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Title: Bias corrected SVM with the Gaussian kernel in the HDLSS context Authors:  Yugo Nakayama - Kyoto University (Japan) [presenting]
Kazuyoshi Yata - University of Tsukuba (Japan)
Makoto Aoshima - University of Tsukuba (Japan)
Abstract: A common feature of high-dimensional data is that the data dimension is high, however, the sample size is relatively low. We call such data HDLSS data. Asymptotic properties of the linear support vector machine (SVM) in the HDLSS context have been previously investigated. We study asymptotic properties of a non-linear SVM in HDLSS settings. We show that the non-linear SVM is heavily biased for imbalanced data. In order to overcome such inconvenience, we propose a bias-corrected SVM (BC-SVM) which is robust against extremely imbalanced data. In particular, we investigate asymptotic properties of the BC-SVM when having the Gaussian kernel. Since the performance of the BC-SVM is influenced by a scale parameter involved in the Gaussian kernel, we discuss a choice of the scale parameter in numerical simulations and actual data analyses.