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| Multi-scale Gaussian Kernel Extreme Learning MachineBased on Maximum Correntropy Criterion |
| LIU Zhao-lun1,2,WU You2,WANG Wei-tao3,ZHANG Chun-lan2,LIU Bin1,2 |
1. The Key Laboratory for Special Fiber and Fiber Sensor of Hebei Province, Yanshan University, Qinhuangdao, Hebei 066004, China
2. School of Information Science and Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China
3. School of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China |
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Abstract In view of the fact that the traditional multi-scale kernel extreme learning machine is sensitive to noise and has a large amount of computation, a multi-scale kernel extreme learning machine which is suitable for Gaussian noise environment is proposed. Firstly, the maximum correntropy criterion is used to replace the traditional minimum mean square error criterion in the multi-scale kernel extreme learning machine to construct the objective function. Secondly, a multi-scale method for randomly generating the scale factors according to the training samples number is applied to the Gaussian kernel function. Finally, the Lagrange multiplier method is used to solve the objective function, and the multi-scale Gaussian kernel extreme learning machine based on the maximum correntropy criterion is derived. Experiments show that the proposed algorithm has higher learning efficiency. Comparing with the traditional multi-scale kernel extreme learning machine, the prediction accuracy on the three UCI benchmark data sets and the application experiment for predicting the f-CaO content of cement clinker,increased by an average of 30.30% and 23.8% respectively.
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Received: 16 May 2019
Published: 24 May 2021
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［1］Huang G B, Zhu Q Y, Siwe C. Extreme learning machine: Theory and applications ［J］. Neurocomputing, 2006, 70(1): 489-501.
［2］Huang G B, Zhou H M, Ding X J, et al. Extreme learning machine for regression and multiclass classification ［J］. IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, 2012, 42(2): 513- 529.
［3］曾启明, 纪震, 李琰, 等, 基于ELM和MA的微型四频天线设计 ［J］. 电子学报, 2014, 42(9): 1693-1698.
Zeng Q M, Ji Z, Li Y, et al. A Miniature Four-Band Antenna Design Using ELM and MA ［J］. Acta Electronica Sinica, 2014, 42(9): 1693-1698.
［4］汪洪桥, 孙富春, 蔡艳宁, 等. 多核学习方法 ［J］. 自动化学报,2010, 36(8): 1037-1050.
Wang H Q, Sun F C, Cai Y N, et al. On Multiple Kernel Learning Methods ［J］. Acta Automatica Sinica, 2010, 36(8): 1037-1050.
［5］Liu X W, Wang L, Huang G B, et al. Multiple kernel extreme learning machine ［J］. Neurocomputing, 2015, 149(Part A): 253-264.
［6］Liu Q, Zhao X G, Hou Z G, et al. Multi-scale wavelet kernel extreme learning machine for EEG feature classification ［C］// IEEE. IEEE International Conference on Cyber Technology in Automation, Control, and Intelligent Systems. 2015: 1546-1551.
［7］Chang P, Li S R, Ge Y L, et al. Computation of reservoir relative permeability curve based on multi-scale wavelet kernel extreme learning machine ［C］// IEEE. Control Conference. 2016: 7179-7184.
［8］王新迎, 韩敏. 多元混沌时间序列的多核极端学习机建模预测 ［J］. 物理学报, 2015, 64(7): 129-135.
Wang Y X, Han M. Multivariate chaotic time series prediction using multiple kernel extreme learning machine［J］. Acta Physica Sinica, 2015, 64(7): 129-135.
［9］Chen Y Q, Fink O, Sansavini G. Combined Fault Location and Classification for Power Transmission Lines Fault Diagnosis with Integrated Feature Extraction ［J］. IEEE Transac-tions on Industrial Electronics, 2018, 65(1): 561- 569.
［10］牛培峰, 史春见, 刘楠, 等. 基于GSA-PELM的锅炉NOx预测模型 ［J］. 计量学报, 2018, 39(5): 741-746.
Niu P F, Shi C J, Liu N, et al. Optimization for NOx Prediction Model from Boilers Based on GSA-PELM［J］. Acta Metrologica Sinica, 2018, 39(5): 741-746.
［11］Santamaria I, Pokharel P P, Principe J C. Generalized correlation function: Definition, properties, and application to blind equalization ［J］. IEEE Transactions on Signal Processing, 2006, 54(6): 2187-2197.
［12］Xing H J, Wang X M. Training extreme learning machine via regularized correntropy criterion［J］.Neural Comput & Applic, 2013, 23(7-8): 1977–1986.
［13］唐哲, 雷迎科. 基于最大相关熵的通信辐射源个体识别方法 ［J］. 通信学报, 2016, 37(12): 171-175.
Tang Z, Lei Y K. Method of individual communication transmitter identification based on maximum correntropy ［J］. Journal on Communications, 2016, 37(12): 171-175.
［14］Chen B D, Wang X, Lu N, et al. Mixture Correntropy for Robust Learning ［J］. Pattern Recognition, 2018, 79: 318-327.
［15］张金凤, 邱天爽, 李森. 冲激噪声环境下基于最大相关熵准则的韧性子空间跟踪新算法 ［J］. 电子学报, 2015, 43(3): 483-488.
Zhang J F, Qiu T S, Li S, et al A Robust PAST Algorithm Based on Maximum Correntropy Criterion for Impulsive Noise Environments ［J］. Acta
Electronica Sinica, 2015, 43(3): 483-488.
［16］王世元, 史春芬, 钱国兵,等. 基于分数阶最大相关熵算法的混沌时间序列预测 ［J］. 物理学报, 2018, 67(1): 283-290.
Wang S Y, Shi C F, Qian G B, et al. Prediction of chaotic time series based on the fractional-order maximum correntropy criterion algorithm ［J］. Acta Physica Sinica, 2018, 67(1): 283-290.
［17］Wang Y D, Zheng W, Zhang D P, et al. Pulsar profile denoising using kernel regression based on maximum correntropy criterion ［J］. Optik-International Journal for Light and Electron Optics, 2017, 130:757-764.
［18］Su Z M, Yang L, Zhu S M, et al. Gaussian mixture image restoration based on maximum correntropy criterion ［J］. Electronics Letters, 2017, 53(11): 715-716.
［19］Asuncion A, Newman D. UCI Machine learning repository ［EB/OL］. (2018-09-24). http://archiveics.uci edu/ml/datasets.html.
［20］Chuang C C, Su S F, Jeng J T, et al. Robust support vector regression networks for function approximation with outliers ［J］. IEEE Transactions on Neural Networks, 2002, 13(6): 1322-1330.
［21］Abrarov S M, Quine B M. Sampling by incomplete cosine expansion of the sinc function: Application to the Voigt/complex error function ［J］. Applied Mathematics & Computation, 2015, 258(C): 425-435.
［22］Xu Y, Ye L L, Qun X Z. Improved dynamic recurrent-based ELM neural network for fault prediction ［J］. Control and Decision, 2015,30(4): 623-629.
［23］Abrarov S M, Quine B M. Sampling by incomplete cosine expansion of the sinc function: Application to the Voigt/complex error function［J］. Applied Mathematics and Computation, 2015, 258: 425-435.
［24］李凡军, 韩红桂, 乔俊飞. 基于灵敏度分析法的ELM剪枝算法 ［J］. 控制与决策, 2014,(6): 1003-1008.
Li F J, Han H G, Qiao J F. Pruning algorithm for extreme learning machine based on sensitivity analysis ［J］. Control and Decision, 2014,(6):1003-1008.
［25］赵朋程, 刘彬, 孙超, 等. 基于IQPSO优化ELM的熟料质量指标软测量研究 ［J］. 仪器仪表学报, 2016, 37(10): 2243-2250.
Zhao P C, Liu B, Sun C, et al. Soft sensor for cement clinker quality indicator based on IQPSO optimize ELM ［J］ Chinese Journal of Scientific Instrument, 2016, 37(10): 2243-2250.
［26］赵彦涛,何永强,贾利颖,等. 基于时间序列单维卷积神经网络的水泥熟料游离钙软测量方法［J］. 计量学报, 2020, 41(9): 1152-1162.
Zhao Y T, He Y Q, Jia L Y, et al. Soft Measurement Method for Cement Clinker f-CaO Based on Time Series Single-dimensional Convolutional Neural Network［J］. Acta Metrologica Sinica, 2020, 41(9): 1152-1162.
［27］刘彬, 赵朋程, 高伟, 等. 基于粒子群算法与连续型深度信念网络的水泥熟料游离氧化钙预测 ［J］. 计量学报, 2018, 39(3): 420-424.
Liu B, Zhao P C, Gao W, et al.Prediction of Cement f-CaO Based on Particle Swarm Optimization and Continuous Deep Belief Network［J］. Acta Metrologica Sinica, 2018, 39(3): 420-424. |
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2021, Vol. 42 
