Journal of Shandong University(Engineering Science) ›› 2020, Vol. 50 ›› Issue (3): 58-65.doi: 10.6040/j.issn.1672-3961.0.2019.295

• Machine Learning & Data Mining • Previous Articles     Next Articles

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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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

CLC Number: 

  • TP181

Fig.1

Label distribution learning in landscape maps"

Fig.2

AKELM-LDL algorithm modeling process"

Table 1

Label distribution learning datasets"

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

Table 2

Evaluation measures for label distribution learning"

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)} $

Table 3

The results in Chebyshev(↓)"

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

Table 4

The results in Clark(↓)"

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

Table 5

The results in Canberra(↓)"

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

Table 6

The results in Kullback-Leibler(↓)"

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

Table 7

The results in Cosine(↑)"

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

Table 8

The results in Intersetion(↑)"

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

Fig.3

Radar graph of the results of six mark distribution learning algorithms"

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[1] ZHANG Yong-hua,WANG An-ling,LIU Fu-ping . The reflected phase angle of low frequent inhomogeneous[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(2): 22 -25 .
[2] KONG Xiang-zhen,LIU Yan-jun,WANG Yong,ZHAO Xiu-hua . Compensation and simulation for the deadband of the pneumatic proportional valve[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(1): 99 -102 .
[3] CHEN Rui, LI Hongwei, TIAN Jing. The relationship between the number of magnetic poles and the bearing capacity of radial magnetic bearing[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(2): 81 -85 .
[4] WANG Bo,WANG Ning-sheng . Automatic generation and combinatory optimization of disassembly sequence for mechanical-electric assembly[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(2): 52 -57 .
[5] LI Ke,LIU Chang-chun,LI Tong-lei . Medical registration approach using improved maximization of mutual information[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(2): 107 -110 .
[6] QIN Tong, SUN Fengrong*, WANG Limei, WANG Qinghao, LI Xincai. 3D surface reconstruction using the shape based interpolation guided by maximal discs[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2010, 40(3): 1 -5 .
[7] LIU Wen-liang, ZHU Wei-hong, CHEN Di, ZHANG Hong-quan. Detection and tracking of moving targets using the morphology match in radar images[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2010, 40(3): 31 -36 .
[8] ZHANG Ying,LANG Yongmei,ZHAO Yuxiao,ZHANG Jianda,QIAO Peng,LI Shanping . Research on technique of aerobic granular sludge cultivationby seeding EGSB anaerobic granular sludge[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(4): 56 -59 .
[9] SUN Dianzhu, ZHU Changzhi, LI Yanrui. [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2009, 39(1): 84 -86 .
[10] HAO Ranhang,CHEN Shouyu . The theory, model and method of water resources evaluationombining quantity with quality[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(3): 46 -50 .
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