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Title of Journal: Int J Mach Learn Cyber

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Abbravation: International Journal of Machine Learning and Cybernetics

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Springer-Verlag

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DOI

10.1016/0014-5793(93)81226-p

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1868-808X

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From Gaussian kernel density estimation to kernel

Authors: Shitong Wang Zhaohong Deng Fulai Chung Wenjun Hu
Publish Date: 2012/02/22
Volume: 4, Issue: 2, Pages: 119-137
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Abstract

This paper explores how a kind of probabilistic systems namely Gaussian kernel density estimation GKDE can be used to interpret several classical kernel methods including the wellknown support vector machine SVM support vector regression SVR oneclass kernel classifier ie support vector data description SVDD or equivalently minimal enclosing ball MEB and the fuzzy systems FS For the SVM we reveal that the classical SVM with Gaussian density kernel attempts to find a noisy GKDE based Bayesian classifier with equal prior probabilities for each class For the SVR the classification based εSVR attempts to obtain two noisy GKDEs for each class in the constructed binary classification dataset and the decision boundary just corresponds to the mapping function of the original regression problem For the MEB or SVDD we reveal the equivalence between it and the integratedsquarederrors ISE criterion based GKDE and by using this equivalence a MEB based classifier with privacypreserving function is proposed for one kind of classification tasks where the datasets contain privacypreserving clouds For the FS we show that the GKDE for a regression dataset is equivalent to the construction of a zeroorder Takagi–Sugeno–Kang TSK fuzzy system based on the same dataset Our extensive experiments confirm the obtained conclusions and demonstrated the effectiveness of the proposed new machine learning and modeling methodsThis work was supported in part by the Hong Kong Polytechnic University under Grants 1ZV5V and GU724 and by the National Natural Science Foundation of China under Grants 60903100 60975027 61170122 and by the Natural Science Foundation of Jiangsu Province under Grant BK2009067 2011NSFJS plus its Key Grant JiangSu 333 expert engineering grant BRA2011142 and 2011 Postgraduate Student’s Creative Research Fund of Jiangsu Province under Grant CXZZ110483

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