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山东大学学报 (工学版) ›› 2020, Vol. 50 ›› Issue (3): 58-65.doi: 10.6040/j.issn.1672-3961.0.2019.295

• 机器学习与数据挖掘 • 上一篇    下一篇

基于核极限学习机自编码器的标记分布学习

王一宾1,2(),李田力1,程玉胜1,2,*(),钱坤1   

  1. 1. 安庆师范大学计算机与信息学院，安徽 安庆 246133
    2. 安徽省高校智能感知与计算重点实验室，安徽 安庆 246133
  • 收稿日期:2019-06-10 出版日期:2020-06-01 发布日期:2020-06-16
  • 通讯作者: 程玉胜 E-mail:wangyb07@mail.ustc.edu.cn;chengyshaq@163.com
  • 作者简介:王一宾(1970—)，男，安徽安庆人，教授，硕士，主要研究方向为软件安全与多标记学习. E-mail: wangyb07@mail.ustc.edu.cn
  • 基金资助:
    安徽省高校重点自然科学基金资助项目(KJ2017A352);安徽省高校重点实验室基金资助项目(ACAIM160102)

Label distribution learning based on kernel extreme learning machine auto-encoder

Yibin WANG1,2(),Tianli LI1,Yusheng CHENG1,2,*(),Kun QIAN1   

  1. 1. School of Computer and Information, Anqing Normal University, Anqing 246133, Anhui, China
    2. The University Key Laboratory of Intelligent Perception and Computing of Anhui Province, Anqing 246133, Anhui, China
  • Received:2019-06-10 Online:2020-06-01 Published:2020-06-16
  • Contact: Yusheng CHENG E-mail:wangyb07@mail.ustc.edu.cn;chengyshaq@163.com
  • Supported by:
    安徽省高校重点自然科学基金资助项目(KJ2017A352);安徽省高校重点实验室基金资助项目(ACAIM160102)

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摘要：

标记分布学习中示例由多个不同重要程度的标记共同标注，而在已有的标记分布学习算法中，大部分均在完备数据集下进行，未考虑数据噪声干扰。针对这一问题，结合自编码器的降噪特性和核极限学习机的稳定性，提出一种基于核极限学习机自编码器的标记分布学习算法。使用核极限学习机自编码器对原始特征空间映射，得到更具鲁棒性的特征表达，构造适应标记分布学习的极限学习机模型作为分类器以提升分类效率及性能。试验结果表明，本文算法较其他对比算法具有一定优势，使用假设检验方法进一步说明所提算法的有效性。

关键词: 标记分布学习, 高斯噪声, 自编码器, 核极限学习机, 鲁棒性

Abstract:

In the label distribution learning framework, the example could be associated with the degree of description of the label. However, most of the algorithms were designed with complete data, and didn′t consider the noise in the data. Therefore, combined the noise reduction characteristics of the auto-encoder and the stability of the kernel extreme learning machine, the Label Distribution Learning Algorithm based on Kernel Extreme Learning Machine with auto-encoder was proposed in this paper. Firstly, we used the auto-encoder in kernel extreme learning machine to map the original feature space to obtain more robust feature representation. Secondly, we constructed the extreme learning machine model that adapted to the label distribution learning as a classifier to improve the classification efficiency and performance. Finally, the experimental results showed the proposed algorithm had certain advantages over other label distribution learning algorithms, and the hypothesis test method further illustrated the effectiveness of the algorithm.

Key words: label distribution learning, Gaussian noise, auto-encoder, kernel extreme learning machine, robustness

中图分类号: 

  • TP181

图1

风景图中的标记分布学习"

图2

AKELM-LDL算法建模过程"

表1

标记分布学习数据集"

数据集 样本数 特征数 标记数
Yeast-alpha 2 465 24 18
Yeast-cdc 2 465 24 15
Yeast-diau 2 465 24 7
Yeast-heat 2 465 24 6
Yeast-spo 2 465 24 6
Yeast-cold 2 465 24 4
Yeast-dtt 2 465 24 4
Yeast-spo5 2 465 24 3
Yeast-elu 2 465 24 14
Human Gene 30 542 36 68
SDU_3DFE 2 500 243 6
Movie 7 755 1 869 5

表2

标记分布评价指标"

评价指标 Chebyshev↓ Clark↓ Canberra↓ Kullback-Leibler↓ Cosine↑ Intersection↑
计算公式 ${\rm{Di}}{{\rm{s}}_1}\left( {D, \hat D} \right) = {\max _j}\left| {{d_j} - {{\hat d}_j}} \right| $ ${\rm{Di}}{{\rm{s}}_2}\left( {D, \hat D} \right) = \sqrt {\sum\limits_{j = 1}^c {\frac{{{{\left( {{d_j} - {{\hat d}_j}} \right)}^2}}}{{{{\left( {{d_j} + {{\hat d}_j}} \right)}^2}}}} } $ ${\rm{Di}}{{\rm{s}}_3}\left( {D, \hat D} \right) = \sum\limits_{j = 1}^c {\frac{{\left| {{d_j} - {{\hat d}_j}} \right|}}{{{d_j} + {{\hat d}_j}}}} $ ${\rm{Di}}{{\rm{s}}_4}\left( {D, \hat D} \right) = \sum\limits_{j = 1}^c {{d_j}\ln \frac{{{d_j}}}{{{{\hat d}_j}}}} $ ${\rm{Si}}{{\rm{m}}_1}\left( {D, \hat D} \right) = \frac{{\sum\limits_{j = 1}^c {{d_j}{{\hat d}_j}} }}{{\sqrt {\sum\limits_{j = 1}^c {{d_j}^2} } \sqrt {\sum\limits_{j = 1}^c {{{\hat d}^2}_j} } }} $ ${\rm{Si}}{{\rm{m}}_2}\left( {D, \hat D} \right) = \sum\limits_{j = 1}^c {\min \left( {{d_j}, {{\hat d}_j}} \right)} $

表3

Chebyshev(↓)评价指标结果"

Datasets PT-Bayes AA-KNN AA-BP SA-IIS SA-BFGS AKELM-LDL
Yeast-alpha 0.099 6±0.005 1 0.014 6±0.000 4 0.036 7±0.001 3 0.017 0±0.000 5 0.013 5±0.000 3 0.013 4±0.000 1
Yeast-cdc 0.108 7±0.010 1 0.017 5±0.000 4 0.038 8±0.002 1 0.020 0±0.000 5 0.016 3±0.000 4 0.016 1±0.000 1
Yeast-elu 0.112 1±0.006 1 0.017 6±0.000 4 0.038 9±0.001 8 0.020 3±0.000 4 0.016 3±0.000 4 0.016 2±0.000 1
Yeast-diau 0.157 7±0.006 9 0.039 1±0.001 3 0.050 1±0.002 0 0.041 2±0.000 9 0.036 7±0.001 2 0.036 6±0.001 0
Yeast-heat 0.174 1±0.010 5 0.044 7±0.001 7 0.053 0±0.002 7 0.046 6±0.001 1 0.042 4±0.001 4 0.041 4±0.001 1
Yeast-spo 0.175 4±0.009 0 0.062 9±0.002 7 0.067 1±0.003 5 0.061 3±0.001 5 0.058 2±0.002 7 0.057 4±0.001 5
Yeast-cold 0.183 1±0.013 3 0.055 0±0.001 7 0.059 1±0.002 6 0.056 6±0.001 6 0.051 1±0.002 1 0.051 0±0.001 3
Yeast-dtt 0.181 8±0.013 4 0.039 7±0.001 7 0.043 3±0.001 5 0.043 6±0.001 3 0.035 9±0.001 4 0.035 8±0.001 4
Yeast-spo5 0.201 3±0.013 3 0.097 0±0.005 4 0.094 2±0.003 5 0.095 0±0.002 3 0.091 4±0.002 2 0.089 7±0.004 6
Movie 0.201 4±0.002 8 0.124 0±0.002 6 0.139 1±0.003 4 0.147 3±0.002 0 0.126 4±0.003 3 0.114 4±0.001 5
SDU_3DFE 0.138 6±0.003 7 0.127 6±0.003 5 0.142 9±0.006 4 0.134 4±0.005 0 0.104 5±0.002 5 0.133 9±0.003 2
Human Gene 0.195 1±0.034 0 0.065 2±0.001 5 0.063 3±0.001 8 0.054 0±0.002 8 0.053 8±0.002 6 0.053 7±0.002 0
Average 5.911 6 3.250 0 4.666 6 4.000 0 2.000 0 1.166 6

表4

Clark(↓)评价指标结果"

Datasets PT-Bayes AA-KNN AA-BP SA-IIS SA-BFGS AKELM-LDL
Yeast-alpha 1.172 9±0.039 5 0.230 5±0.004 1 0.734 9±0.031 1 0.261 4±0.007 1 0.210 1±0.003 9 0.209 5±0.006 8
Yeast-cdc 1.080 1±0.061 9 0.235 4±0.004 9 0.595 7±0.036 2 0.257 8±0.006 3 0.216 2±0.005 2 0.213 7±0.004 5
Yeast-elu 1.034 3±0.049 6 0.217 1±0.005 7 0.544 9±0.027 9 0.240 4±0.003 5 0.199 2±0.003 5 0.198 5±0.004 2
Yeast-diau 0.753 1±0.033 3 0.211 0±0.006 2 0.275 3±0.010 4 0.221 5±0.005 2 0.199 1±0.006 4 0.198 3±0.005 4
Yeast-heat 0.683 8±0.038 6 0.193 9±0.007 0 0.232 1±0.013 2 0.201 0±0.004 7 0.184 3±0.005 8 0.179 3±0.004 3
Yeast-spo 0.684 3±0.030 2 0.266 8±0.010 3 0.290 7±0.016 4 0.262 4±0.007 4 0.249 5±0.012 5 0.246 2±0.004 6
Yeast-cold 0.495 4±0.035 1 0.149 7±0.004 7 0.160 9±0.006 9 0.153 2±0.004 9 0.139 7±0.006 2 0.139 1±0.003 1
Yeast-dtt 0.498 6±0.035 8 0.107 5±0.005 1 0.118 3±0.004 2 0.117 2±0.003 9 0.097 8±0.003 9 0.097 7±0.003 6
Yeast-spo5 0.418 0±0.027 8 0.195 8±0.011 3 0.189 5±0.007 3 0.191 4±0.005 1 0.184 4±0.003 6 0.181 2±0.010 4
Movie 0.806 5±0.008 6 0.548 8±0.010 2 0.640 5±0.016 5 0.582 4±0.007 6 0.551 9±0.012 9 0.527 2±0.034 8
SDU_3DFE 0.412 5±0.007 0 0.403 1±0.008 7 0.465 4±0.019 9 0.413 8±0.007 2 0.349 7±0.005 9 0.405 2±0.009 2
Human Gene 4.639 3±0.171 6 2.388 0±0.022 9 3.686 5±0.062 9 2.134 9±0.031 6 2.118 9±0.033 0 2.131 4±0.002 0
Average 5.833 3 3.250 0 4.911 6 3.833 3 1.911 6 1.250 0

表5

Canberra(↓)评价指标结果"

Datasets PT-Bayes AA-KNN AA-BP SA-IIS SA-BFGS AKELM-LDL
Yeast-alpha 4.193 7±0.149 2 0.753 2±0.014 0 2.420 8±0.095 6 0.861 8±0.023 2 0.682 3±0.014 7 0.680 4±0.024 1
Yeast-cdc 3.541 2±0.225 8 0.712 1±0.014 7 1.798 6±0.108 4 0.783 1±0.015 7 0.647 9±0.017 3 0.640 1±0.017 0
Yeast-elu 3.277 8±0.171 2 0.641 9±0.017 9 1.598 3±0.083 0 0.712 5±0.009 3 0.584 0±0.007 3 0.581 3±0.004 2
Yeast-diau 1.708 6±0.084 0 0.453 9±0.015 1 0.594 4±0.020 7 0.478 7±0.010 1 0.427 0±0.013 5 0.425 7±0.010 8
Yeast-heat 1.444 0±0.082 7 0.390 3±0.013 5 0.467 1±0.023 6 0.404 2±0.009 8 0.367 8±0.010 2 0.357 4±0.008 7
Yeast-spo 1.443 1±0.068 9 0.549 0±0.022 0 0.595 1±0.033 7 0.539 4±0.015 9 0.513 8±0.024 1 0.506 3±0.008 7
Yeast-cold 0.866 9±0.062 0 0.259 3±0.007 2 0.277 3±0.012 3 0.264 9±0.008 5 0.240 6±0.009 3 0.239 7±0.005 4
Yeast-dtt 0.871 9±0.064 9 0.184 7±0.008 1 0.204 1±0.007 6 0.202 7±0.007 2 0.167 9±0.006 6 0.167 8±0.005 3
Yeast-spo5 0.648 8±0.045 0 0.300 3±0.017 0 0.291 1±0.011 2 0.293 9±0.007 7 0.283 0±0.006 4 0.277 9±0.015 2
Movie 1.563 5±0.018 8 1.055 3±0.021 0 1.223 8±0.030 5 1.119 9±0.016 4 1.063 5±0.026 0 0.999 5±0.036 1
SDU_3DFE 0.902 5±0.016 0 0.831 5±0.019 3 0.982 3±0.038 5 0.896 9±0.018 0 0.728 3±0.013 8 0.889 8±0.003 9
HumanGene 33.915 0±1.480 0 16.277 4±0.174 0 25.297 2±0.487 0 14.633 4±0.249 0 14.511 6±0.252 0 14.592 7±0.290 9
Average 5.916 6 3.333 3 4.833 3 3.750 0 1.911 6 1.250 0

表6

Kullback-Leibler(↓)评价指标结果"

Datasets PT-Bayes AA-KNN AA-BP SA-IIS SA-BFGS AKELM-LDL
Yeast-alpha 0.277 6±0.023 8 0.006 5±0.000 2 0.087 2±0.947 5 0.008 5±0.000 4 0.005 6±0.000 3 0.005 5±0.000 1
Yeast-cdc 0.283 1±0.042 1 0.008 2±0.000 3 0.067 2±0.009 8 0.009 9±0.000 5 0.007 0±0.000 3 0.006 9±0.000 1
Yeast-elu 0.282 5±0.032 8 0.007 3±0.000 4 0.060 8±0.009 2 0.009 1±0.000 3 0.006 2±0.000 2 0.006 1±0.000 1
Yeast-diau 0.269 8±0.027 6 0.014 9±0.000 9 0.026 4±0.002 4 0.015 7±0.000 6 0.012 9±0.000 9 0.012 8±0.000 1
Yeast-heat 0.268 4±0.034 5 0.014 4±0.001 0 0.021 6±0.002 9 0.015 2±0.000 7 0.012 8±0.000 7 0.012 2±0.000 1
Yeast-spo 0.278 8±0.039 8 0.029 1±0.002 3 0.033 2±0.003 9 0.026 8±0.001 5 0.024 6±0.002 3 0.024 0±0.000 1
Yeast-cold 0.217 4±0.035 6 0.013 9±0.001 1 0.016 2±0.001 6 0.014 6±0.001 0 0.012 2±0.001 2 0.012 1±0.000 1
Yeast-dtt 0.226 4±0.039 3 0.007 4±0.000 8 0.008 9±0.000 6 0.008 0±0.000 6 0.006 2±0.000 6 0.006 1±0.000 1
Yeast-spo5 0.206 6±0.042 7 0.034 7±0.003 9 0.031 2±0.002 3 0.031 4±0.001 5 0.029 3±0.001 2 0.028 6±0.002 9
Movie 0.729 7±0.059 0 0.117 7±0.005 1 0.166 4±0.010 7 0.131 7±0.004 6 0.118 9±0.006 0 0.100 3±0.002 7
SDU_3DFE 0.084 9±0.002 9 0.081 8±0.003 9 0.102 3±0.009 6 0.081 9±0.004 0 0.054 1±0.002 2 0.072 6±0.003 3
Human Gene 1.803 5±0.148 7 0.301 9±0.007 2 0.598 4±0.022 1 0.240 6±0.012 1 0.238 6±0.011 2 0.238 7±0.009 8
Average 6.000 0 3.333 3 4.833 3 3.750 0 1.911 6 1.166 6

表7

Cosine(↑)评价指标结果"

Datasets PT-Bayes AA-KNN AA-BP SA-IIS SA-BFGS AKELM-LDL
Yeast-alpha 0.848 5±0.007 0 0.993 6±0.000 2 0.947 5±0.003 2 0.991 4±0.000 4 0.994 6±0.000 3 0.994 7±0.000 1
Yeast-cdc 0.850 8±0.013 0 0.992 1±0.000 3 0.956 4±0.004 5 0.990 2±0.000 4 0.993 3±0.000 3 0.993 4±0.000 1
Yeast-elu 0.853 1±0.009 2 0.992 9±0.000 4 0.959 7±0.003 9 0.991 0±0.000 3 0.994 0±0.002 0 0.994 1±0.000 1
Yeast-diau 0.863 8±0.007 0 0.986 3±0.000 9 0.977 3±0.001 7 0.985 3±0.000 5 0.988 1±0.007 0 0.988 2±0.000 1
Yeast-heat 0.866 8±0.010 3 0.986 3±0.000 9 0.980 3±0.002 0 0.985 4±0.000 6 0.987 8±0.000 6 0.988 4±0.000 1
Yeast-spo 0.861 1±0.009 3 0.972 7±0.002 2 0.969 5±0.003 2 0.974 7±0.001 3 0.977 0±0.002 0 0.977 5±0.000 1
Yeast-cold 0.893 6±0.009 5 0.986 8±0.000 8 0.984 8±0.001 4 0.986 1±0.000 8 0.988 6±0.001 0 0.988 7±0.000 1
Yeast-dtt 0.895 0±0.009 8 0.992 9±0.000 6 0.991 6±0.000 5 0.991 5±0.000 5 0.994 1±0.000 4 0.994 2±0.000 1
Yeast-spo5 0.898 0±0.010 6 0.969 4±0.003 3 0.972 3±0.001 8 0.972 1±0.001 2 0.974 1±0.000 9 0.974 8±0.002 3
Movie 0.849 5±0.002 2 0.922 4±0.003 2 0.902 8±0.004 5 0.908 1±0.003 0 0.923 5±0.003 7 0.934 2±0.001 5
SDU_3DFE 0.917 9±0.002 8 0.920 2±0.003 5 0.903 7±0.006 9 0.920 3±0.003 6 0.947 0±0.002 2 0.929 6±0.002 9
Human Gene 0.457 0±0.047 7 0.767 4±0.004 0 0.687 6±0.009 8 0.831 6±0.005 5 0.833 3±0.005 3 0.832 1±0.004 3
Average 5.911 6 3.500 0 4.833 3 3.750 0 1.833 3 1.166 6

表8

Intersetion(↑)评价指标结果"

Datasets PT-Bayes AA-KNN AA-BP SA-IIS SA-BFGS AKELM-LDL
Yeast-alpha 0.772 5±0.007 8 0.958 4±0.000 8 0.874 0±0.004 3 0.951 8±0.001 3 0.962 3±0.000 9 0.962 4±0.001 4
Yeast-cdc 0.771 1±0.014 6 0.953 1±0.001 0 0.886 7±0.006 3 0.947 8±0.000 9 0.957 4±0.001 2 0.957 9±0.001 3
Yeast-elu 0.772 7±0.010 9 0.954 7±0.001 3 0.891 7±0.005 2 0.949 1±0.000 7 0.958 8±0.000 5 0.959 0±0.001 1
Yeast-diau 0.769 0±0.010 8 0.937 0±0.002 2 0.917 7±0.002 8 0.933 1±0.001 3 0.940 8±0.001 9 0.941 0±0.001 5
Yeast-heat 0.770 8±0.012 2 0.935 9±0.002 2 0.923 5±0.003 5 0.933 2±0.001 6 0.939 7±0.001 6 0.941 4±0.001 4
Yeast-spo 0.769 1±0.010 8 0.909 5±0.003 7 0.902 2±0.005 3 0.910 9±0.002 6 0.915 4±0.003 7 0.916 6±0.001 4
Yeast-cold 0.796 5±0.013 9 0.936 0±0.001 6 0.931 7±0.003 1 0.934 4±0.002 0 0.940 7±0.002 1 0.940 9±0.001 4
Yeast-dtt 0.796 4±0.014 7 0.954 4±0.001 8 0.949 6±0.001 9 0.949 6±0.001 8 0.958 6±0.001 6 0.958 6±0.001 2
Yeast-spo5 0.798 7±0.013 3 0.903 0±0.005 4 0.905 8±0.003 5 0.905 0±0.002 3 0.908 6±0.002 2 0.910 3±0.004 6
Movie 0.722 6±0.002 8 0.822 4±0.003 8 0.797 6±0.005 1 0.803 2±0.003 3 0.822 1±0.004 6 0.836 4±0.001 6
SDU_3DFE 0.838 8±0.003 2 0.847 9±0.003 8 0.823 6±0.006 7 0.839 4±0.003 7 0.870 9±0.002 7 0.848 8±0.003 9
Human Gene 0.477 9±0.024 3 0.741 7±0.002 7 0.636 2±0.007 8 0.781 4±0.004 0 0.783 4±0.003 9 0.781 6±0.004 1
Average 5.911 6 3.333 3 4.833 3 3.833 3 1.911 6 1.166 6

图3

6种标记分布学习算法结果的雷达图"

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