Leave one support vector out cross validation for fast estimation of generalization errors

摘要

A Support Vector Classifier (SVC) is formulated in terms of a kernel. The bandwidth of the kernel affects the generalization performance of the SVC. This paper presents a Leave One Support Vector Out Cross Validation (LOSVO-CV) algorithm for estimating the optimal bandwidth of the kernel for classification purpose. The proposed algorithm is based on the Leave One Out Cross Validation (LOO-CV) algorithm (Numer. Math. 31 (1979) 377) that was proposed to find the optimal bandwidth but difficult to be implemented due to its large amount of computation. The properties of LOSVO-CV are analyzed in comparison with the LOO-CV. The simulation study demonstrates that the LOSVO-CV is a fast algorithm and it has the same generalization performance optimized by a bootstrap method (Neural Process. Lett. 11 (2000) 51) which can find an optimal bandwidth of the kernel of the SVC. The LOSVO-CV algorithm is able to provide consistent results with different sizes of a benchmark data set which is obtained from the University of California (UCI) repository.