Uniqueness of the SVM Solution

By C. Burges, David J. Crisp. 1999

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Citations in the corpus

Some Properties of Regularized Kernel Methods (2004, background): “In particular our results on uniqueness of SVM solution are similar to those in Burges and Crisp (2000, 2003) but do not make use of the dual formulation.”
Strictly Positive Definite Functions on a Real Inner Product Space (2004, unknown): “Learning Theory, see e.g., Burges, Crisp [ 2 ], Smolla, Sch olkopf, M uller [8], Steinwart [9], [10], and Vapnik [11].”
SVM incremental learning, adaptation and optimization (2003, background): “2There is the potential for a degenerate solution to arise if the regularization parameterC is set too low such that both examples become error vectors [2].”
On the Influence of the Kernel on the Consistency of Support Vector Machines (2001, methodology): “For an introduction to the 1-SMC as well as for implementation techniques we refer to Cristianini & Shawe-Taylor (2000, Ch. 6 and 7) and Vapnik (1998, Ch. 10) Burges & Crisp (2000) proved that in general the optimization problem (10) has no unique solution.”
Duality and Geometry in SVM Classifiers (2000, background): “They will produce the exact same separating plane or an equally good plane if multiple solutions exist (see Burges & Crisp, 1999 ).”
Gradient Starvation: A Learning Proclivity in Neural Networks (2020, background): “While primal and dual dynamics are not guaranteed to match, the solution they converge to is guaranteed to match [21], and that is what our theory builds upon.”
Analysis of support vector machines (2002, background): “Burges and Crisp [4] derive conditions in which the dual solution is unique but the primal solution is non-unique.”
Estimating the Generalization Performance of an SVM Efficiently (2000, background): “While it is highly unlikely in practice that one gets a solution of OP2 with only bounded support vectors, it is theoretically possible see Burges & Crisp, 1999; Rifkin et al., 1999, for a thorough discussion .”