Cross Validation Through Two-Dimensional Solution Surface for Cost-Sensitive SVM

Bin Gu, Victor S. Sheng, Keng Yeow Tay, Walter Romano, Shuo Li

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


Model selection plays an important role in cost-sensitive SVM (CS-SVM). It has been proven that the global minimum cross validation (CV) error can be efficiently computed based on the solution path for one parameter learning problems. However, it is a challenge to obtain the global minimum CV error for CS-SVM based on one-dimensional solution path and traditional grid search, because CS-SVM is with two regularization parameters. In this paper, we propose a solution and error surfaces based CV approach (CV-SES). More specifically, we first compute a two-dimensional solution surface for CS-SVM based on a bi-parameter space partition algorithm, which can fit solutions of CS-SVM for all values of both regularization parameters. Then, we compute a two-dimensional validation error surface for each CV fold, which can fit validation errors of CS-SVM for all values of both regularization parameters. Finally, we obtain the CV error surface by superposing K validation error surfaces, which can find the global minimum CV error of CS-SVM. Experiments are conducted on seven datasets for cost sensitive learning and on four datasets for imbalanced learning. Experimental results not only show that our proposed CV-SES has a better generalization ability than CS-SVM with various hybrids between grid search and solution path methods, and than recent proposed cost-sensitive hinge loss SVM with three-dimensional grid search, but also show that CV-SES uses less running time.

Original languageEnglish
Article number7487020
Pages (from-to)1103-1121
Number of pages19
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number6
StatePublished - Jun 1 2017


  • Solution surface
  • cost-sensitive support vector machine
  • cross validation
  • solution path
  • space partition


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