling the number of SVs.”
Advances in Large Margin Classifiers (2000, methodology): “Note that w will typically no more correspond to the image of just a single vector from input space (cf. Schölkopf et al. (1998a) for a formula to compute the pre-image if it exists), in other words,wmay not be directly accessible any more.”
Machine Recognition of Music Emotion: A Review (2012, methodology): “A popular implementation of SVR is the LIBMSVM library [Chang and Lin 2001].”
Composite Binary Losses (2009, background): “on noise (some heavy-tail noise mixed in with the Gaussian noise often assumed in designing estimators). There are some results about particular machine learning algorithms being robust in that sense [43]. \Robust" is also used to mean robustness with respect to random attribute noise [48], rob”
Working Set Selection Using Second Order Information for Training Support Vector Machines (2005, background): “Another formula which needs special attention is ν-SVM (Schölkopf et al., 2000), which solves a problem with one more linear constraint:”
Using Free Energy Principle For Blind Image Quality Assessment (2015, methodology): “• Second, the overall distorted images are randomly separated into training and testing groups, and themodel is then acquired using support vector regressor (SVR) [44] on the extracted features of images in the training group and the corresponding subjective MOS values.”
LIBSVM: A library for support vector machines (2011, neutral): “Many techniques, for example, Fine and Scheinberg (2001); Lee and Mangasarian (2001); Keerthi et al. (2006); Segata and Blanzieri (2010), have been developed to obtain an approximate model, but these are beyond the scope of our discussion.”
Fast cross-validation via sequential testing (2012, methodology): “To evaluate how the choice of learning method influences the performance of the CVST algorithm, we compare kernel logistic regression (KLR) against a ν-Support Vector Machine (SVM) for classification problems and kernel ridge regression (KRR) versus νSVR for regression problems each using a Gaussian”
Kernel Sliced Inverse Regression with Applications to Classification (2008, background): “For additional discussion of this issue, such as issues surrounding the low-rank approximations of Gram matrices, see Smola and Sch¨olkopf (2000) and Williams and Seeger (2001).”