基于多尺度重采樣思想的類指數(shù)核函數(shù)構(gòu)造
doi: 10.11999/JEIT151101
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2.
(清華大學航空航天學院流體力學所 北京 100084) ②(中國空氣動力研究與發(fā)展中心 綿陽 621000) ③(大慶地區(qū)防洪工程管理處 大慶 163311)
基金項目:
國家自然科學基金(11472158)
Design of An Exponential-like Kernel Function Based on Multi-scale Resampling
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2.
(Fluid Dynamics Institute, School of Aerospace, Tsinghua University, Beijing 100084, China)
Funds:
The National Natural Science Foundation of China (11472158)
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摘要: 該文按照多尺度重采樣思想，構(gòu)造了一種類指數(shù)分布的核函數(shù)(ELK)，并在核回歸分析和支持向量機分類中進行了應用，發(fā)現(xiàn)ELK對局部特征具有捕捉優(yōu)勢。ELK分布僅由分析尺度決定，是單參數(shù)核函數(shù)。利用ELK對階躍信號和多普勒信號進行Nadaraya-Watson回歸分析，結(jié)果顯示ELK降噪和階躍捕捉效果均優(yōu)于常規(guī)Gauss核，整體效果接近或優(yōu)于局部加權(quán)回歸散點平滑法(LOWESS)。多個UCI數(shù)據(jù)集的SVM分析顯示，ELK與徑向基函數(shù)(RBF)分類效果相當，但比RBF具有更強的局域性，因此具有更細致的分類超平面，同時分類不理想時可能產(chǎn)生更多的支持向量。對比而言，ELK對調(diào)節(jié)參數(shù)敏感性低，這一性質(zhì)有助于減少參數(shù)優(yōu)選的計算量。單參數(shù)的ELK對局域特征的良好捕捉能力，有助于這類核函數(shù)在相關(guān)領(lǐng)域得到推廣。
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關(guān)鍵詞:
- 多尺度重采樣 /
- Nadaraya-Watson回歸 /
- 支持向量機 /
- 類指數(shù)核函數(shù)
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. -
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