Simplified Support Vector Decision Rules

By C. Burges. 1996

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Fastfood: Approximate Kernel Expansions in Loglinear Time (2014, background): “• We denote the number of (nonlinear) basis functions by n. Reduced Set Expansions Burges (1996) focused on compressing function expansions after the problem was solved by means of reduced-set expansions.”
Learning to rank using gradient descent (2005, methodology): “Rather than learning with the quadratic kernel and then applying a reduced set method (Burges, 1996), we simply added a further step of preprocessing, taking the features, and Learning to Rank using Gradient Descent Table 3.”
Kernel PCA for novelty detection (2007, methodology): “However, this number could be reduced using so-called ‘reduced-set methods’ [24,25].”
Efficient Classification for Additive Kernel SVMs (2013, background): “These sets of points can be the set of input points themselves, as in the work of Burges [6], Osuna and Girosi [43], where the most representative support vectors are kept as a postprocessing step.”
Bayes Meets Bellman: The Gaussian Process Approach to Temporal Difference Learning (2003, methodology): “¢(x~) = Ea~,j¢(:~j) + ¢~es, where IlCresH 2 v. j-----1 (3.15) In order to be able to compute at at each time step, we need to update I~t i whenever the dictionary is appended with a new state.”
Dimension Reduction: A Guided Tour (2010, background): “3 This monograph is a revised and extended version of Burges [17]. express ideas and to illustrate strengths and weaknesses of a method, high dimensional data has qualitatively different behavior from twoor three-dimensional data.”
Mathematical Programming for Data Mining: Formulations and Challenges (1999, background): “minimizing training set error), SVMs incorporate structured risk minimization [120, 28] which minimizes an upper bound on the generalization error.”
Sensitivity of Support Vector Machines to Random Feature Selection in Classification of Hyperspectral Data (2010, methodology): “Moreover, the reduced-set approach, which was originally developed for binary SVM [43] and later extended to the multiclass case [44], can be directly adapted, because an ensemble of SVM can be seen as an ensemble of binary SVM.”
Survey on supervised machine learning techniques for automatic text classification (2019, methodology): “13 to be easy for using as follows: x xρ + r wo‖wo‖ (13) In Burges (1996), the researcher has displayed the measures sound by a worthy performance evaluation on large datasets.”
Breaking the curse of kernelization: budgeted stochastic gradient descent for large-scale SVM training (2012, methodology): “Bounding the space complexity of SVM classifiers has been an active research since the early days of SVM. SVM reduced set methods (Burges, 1996; Schölkopf et al., 1999) start by training a standard SVM on the complete data and then find a sparse approximation by minimizing Euclidean distance…”
Learning using privileged information: similarity control and knowledge transfer (2015, methodology): “However, for the special homogeneous quadratic kernel K * (x * i , x * j ) = (x * i , x * j ) 2 , this problem has a simple exact solution (Burges, 1996 ).”
Sparse Bayesian Learning and the Relevance Vector Machine (2001, background): “Some form of post-processing is often required to reduce computational complexity (Burges, 1996; Burges and Scholkopf, 1997).”
Nonlinear Component Analysis as a Kernel Eigenvalue Problem (1998, methodology): “vastly faster than linear principal component extraction in F. Still, in some cases (e.g., if we were to extract principal components as a preprocessing step for classification), we might want to speed things up. This can be done by a technique proposed by Burges (1996) in the context of support v”
Support vector tracking (2004, unknown): “To speed up the classification phase, we used the Reduced Set Method [5] to reduce the number of support vectors from 2; 000 to 400.”