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

HU Zhanwei; JIAO Liguo; XU Shengjin; HUANG Yong

doi:10.11999/JEIT151101

Volume 38 Issue 7

Jul. 2016

Turn off MathJax

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2016 > 38(7): 1689-1695

HU Zhanwei, JIAO Liguo, XU Shengjin, HUANG Yong. Design of An Exponential-like Kernel Function Based on Multi-scale Resampling[J]. Journal of Electronics & Information Technology, 2016, 38(7): 1689-1695. doi: 10.11999/JEIT151101

Citation:

HU Zhanwei, JIAO Liguo, XU Shengjin, HUANG Yong. Design of An Exponential-like Kernel Function Based on Multi-scale Resampling[J]. Journal of Electronics & Information Technology, 2016, 38(7): 1689-1695. doi: 10.11999/JEIT151101

Citation:

PDF( 1109 KB)

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

doi: 10.11999/JEIT151101

1.
2.
(Fluid Dynamics Institute, School of Aerospace, Tsinghua University, Beijing 100084, China)

Funds:

The National Natural Science Foundation of China (11472158)

Received Date: 2015-09-25
Rev Recd Date: 2016-05-03
Publish Date: 2016-07-19

Abstract

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

FullText(HTML)

References(25)

References

SMOLA A J and SCHLKOPF B. On a kernel-based method for pattern recognition, regression, approximation, and operator inversion[J]. Lgorithmica, 1998, 22(1): 211-231. doi: 10.1007/PL00013831.

KOHLER M, SCHINDLER A, and SPERLICH S. A review and comparison of bandwidth selection methods for kernel regression [J]. International Statistical Review, 2014, 82(2): 243-274. doi: 10.1111/insr.12039.

DAS D, DEVI R, PRASANNA S, et al. Performance comparison of online handwriting recognition system for assamese language based on HMM and SVM modelling[J]. International Journal of Computer Science Information Technology, 2014, 6(5): 87-95. doi: 10.5121/csit.2014.4717.

HASTIE T and LOADER C. Local regression: Automatic kernel carpentry[J]. Statistical Science, 1993, 8(2): 120-143. doi: 10.1214/ss/1177011002.

SCHLKOPF B, SMOLA A, and MLLER K R. Nonlinear component analysis as a kernel eigenvalue problem[J]. Neural Computation, 1998, 10(5): 1299-1319. doi: 10.1162/ 089976698300017467.

BUCAK S S, JIN R, and JAIN A K. Multiple kernel learning for visual object recognition: A review [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014, 36(7): 1354-1369. doi: 10.1109/TPAMI.2013.212.

BACH F R, LANCKRIET G R, and JORDAN M I. Multiple kernel learning, conic duality, and the SMO algorithm[C]. Proceedings of the Twenty-first International Conference on Machine Learning, Banff, Canada, 2004: 1-6. doi: 10.1145/1015330.1015424.

吴涛, 贺汉根, 贺明科. 基于插值的核函数构造[J]. 计算机学报, 2003, 26(8): 990-996.

WU Tao, HE Hangen, and HE Mingke. Interpolation based kernel functions construction[J]. Chinese Journal of Computers, 2003, 26(8): 990-996.

JAIN P, KULIS B, and DHILLON I S. Inductive regularized learning of kernel functions[C]. Proceedings of the Advances in Neural Information Processing Systems, Vancouver, Canada, 2010: 946-954.

ZHANG L, ZHOU W, and JIAO L. Wavelet support vector machine[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2004, 34(1): 34-39. doi: 10.1109/TSMCB.2003.811113.

NADARAYA E A. On estimating regression[J]. Theory of Probability Its Applications, 1964, 9(1): 141-142. doi: 10.1137/1109020.

WASSERMAN L著, 吴喜之译. 现代非参数统计[M]. 北京: 科学出版社, 2008: 163-179.

WATSON G S. Smooth regression analysis[J]. Sankhyā: The Indian Journal of Statistics, Series A, 1964, 26(4): 359-372.

CRISTIANINI N and SHAWE-TAYLOR J. An Introduction to Support Vector Machines and Other Kernel-based Learning Methods[M]. Cambridge: Cambridge University Press, 2000: 93-112.

VLADIMIR V N and VAPNIK V. Statistical Learning Theory[M]. New York: Wiley, 1998: 293-394.

CHANG C C and LIN C J. LIBSVM: A library for support vector machines[J]. ACM Transactions on Intelligent Systems and Technology, 2011, 2(3): 27. doi: 10.1145 /1961189.1961199.

REN Y and BAI G. Determination of optimal SVM parameters by using GA/PSO[J]. Journal of Computers, 2010, 5(8): 1160-1168. doi: 10.4304/jcp.5.8.1160-1168.

SARAFIS I, DIOU C, and TSIKRIKA T. Weighted SVM from click through data for image retrieval[C]. 2014 IEEE International Conference on Image Processing (ICIP 2014), Paris, 2014: 3013-3017. doi: 10.1109/ICIP.2014.7025609.

SONKA M, HLAVAC V, and BOYLE R. Image Processing, Analysis, and Machine Vision[M]. Kentucky: Cengage Learning, 2014: 257-749. doi: 10.1007/978-1-4899-3216-7.

SELLAM V and JAGADEESAN J. Classification of normal and pathological voice using SVM and RBFNN[J]. Journal of Signal and Information Processing, 2014, 5(1): 1-7. doi: 10. 4236/jsip.2014.51001.

高晋占. 微弱信号检测[M]. 北京: 清华大学出版社有限公司, 2004: 154-299.

GAO Jinzhan. Weak Signal Detection[M]. Beijing: Tsinghua University Press Ltd., 2004: 154-299.

MERCER J. Functions of positive and negative type, and their connection with the theory of integral equations[J]. Philosophical Transactions of the Royal Society of London Series A, Containing Papers of a Mathematical or Physical Character, 1909, 209(456): 415-446. doi: 10.1098/rsta.1909. 0016.

MARRON J and CHUNG S. Presentation of smoothers: The family approach[J]. Computational Statistics, 2001, 16(1): 195-207. doi: 10.1007/s001800100059.

Relative Articles

Supplements(0)

Cited By

Proportional views