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基于压缩感知的多尺度最小二乘支持向量机

王琴 沈远彤

王琴, 沈远彤. 基于压缩感知的多尺度最小二乘支持向量机. 自动化学报, 2016, 42(4): 631-640. doi: 10.16383/j.aas.2016.c150296
引用本文: 王琴, 沈远彤. 基于压缩感知的多尺度最小二乘支持向量机. 自动化学报, 2016, 42(4): 631-640. doi: 10.16383/j.aas.2016.c150296
WANG Qin, SHEN Yuan-Tong. Multi-scale Least Squares Support Vector Machine Using Compressive Sensing. ACTA AUTOMATICA SINICA, 2016, 42(4): 631-640. doi: 10.16383/j.aas.2016.c150296
Citation: WANG Qin, SHEN Yuan-Tong. Multi-scale Least Squares Support Vector Machine Using Compressive Sensing. ACTA AUTOMATICA SINICA, 2016, 42(4): 631-640. doi: 10.16383/j.aas.2016.c150296

基于压缩感知的多尺度最小二乘支持向量机

doi: 10.16383/j.aas.2016.c150296
基金项目: 

国家自然科学基金 11301120

详细信息
    作者简介:

    沈远彤, 中国地质大学(武汉)数学与物理学院教授.主要研究方向为信号处理, 数据挖掘, 小波分析.E-mail:whsyt@163.com

    通讯作者:

    王琴, 海南医学院信息技术部讲师.主要研究方向为小波分析, 人工智能, 机器学习.本文通信作者.E-mail:wq-1018@163.com

Multi-scale Least Squares Support Vector Machine Using Compressive Sensing

Funds: 

National Natural Science Foundation of China 11301120

More Information
    Author Bio:

    Professor at the School of Mathematics and Physics, China University of Geosciences. His research interest covers signal processing, data mining, and wavelet analysis

    Corresponding author: WANG Qin Lecturer in the Department of Information Technology, Hainan Medical University. Her research interest covers wavelet analysis, artificial intelligence, and machine learning. Corresponding author of this paper
  • 摘要: 提出一种基于压缩感知(Compressive sensing, CS)和多分辨分析(Multi-resolution analysis, MRA)的多尺度最小二乘支持向量机(Least squares support vector machine, LS-SVM). 首先将多尺度小波函数作为支持向量核, 推导出多尺度最小二乘支持向量机模型, 然后基于压缩感知理论, 利用最小二乘匹配追踪(Least squares orthogonal matching pursuit, LS-OMP)算法对多尺度最小二乘支持向量机的支持向量进行稀疏化, 最后用稀疏的支持向量实现函数回归. 实验结果表明, 本文方法利用不同尺度小波核逼近信号的不同细节, 而且以比较少的支持向量能达到很好的泛化性能, 大大降低了运算成本, 相比普通最小二乘支持向量机, 具有更优越的表现力.
  • 图  1  多尺度LS-SVM模型

    Fig.  1  Multi-scale LS-SVM model

    图  2  两尺度径向基小波核LS-SVM的实验结果

    Fig.  2  Experimental results of two-scale RBF wavelet kernel LS-SVM

    图  3  标准LS-SVM、稀疏LS-SVM、两尺度LS-SVM、稀 疏两尺度LS-SVM 四算法在不同稀疏度下NMSE 比较

    Fig.  3  NMSE comparison of standard LS-SVM, sparse LS-SVM, two-scale LS-SVM, sparse two-scale LS-SVM algorithms under di®erent sparse degrees

    图  4  标准LS-SVM和两尺度LS-SVM的回归结果比较

    Fig.  4  Regression results comparison of standard LS-SVM and two-scale LS-SVM

    图  5  测试样本曲线图

    Fig.  5  Test sample curve

    图  6  90% 稀疏度两尺度LS-SVM 逼近效果

    Fig.  6  Approximation result of 90% sparse degree two-scale LS-SVM

    图  7  90% 稀疏度标准LS-SVM 逼近效果

    Fig.  7  Approximation result of 90% sparse degree standard LS-SV

    图  8  标准LS-SVM 和两尺度LS-SVM 在50% 稀疏度下拟合结果比较

    Fig.  8  Approximation results comparison of standard LS-SVM and two-scale LS-SVM under 50% sparse degree

    图  9  标准LS-SVM 和两尺度LS-SVM 在不同稀疏度下 NMSE 比较

    Fig.  9  NMSE comparison of standard LS-SVM and two-scale LS-SVM under di®erent sparse degrees

    图  10  机械臂数据

    Fig.  10  Robot arm data

    图  11  标准LS-SVM、稀疏LS-SVM、两尺度LS-SVM、稀 疏两尺度LS-SVM 四算法在不同稀疏度下NMSE 比较

    Fig.  11  NMSE comparison of standard LS-SVM, sparse LS-SVM, two-scale LS-SVM, sparse two-scale LS-SVM algorithms under di®erent sparse degrees

    图  12  标准LS-SVM 和两尺度LS-SVM 在50% 稀疏度下的拟合结果比较

    Fig.  12  Approximation results comparison of standard LS-SVM and two-scale LS-SVM under 50% sparse degree

    表  1  不同小波核函数的两尺度LS-SVM NMSE 比较

    Table  1  NMSE comparison of two-scale LS-SVM with di®erent wavelet kernel functions

    核函数 参数选择 准确率(NMSE)
    RBF 小波核 $\gamma_1=50, \gamma_2=100, \sigma_1^2=0.5, \sigma_2^2=3.5$ -47.1780
    Morlet 小波核 $\gamma_1=80, \gamma_2=150, \sigma_1^2=0.8, \sigma_2^2=4$ -46.4707
    Mexican hat 小波核 $\gamma_1=100, \gamma_2=200, \sigma_1^2=0.35, \sigma_2^2=6.25$ -46.6829
    下载: 导出CSV

    表  2  不同核函数的两尺度LS-SVM NMSE 比较

    Table  2  NMSE comparison of two-scale LS-SVM with di®erent kernel functions

    核函数 参数选择 准确率(NMSE)
    RBF 小波核 $\gamma_1=50, \gamma_2=100, \sigma_1^2=0.5, \sigma_2^2=3.5$ -47.1780
    RBF 核 $\gamma_1=100, \gamma_2=200, \sigma_1^2=0.3, \sigma_2^2=3$ -44.7617
    Sinc 小波核 $\gamma_1=60, \gamma_2=220, \sigma_1^2=0.5, \sigma_2^2=5$ -44.1170
    下载: 导出CSV

    表  3  不同多核学习方法NMSE 比较

    Table  3  NMSE comparison of di®erent multi-kernel learning methods

    算法 核函数 准确率(NMSE)
    本文方法 小波多尺度核 -47.1780
    MSLP-SVR[14] 组合RBF核 -44.0920
    多核LS-SVM[15] 组合RBF核 -45.0612
    SKLSSVR[16] 线性核与RBF核-44.3539
    下载: 导出CSV

    表  4  稀疏两尺度LS-SVM 和稀疏标准LS-SVM 在不同稀疏度下NMSE 比较

    Table  4  NMSE comparison of sparse two-scale LS-SVM and sparse standard LS-SVM algorithms under di®erent sparse degrees

    稀疏度(%)
    908070605040302010
    NMSE两尺度-52.8800-59.7540-69.7735-72.7535-72.9664-72.9800-72.9805-72.9805-72.9805
    标准-49.9373-54.9217-58.7773-63.1308-64.8218-65.3600-65.4205-65.4312-65.4312
    下载: 导出CSV
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出版历程
  • 收稿日期:  2015-05-15
  • 录用日期:  2015-12-28
  • 刊出日期:  2016-04-01

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