Core Vector Machines: Fast SVM Training on Very Large Data Sets

By Ivor Wai-Hung Tsang, James T. Kwok, Pak-Ming Cheung. 2005

1,123 citations recorded by the source corpus.

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Dataset Distillation (2018, background): “Similarly, core-set construction (Bachem et al., 2017; Tsang et al., 2005; Har-Peled & Kushal, 2007; Sener & Savarese, 2018) and instance selection (Olvera-López et al.”
Distilled One-Shot Federated Learning (2020, methodology): “These methods include dataset pruning [1] and core set construction [2, 31, 27], which keep the examples that are measured to be more useful for training and remove the rest.”
Quasi-Monte Carlo Feature Maps for Shift-Invariant Kernels (2014, methodology): “Another well known approach is the Core Vector Machines (Tsang et al., 2005) which draws on approximation algorithms from computational geometry to scale up a class of kernel methods that can be reformulated in terms of the minimum enclosing ball problem.”
A Wholistic View of Continual Learning with Deep Neural Networks: Forgotten Lessons and the Bridge to Active and Open World Learning (2020, methodology): “Similarly, SVM based core vector machines (Tsang et al., 2005) use a set of minimum enclosing balls to create a core set that best approximates the entire distribution.”
An Equivalence between the Lasso and Support Vector Machines (2013, background): “This fact is known in the SVM literature (Sch¨olkopf & Smola, 2002; Keerthi et al., 2000; Tsang et al., 2005), and can be formalized as follows: The two-class soft-margin SVM with squared loss is given by the optimization problem min Here C > 0 is the regularization parameter, and ρ/ k ¯ w k is the…”
How to Scale Up Kernel Methods to Be As Good As Deep Neural Nets (2014, methodology): “Alternative approaches exploit the equivalence between SVMs and sparse greedy approximation and solve SVMs approximately with a smaller subset of examples called coresets(2) [49, 12].”
Random Features for Large-Scale Kernel Machines (2007, methodology): “We focus our comparisons against the Core Vector Machine [14] because it was shown in [14] to be both faster and more accurate than other known approaches for training kernel machines, including, in most cases, random sampling of datapoints [8].”
A Distributed Frank-Wolfe Algorithm for Communication-Efficient Sparse Learning (2014, methodology): “The dual problem of L2-loss SVM with kernel k is as follows [31, 32]:”
Review on Studies and Advances of Machine Learning Approaches (2013, background): “After the developments in recent years, SVM has become a hot spot of machine learning, and has been successfully applied in many fields [11-15].”
Machine Learning With Big Data: Challenges and Approaches (2017, background): “For example, the standard support vector machine (SVM) algorithm has a training time complexity of O(m3) and a space complexity of O(m2) [29], where m is the number of training samples.”
Replicability is not Reproducibility:Nor is it Good Science (2009, background): “Sonnenburg et al. (2007) point to a debate between authors Tsang et al. (2005); Loosli and Canu (2007); Tsang and Kwok (2007) to support their position.”
Submodularity in Data Subset Selection and Active Learning (2015, background): “Many machine learning problems including SVMs, k-means clustering , k-median clustering, and Gaussian mixtures (Tsang et al., 2005; Har-Peled & Mazumdar, 2004; Feldman et al., 2011) can be approximately solved on a coreset.”
Fast Stochastic Frank-Wolfe Algorithms for Nonlinear SVMs (2010, methodology): “The alternative formulation, which was proposed and successfully utilized by core vector machines [24], is a variant of L2-SVM.”
Practical Coreset Constructions for Machine Learning (2017, methodology): “X Tsang et al. [2005] show that many kernel methods can be equivalently formulated as MEB problems.”
Soft-Label Dataset Distillation and Text Dataset Distillation (2019, methodology): “Several methods aim to ‘prune’ a dataset, or create a ‘coreset’, by leaving in only examples that are determined to be useful (Angelova et al., 2005; Bachem et al., 2017; Sener and Savarese, 2017; Tsang et al., 2005).”
Real-time human action recognition based on depth motion maps (2013, background): “In [10], the computational complexity of SVM is stated as O(r(3)) [31].”
Breaking the curse of kernelization: budgeted stochastic gradient descent for large-scale SVM training (2012, methodology): “SimpleSVM (Vishwanathan et al., 2003), LASVM (Bordes et al., 2005), CVM (Tsang et al., 2005) and parallel SVMs (Zhu et al., 2009) are among the few successful attempts to train kernel SVM from large data.”