Gaussian kernel optimization: Complex problem and a simple solution |
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Authors: | Jiang-Bo Yin Tao Li Hong-Bin Shen[Author vitae] |
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Affiliation: | aDepartment of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China;bDepartment of Mathematics, Shanghai Jiaotong University, 800 Dongchuan Road, Shanghai 200240, China |
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Abstract: | The Gaussian kernel function implicitly defines the feature space of an algorithm and plays an essential role in the application of kernel methods. The parameter of Gaussian kernel function is a scalar that has significant influences on final results. However, until now, it is still unclear how to choose an optimal kernel parameter. In this paper, we propose a novel data-driven method to optimize the Gaussian kernel parameter, which only depends on the original dataset distribution and yields a simple solution to this complex problem. The proposed method is task irrelevant and can be used in any Gaussian kernel-based approach, including supervised and unsupervised machine learning. Simulation experiments demonstrate the efficacy of the obtained results. A user-friendly online calculator is implemented at: www.csbio.sjtu.edu.cn/bioinf/kernel/ for public use. |
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Keywords: | Gaussian kernel function Noncentral chi-square distribution Supervised learning Unsupervised learning |
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