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密度敏感鲁棒模糊核主成分分析算法

陶新民 常瑞 沈微 李晨曦 王若彤 刘艳超

陶新民, 常瑞, 沈微, 李晨曦, 王若彤, 刘艳超. 密度敏感鲁棒模糊核主成分分析算法. 自动化学报, 2020, 46(2): 358-372. doi: 10.16383/j.aas.2018.c170590
引用本文: 陶新民, 常瑞, 沈微, 李晨曦, 王若彤, 刘艳超. 密度敏感鲁棒模糊核主成分分析算法. 自动化学报, 2020, 46(2): 358-372. doi: 10.16383/j.aas.2018.c170590
TAO Xin-Min, CHANG Rui, SHEN Wei, LI Chen-Xi, WANG Ruo-Tong, LIU Yan-Chao. Density-sensitive Robust Fuzzy Kernel Principal Component Analysis Algorithm. ACTA AUTOMATICA SINICA, 2020, 46(2): 358-372. doi: 10.16383/j.aas.2018.c170590
Citation: TAO Xin-Min, CHANG Rui, SHEN Wei, LI Chen-Xi, WANG Ruo-Tong, LIU Yan-Chao. Density-sensitive Robust Fuzzy Kernel Principal Component Analysis Algorithm. ACTA AUTOMATICA SINICA, 2020, 46(2): 358-372. doi: 10.16383/j.aas.2018.c170590

密度敏感鲁棒模糊核主成分分析算法

doi: 10.16383/j.aas.2018.c170590
基金项目: 

中央高校基本科研业务费专项资金 2572017EB02

中央高校基本科研业务费专项资金 2572017CB07

东北林业大学双一流科研启动基金 411112438

哈尔滨市科技局创新人才基金 2017RAXXJ018

国家自然基金 31570547

详细信息
    作者简介:

    常瑞  东北林业大学工程技术学院硕士研究生.主要研究方向为模式识别与信号处理. E-mail: m15765549429@163.com

    沈微  东北林业大学工程技术学院讲师.主要研究方向为数据分析, 物流系统规划与管理咨询, 系统建模与优化. E-mail: Shenwei@nefu.edu.cn

    李晨曦  东北林业大学工程技术学院硕士研究生.主要研究方向为不均衡数据分类和故障诊断. E-mail: chenxili@nefu.edu.cn

    王若彤  东北林业大学工程技术学院硕士研究生.主要研究方向为人工智能和聚类分析. E-mail: celia wangrt@163.com

    刘艳超  东北林业大学工程技术学院硕士研究生.主要研究方向为物联网技术应用, 模式识别与信号处理. E-mail: liuyanchao@nefu.edu.cn

    通讯作者:

    陶新民  东北林业大学工程技术学院教授. 2005年获哈尔滨工业大学博士学位.主要研究方向为智能信号处理, 软计算方法, 模式识别.本文通信作者. E-mail: taoxinmin@nefu.edu.cn

Density-sensitive Robust Fuzzy Kernel Principal Component Analysis Algorithm

Funds: 

the Fundamental Research Funds for the Central Universities 2572017EB02

the Fundamental Research Funds for the Central Universities 2572017CB07

Two first-class scientific research foundation of Northeast Forestry University 411112438

Innovative talent fund of Harbin science and technology Bureau 2017RAXXJ018

National Natural Foundation of China 31570547

More Information
    Author Bio:

    CHANG Rui  Master student at the College of Engineering & Technology, Northeast Forestry University. Her research interest covers pattern recognition and signal processing

    SHEN Wei  Lecturer at the College of Engineering & Technology, Northeast Forestry University. His research interest covers data analysis, logistics system planning and management consulting, and system modeling and optimization

    LI Chen-Xi  Master student at the College of Engineering & Technology, Northeast Forestry University. Her research interest covers imbalanced data classification and fault diagnosis

    WANG Ruo-Tong  Master student at the College of Engineering & Technology, Northeast Forestry University. Her research interest covers artificial intelligence and cluster analysis

    LIU Yan-Chao  Master student at the College of Engineering & Technology, Northeast Forestry University. His research interest covers application of Internet of things technology, pattern recognition, and signal processing

    Corresponding author: TAO Xin-Min  Professor at the College of Engineering & Technology, Northeast Forestry University. He received his Ph. D. degree from Harbin Institute of Technology in 2005. His research interest covers intelligent signal processing, soft computing method, and pattern recognition. Corresponding author of this paper
  • 摘要: 针对传统核主成分分析算法(Kernel principal component analysis, KPCA)对野性样本点敏感等缺陷, 提出一种密度敏感鲁棒模糊核主成分分析算法(Density-Sensitive robust fuzzy kernel principal component analysis, DRF-KPCA).该算法首先通过引入相对密度确定样本初始隶属度, 并构建出基于重构误差的隶属度确定方法, 同时采用最优梯度下降法实现隶属度的更新, 有效解决了传统核主成分分析算法对野性样本点敏感导致的主成分偏移等问题.最后, 通过简化重构误差的计算公式, 大大降低了算法的计算复杂度和运行时间.实验部分, 利用有野性样本点和无野性样本点的数据集对本文算法、KPCA及其他改进算法的主成分分析性能进行测试, 结果表明DRF-KPCA能有效消除野性样本点对主元分布的影响.此外, 试验通过分析参数对算法性能的影响给出了合理的参数取值建议.最后将本文算法与其他算法应用到分类问题中进行对比, 实验表明本文算法的分类性能较其他算法有显著提高.
    Recommended by Associate Editor HU Qing-Hua
    1)  本文责任编委 胡清华
  • 图  1  传统PCA算法对有无野性样本点数据集的主成分分布图

    Fig.  1  The first principal component distribution using PCA algorithm on both the original data and the data with outliers

    图  2  不同KPCA算法的第一主元分布图

    Fig.  2  The first principal component of different KPCA algorithms

    图  3  不同KPCA算法的第二主元分布图

    Fig.  3  The second principal component of different KPCA algorithms

    图  4  三种算法的性能对比图

    Fig.  4  Comparison of the statistics results of E evaluation indicator of three algorithms

    图  5  模糊化系数(p)对算法性能的影响

    Fig.  5  Influence on the proposed algorithm performance of the fuzzy weight (p)

    图  6  不同正则化控制参数(σ2)对算法性能的影响

    Fig.  6  Influence on the proposed algorithm performance of the regularization parameters (σ2)

    图  7  不同密度控制权重(ω)对算法性能的影响

    Fig.  7  Influence on the proposed algorithm performance of the density control parameters (ω)

    图  8  不同平滑参数(s)对算法性能的影响

    Fig.  8  Influence on the proposed algorithm performance of the smooth parameters (s)

    图  9  不同算法对不同数据的性能比较

    Fig.  9  The performance comparison of different algorithms on different data

    图  10  不同算法对不同数据集的平均迭代时间比较

    Fig.  10  Comparison of average iteration time for different data sets by different algorithms

    图  11  不同算法对SMK-CAN-187高维数据的降维性能对比

    Fig.  11  Classification error rate of different algorithms with different reduced dimensions on SMK-CAN-187 dataset

    表  1  不同UCI数据的三种KPCA算法分类性能对比

    Table  1  Classification performance of three kinds of KPCA algorithm for different UCI datasets

    Dataset Class (N) : Dimension KPCA GMM-PCA RFK-PCA DRF-KPCA
    yeast 1 (463) : 2 (429) : 8 31.11±4.88 38.26±3.27 37.66±6.23 31.14±1.24
    1 (463) : 3 (244) : 8 23.94±3.22 30.24±4.21 26.79±5.15 24.01±0.98
    2 (429) : 3 (244) : 8 16.18±3.67 18.96±1.35 19.01±4.11 16.46±0.79
    letter H ((734) : R (758) : 16 10.67±2.15 9.17±3.66 7.16±2.35 5.48±0.07
    S (748) : Z (734) : 16 9.39±2.01 9.01±1.47 4.14 ± 1.97 2.13±0.09
    H (734) : O (753) : 16 10.74±2.46 12.01±3.53 9.45 ± 4.02 7.14±0.02
    german 1 (700: 2 (300) : 24 23.12±3.48 24.44±4.87 25.38±5.96 22.24±1.01
    haberman 1 (225) : 2 (81) : 3 17.46±3.16 17.32±2.55 16.73±4.98 15.12±0.49
    ionophere 1 (225) : -1 (126) : 34 8.33±2.13 8.03±2.98 7.57±3.19 5.37±0.07
    pima 1 (268) : 0 (500) : 8 25.71±4.01 29.63±4.76 31.88±6.23 25.33±1.11
    phoneme 1 (1 586) : 0 (3 818) : 5 11.12±2.16 10.06±2.93 9.67±3.98 7.21±0.12
    sonar 1 (111) : -1 (97) : 60 7.29±1.22 7.56±1.43 6.12 ± 2.79 5.32±0.02
    1 (1 528) : 2 (1 307) : 8 37.59±4.32 43.39±5.09 48.24±7.94 37.43±1.22
    abalone 1 (1 528) : 3 (1 342) : 8 23.69±3.12 23.33±2.78 24.18 ± 5.12 20.59±1.03
    2 (1307) : 3 (1 342) : 8 12.83±1.22 10.74±1.07 11.24 ± 3.01 9.11±0.22
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  • 收稿日期:  2017-10-19
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