Simple estimate of the width in Gaussian kernel with adaptive scaling technique
Simple estimate of the width in Gaussian kernel with adaptive scaling technique
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DOI：
10.1016/j.asoc.2011.07.011
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
S. Kitayama;K. Yamazaki
中科院分区：
文献类型：
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作者：
S. Kitayama;K. Yamazaki
本文提出了一种基于自适应缩放技术来估计高斯核宽度的简单方法。高斯核广泛应用于径向基函数（RBF）网络、支持向量机（SVM）、最小二乘支持向量机（LS-SVM）、克里金模型等。众所周知，高斯核的宽度在这些机器学习技术中起着重要作用。确定最佳宽度是一项耗时的任务。因此，优选以简单的方式确定宽度。在本文中，我们首先研究 Nakayama 等人提出的宽度简单估计。通过检验，给出了简单估计宽度的四个充分条件。然后，提出了一种新的简单宽度估计。为了获得建议的宽度估计值，所有尺寸均等比例缩放。还开发了一种称为自适应缩放技术的简单技术。预计所提出的估计宽度的简单方法适用于采用高斯核的广泛机器学习技术。通过实例，检验了所提出的简单宽度估计方法的有效性。
This paper presents a simple method to estimate the width of Gaussian kernel based on an adaptive scaling technique. The Gaussian kernel is widely employed in radial basis function (RBF) network, support vector machine (SVM), least squares support vector machine (LS-SVM), Kriging models, and so on. It is widely known that the width of the Gaussian kernel in these machine learning techniques plays an important role. Determination of the optimal width is a time-consuming task. Therefore, it is preferable to determine the width with a simple manner. In this paper, we first examine a simple estimate of the width proposed by Nakayama et al. Through the examination, four sufficient conditions for the simple estimate of the width are described. Then, a new simple estimate for the width is proposed. In order to obtain the proposed estimate of the width, all dimensions are equally scaled. A simple technique called the adaptive scaling technique is also developed. It is expected that the proposed simple method to estimate the width is applicable to wide range of machine learning techniques employing the Gaussian kernel. Through examples, the validity of the proposed simple method to estimate the width is examined.