基于多尺度重采样思想的类指数核函数构造

胡站伟; 焦立国; 徐胜金; 黄勇

doi:10.11999/JEIT151101

基于多尺度重采样思想的类指数核函数构造

doi: 10.11999/JEIT151101

2.
(清华大学航空航天学院流体力学所北京 100084) ②(中国空气动力研究与发展中心绵阳 621000) ③(大庆地区防洪工程管理处大庆 163311)

基金项目:

国家自然科学基金(11472158)

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- 被引次数: 0
出版历程
- 收稿日期: 2015-09-25
- 修回日期: 2016-05-03
- 刊出日期: 2016-07-19

Design of An Exponential-like Kernel Function Based on Multi-scale Resampling

2.
(Fluid Dynamics Institute, School of Aerospace, Tsinghua University, Beijing 100084, China)

Funds:

The National Natural Science Foundation of China (11472158)

摘要

摘要: 该文按照多尺度重采样思想，构造了一种类指数分布的核函数(ELK)，并在核回归分析和支持向量机分类中进行了应用，发现ELK对局部特征具有捕捉优势。ELK分布仅由分析尺度决定，是单参数核函数。利用ELK对阶跃信号和多普勒信号进行Nadaraya-Watson回归分析，结果显示ELK降噪和阶跃捕捉效果均优于常规Gauss核，整体效果接近或优于局部加权回归散点平滑法(LOWESS)。多个UCI数据集的SVM分析显示，ELK与径向基函数(RBF)分类效果相当，但比RBF具有更强的局域性，因此具有更细致的分类超平面，同时分类不理想时可能产生更多的支持向量。对比而言，ELK对调节参数敏感性低，这一性质有助于减少参数优选的计算量。单参数的ELK对局域特征的良好捕捉能力，有助于这类核函数在相关领域得到推广。
- 多尺度重采样 /
- Nadaraya-Watson回归 /
- 支持向量机 /
- 类指数核函数
Abstract: Based on multi-scale resampling, an Exponential-Like Kernel (ELK) function is designed, and evaluated with local feature extraction in kernel regression and Support Vector Machine (SVM) classification. The ELK is a one-parameter kernel, whose distribution is controlled only by the resolution of analysis. With block and Doppler noisy signals, Nadaraya-Watson regression with ELK mainly shows more noise and step error than with Gaussian kernel, it also has better precision and is more robust than LOcally WEighted Scatterplot Smoothing (LOWESS). Data sets from the UCI Machine Learning Repository used in SVM test demonstrate that, ELK has nearly equal classification accuracy as RBF does, and its locality results in more detailed margin hyperplanes, in consequence, a big number of support vectors in low classification accuracy situation. Moreover, the insensitivity?of ELK to the adjustive coefficient in kernel methods shows the potential to facilitate the parameter optimization progress. ELK, as a single parameter kernel with significant locality, is hopefully to be extensively used in relative kernel methods.
- Multi-scale resampling /
- Nadaraya-Watson regression /
- Support Vector Machine (SVM) /
- Exponential- Like Kernel (ELK) function

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