一种基于嵌入式的弱标记分类算法

doi:10.13232/j.cnki.jnju.2020.04.013

南京大学学报(自然科学版) ›› 2020, Vol. 56 ›› Issue (4): 549–560.doi: 10.13232/j.cnki.jnju.2020.04.013

一种基于嵌入式的弱标记分类算法

李亚重¹,杨有龙¹(),仇海全^1,²

^1.西安电子科技大学数学与统计学院，西安，710126
^2.安徽科技学院信息与网络工程学院，蚌埠，233030

收稿日期:2020-03-03 出版日期:2020-07-30 发布日期:2020-08-06
通讯作者: 杨有龙 E-mail:ylyang@mail.xidian.edu.cn
基金资助:
国家自然科学基金(61573266);安徽省高校自然科学研究重点项目(KJ2019A0816)

Label embedding for weak label classification

Yachong Li¹,Youlong Yang¹(),Haiquan Qiu^1,²

^1.School of Mathematics and Statistics，Xidian University，Xi'an, 710126，China
^2.College of Information & Network Engineering，Anhui Science and Technology University，Bengbu，233030，China

Received:2020-03-03 Online:2020-07-30 Published:2020-08-06
Contact: Youlong Yang E-mail:ylyang@mail.xidian.edu.cn

摘要/Abstract

摘要：

对于高维标签的分类问题，标签嵌入法已经受到广泛关注.现有的嵌入方法大都需要完整的标签信息，也没有将特征空间考虑在内；同时，由于数据进行人工标注的成本高以及噪声干扰等原因，仅能获得数据的部分标签信息，使得含有缺失标签的高维标签分类问题变得更加复杂.为解决这一问题，提出一种弱标记嵌入算法（Label Embedding for Weak Label Classification，LEWL）.该算法利用矩阵的低秩分解模型，结合样本的流形结构恢复缺失标签；同时采用希尔伯特?施密特独立标准技术(Hilbert?Schmidt Independence Criterion，HSIC)使特征和标签相互作用，联合学习获得一个低维的嵌入空间，可以有效地减少模型的训练时间.通过在七个多标签数据集上与其他算法的对比实验，结果表明了所提算法的有效性.

关键词: 弱标记学习, 标签嵌入, 低秩分解, 希尔伯特?施密特独立标准, 缺失标签

Abstract:

For the classification of high?dimensional labels，label embedding has attracted extensive attention of researchers in recent years. Current embedding methods require complete label information and do not take feature information into consideration. Meanwhile，due to the high cost of manual labeling and interference of noise，only part of the label information can be obtained. This makes the classification problem of high?dimensional labels with missing labels more complicated. To end this，a Label Embedding method for Weak Label Classification (LEWL) is proposed in this paper. The algorithm uses the low?rank factorization model on the label matrix and the flow pattern structure of the samples to recover the missing labels. In the meantime，the HSIC (Hilbert?Schmidt Independence Criterion) technique is adopted to obtain the low dimensional embedding space by making feature and labels interact with each other for joint learning，which can effectively reduce the training time of the model. Compared with other methods on seven data sets，comprehensive experimental results validate the effectiveness of proposed approach.

Key words: weak label classification, label embedding, the low?rank factorization on the matrix, HSIC(Hilbert?Schmidt Independence Criterion), missing labels

中图分类号:

TP301.6

李亚重,杨有龙,仇海全. 一种基于嵌入式的弱标记分类算法[J]. 南京大学学报(自然科学版), 2020, 56(4): 549–560.

Yachong Li,Youlong Yang,Haiquan Qiu. Label embedding for weak label classification[J]. Journal of Nanjing University(Natural Sciences), 2020, 56(4): 549–560.

图/表 12

表1

表2

缺失标签在平均精度上的恢复结果"

Data set	$ρ$	LEWL	MLML	LRML	CPLST	BR
Emotions	0.3	0.918 $±$ 0.008	0.920 $±$ 0.0044	0.843 $±$ 0.011	0.886 $±$ 0.005	0.886 $±$ 0.005
Emotions	0.7	0.839 $±$ 0.011	0.846 $±$ 0.012	0.772 $±$ 0.013	0.781 $±$ 0.010	0.781 $±$ 0.010
Yeast	0.3	0.894 $±$ 0.003	0.891 $±$ 0.001	0.792 $±$ 0.010	0.869 $±$ 0.002	0.869 $±$ 0.002
Yeast	0.7	0.811 $±$ 0.004	0.805 $±$ 0.003	0.716 $±$ 0.011	0.738 $±$ 0.005	0.738 $±$ 0.005
CAL500	0.3	0.832 $±$ 0.006	0.791 $±$ 0.005	0.784 $±$ 0.014	0.816 $±$ 0.004	0.816 $±$ 0.004
CAL500	0.7	0.663 $±$ 0.006	0.633 $±$ 0.007	0.652 $±$ 0.010	0.623 $±$ 0.004	0.623 $±$ 0.004
Medical	0.3	0.790 $±$ 0.019	0.776 $±$ 0.029	0.772 $±$ 0.042	0.766 $±$ 0.021	0.766 $±$ 0.021
Medical	0.7	0.602 $±$ 0.024	0.588 $±$ 0.029	0.531 $±$ 0.044	0.542 $±$ 0.009	0.542 $±$ 0.009
Langlog	0.3	0.860 $±$ 0.005	0.811 $±$ 0.002	0.852 $±$ 0.031	0.827 $±$ 0.002	0.827 $±$ 0.002
Langlog	0.7	0.709 $±$ 0.006	0.667 $±$ 0.003	0.704 $±$ 0.022	0.643 $±$ 0.006	0.643 $±$ 0.006
Enron	0.3	0.819 $±$ 0.007	0.823 $±$ 0.006	0.764 $±$ 0.051	0.795 $±$ 0.006	0.795 $±$ 0.006
Enron	0.7	0.632 $±$ 0.020	0.667 $±$ 0.028	0.543 $±$ 0.058	0.585 $±$ 0.013	0.585 $±$ 0.013
Corel5k	0.3	0.749 $±$ 0.005	0.735 $±$ 0.006	0.742 $±$ 0.004	0.733 $±$ 0.002	0.733 $±$ 0.002
Corel5k	0.7	0.515 $±$ 0.008	0.510 $±$ 0.011	0.513 $±$ 0.009	0.511 $±$ 0.004	0.511 $±$ 0.004

表2

表3

缺失标签在Macro F1上的恢复结果"

Data set	$ρ$	LEWL	MLML	LRML	CPLST	BR
Emotions	0.3	0.882 $±$ 0.009	0.905 $±$ 0.006	0.857 $±$ 0.048	0.847 $±$ 0.013	0.847 $±$ 0.013
Emotions	0.7	0.775 $±$ 0.010	0.801 $±$ 0.009	0.814 $±$ 0.035	0.666 $±$ 0.011	0.666 $±$ 0.011
Yeast	0.3	0.883 $±$ 0.007	0.874 $±$ 0.006	0.805 $±$ 0.015	0.850 $±$ 0.003	0.85 $±$ 0.003
Yeast	0.7	0.749 $±$ 0.008	0.738 $±$ 0.007	0.717 $±$ 0.023	0.660 $±$ 0.002	0.66 $±$ 0.002
CAL500	0.3	0.845 $±$ 0.004	0.776 $±$ 0.005	0.755 $±$ 0.021	0.849 $±$ 0.008	0.849 $±$ 0.008
CAL500	0.7	0.667 $±$ 0.007	0.633 $±$ 0.007	0.643 $±$ 0.020	0.657 $±$ 0.012	0.657 $±$ 0.012
Medical	0.3	0.804 $±$ 0.053	0.783 $±$ 0.029	0.755 $±$ 0.005	0.796 $±$ 0.049	0.796 $±$ 0.049
Medical	0.7	0.566 $±$ 0.042	0.593 $±$ 0.029	0.565 $±$ 0.006	0.557 $±$ 0.038	0.557 $±$ 0.038
Langlog	0.3	0.859 $±$ 0.002	0.856 $±$ 0.002	0.855 $±$ 0.041	0.85 $±$ 0.001	0.85 $±$ 0.001
Langlog	0.7	0.685 $±$ 0.003	0.683 $±$ 0.003	0.682 $±$ 0.066	0.663 $±$ 0.005	0.663 $±$ 0.005
Enron	0.3	0.845 $±$ 0.013	0.822 $±$ 0.006	0.754 $±$ 0.016	0.822 $±$ 0.015	0.822 $±$ 0.015
Enron	0.7	0.633 $±$ 0.033	0.648 $±$ 0.028	0.63 $±$ 0.013	0.651 $±$ 0.014	0.651 $±$ 0.014
Corel5k	0.3	0.817 $±$ 0.012	0.785 $±$ 0.007	0.801 $±$ 0.025	0.813 $±$ 0.017	0.813 $±$ 0.017
Corel5k	0.7	0.619 $±$ 0.011	0.605 $±$ 0.013	0.614 $±$ 0.021	0.612 $±$ 0.016	0.612 $±$ 0.016

表3

表4

缺失标签在排序损失上的恢复结果"

Data set	$ρ$	LEWL	MLML	LRML	CPLST	BR
Emotions	0.3	0.132 $±$ 0.010	0.133 $±$ 0.013	0.229 $±$ 0.017	0.262 $±$ 0.0121	0.262 $±$ 0.012
Emotions	0.7	0.274 $±$ 0.005	0.271 $±$ 0.011	0.324 $±$ 0.016	0.498 $±$ 0.018	0.498 $±$ 0.018
Yeast	0.3	0.116 $±$ 0.003	0.138 $±$ 0.002	0.209 $±$ 0.008	0.261 $±$ 0.003	0.261 $±$ 0.003
Yeast	0.7	0.227 $±$ 0.004	0.258 $±$ 0.007	0.288 $±$ 0.007	0.502 $±$ 0.007	0.502 $±$ 0.007
CAL500	0.3	0.130 $±$ 0.001	0.239 $±$ 0.006	0.249 $±$ 0.011	0.259 $±$ 0.0055	0.259 $±$ 0.005
CAL500	0.7	0.248 $±$ 0.001	0.394 $±$ 0.011	0.339 $±$ 0.009	0.503 $±$ 0.006	0.503 $±$ 0.006
Medical	0.3	0.107 $±$ 0.007	0.254 $±$ 0.011	0.155 $±$ 0.008	0.257 $±$ 0.022	0.257 $±$ 0.022
Medical	0.7	0.148 $±$ 0.022	0.444 $±$ 0.012	0.205 $±$ 0.012	0.505 $±$ 0.011	0.505 $±$ 0.011
Langlog	0.3	0.170 $±$ 0.004	0.233 $±$ 0.004	0.204 $±$ 0.051	0.251 $±$ 0.002	0.251 $±$ 0.002
Langlog	0.7	0.332 $±$ 0.012	0.339 $±$ 0.007	0.342 $±$ 0.018	0.493 $±$ 0.007	0.493 $±$ 0.007
Enron	0.3	0.129 $±$ 0.008	0.191 $±$ 0.010	0.213 $±$ 0.043	0.257 $±$ 0.008	0.257 $±$ 0.008
Enron	0.7	0.272 $±$ 0.029	0.363 $±$ 0.021	0.291 $±$ 0.043	0.513 $±$ 0.011	0.513 $±$ 0.011
Corel5k	0.3	0.108 $±$ 0.002	0.271 $±$ 0.008	0.178 $±$ 0.008	0.259 $±$ 0.003	0.259 $±$ 0.003
Corel5k	0.7	0.403 $±$ 0.004	0.496 $±$ 0.014	0.356 $±$ 0.007	0.503 $±$ 0.004	0.503 $±$ 0.004

表4

表5

表6

测试数据在平均精度上的预测结果"

Data set	$ρ$	LEWL	MLML	LRML	CPLST	BR
Emotions	0.3	0.732 $±$ 0.026	0.716 $±$ 0.01999	0.729 $±$ 0.0222	0.662 $±$ 0.038	0.645 $±$ 0.020
Emotions	0.7	0.708 $±$ 0.012	0.687 $±$ 0.039	0.682 $±$ 0.016	0.558 $±$ 0.023	0.568 $±$ 0.021
Yeast	0.3	0.708 $±$ 0.006	0.654 $±$ 0.005	0.441 $±$ 0.024	0.587 $±$ 0.004	0.573 $±$ 0.005
Yeast	0.7	0.698 $±$ 0.005	0.648 $±$ 0.008	0.44 $±$ 0.026	0.448 $±$ 0.008	0.450 $±$ 0.003
CAL500	0.3	0.365 $±$ 0.017	0.31 $±$ 0.013	0.202 $±$ 0.011	0.248 $±$ 0.012	0.248 $±$ 0.004
CAL500	0.7	0.369 $±$ 0.013	0.307 $±$ 0.013	0.197 $±$ 0.009	0.170 $±$ 0.008	0.175 $±$ 0.009
Medical	0.3	0.805 $±$ 0.025	0.734 $±$ 0.009	0.775 $±$ 0.008	0.675 $±$ 0.049	0.289 $±$ 0.029
Medical	0.7	0.718 $±$ 0.039	0.685 $±$ 0.018	0.721 $±$ 0.038	0.332 $±$ 0.030	0.112 $±$ 0.011
Langlog	0.3	0.543 $±$ 0.019	0.419 $±$ 0.016	0.410 $±$ 0.017	0.461 $±$ 0.048	0.469 $±$ 0.019
Langlog	0.7	0.530 $±$ 0.016	0.531 $±$ 0.019	0.399 $±$ 0.017	0.308 $±$ 0.029	0.309 $±$ 0.011
Enron	0.3	0.536 $±$ 0.041	0.395 $±$ 0.051	0.348 $±$ 0.007	0.331 $±$ 0.045	0.296 $±$ 0.043
Enron	0.7	0.493 $±$ 0.054	0.346 $±$ 0.055	0.252 $±$ 0.011	0.213 $±$ 0.020	0.197 $±$ 0.025
Corel5k	0.3	0.038 $±$ 0.003	0.027 $±$ 0.008	0.027 $±$ 0.005	0.030 $±$ 0.007	0.027 $±$ 0.007
Corel5k	0.7	0.022 $±$ 0.002	0.025 $±$ 0.007	0.026 $±$ 0.004	0.027 $±$ 0.007	0.023 $±$ 0.007

表6

表7

测试数据在Macro F1上的预测结果"

Data set	$ρ$	LEWL	MLML	LRML	CPLST	BR
Emotions	0.3	0.606 $±$ 0.057	0.576 $±$ 0.051	0.616 $±$ 0.036	0.429 $±$ 0.069	0.389 $±$ 0.021
Emotions	0.7	0.596 $±$ 0.038	0.523 $±$ 0.061	0.610 $±$ 0.036	0.152 $±$ 0.033	0.160 $±$ 0.041
Yeast	0.3	0.461 $±$ 0.004	0.334 $±$ 0.011	0.367 $±$ 0.008	0.251 $±$ 0.009	0.234 $±$ 0.009
Yeast	0.7	0.452 $±$ 0.006	0.313 $±$ 0.008	0.366 $±$ 0.009	0.058 $±$ 0.009	0.062 $±$ 0.004
CAL500	0.3	0.234 $±$ 0.012	0.073 $±$ 0.007	0.212 $±$ 0.011	0.035 $±$ 0.005	0.046 $±$ 0.003
CAL500	0.7	0.232 $±$ 0.008	0.066 $±$ 0.008	0.205 $±$ 0.010	0.008 $±$ 0.002	0.015 $±$ 0.002
Medical	0.3	0.358 $±$ 0.032	0.311 $±$ 0.012	0.325 $±$ 0.002	0.310 $±$ 0.023	0.098 $±$ 0.018
Medical	0.7	0.306 $±$ 0.020	0.258 $±$ 0.008	0.287 $±$ 0.019	0.171 $±$ 0.029	0.01 $±$ 0.003
Langlog	0.3	0.448 $±$ 0.018	0.164 $±$ 0.011	0.389 $±$ 0.028	0.171 $±$ 0.025	0.185 $±$ 0.014
Langlog	0.7	0.434 $±$ 0.017	0.232 $±$ 0.009	0.374 $±$ 0.029	0.048 $±$ 0.009	0.059 $±$ 0.0120.
Enron	0.3	0.166 $±$ 0.011	0.065 $±$ 0.013	0.120 $±$ 0.015	0.063 $±$ 0.009	0.042 $±$ 0.008
Enron	0.7	0.149 $±$ 0.010	0.051 $±$ 0.014	0.101 $±$ 0.016	0.022 $±$ 0.004	0.013 $±$ 0.011
Corel5k	0.3	0.025 $±$ 0.001	0.018 $±$ 0.005	0.020 $±$ 0.003	0.010 $±$ 0.003	0.009 $±$ 0.003
Corel5k	0.7	0.019 $±$ 0.001	0.015 $±$ 0.006	0.016 $±$ 0.003	0.007 $±$ 0.004	0.006 $±$ 0.002

表7

表8

测试数据在排序损失上的预测结果"

Data set	$ρ$	LEWL	MLML	LRML	CPLST	BR
Emotions	0.3	0.446 $±$ 0.024	0.509 $±$ 0.042	0.441 $±$ 0.019	0.692 $±$ 0.052	0.731 $±$ 0.018
Emotions	0.7	0.457 $±$ 0.030	0.561 $±$ 0.071	0.453 $±$ 0.016	0.924 $±$ 0.023	0.915 $±$ 0.013
Yeast	0.3	0.385 $±$ 0.008	0.484 $±$ 0.009	0.709 $±$ 0.007	0.652 $±$ 0.008	0.679 $±$ 0.011
Yeast	0.7	0.401 $±$ 0.011	0.496 $±$ 0.013	0.722 $±$ 0.005	0.940 $±$ 0.011	0.933 $±$ 0.011
CAL500	0.3	0.461 $±$ 0.011	0.577 $±$ 0.006	0.518 $±$ 0.012	0.890 $±$ 0.014	0.885 $±$ 0.003
CAL500	0.7	0.457 $±$ 0.011	0.584 $±$ 0.018	0.528 $±$ 0.008	0.972 $±$ 0.008	0.969 $±$ 0.005
Medical	0.3	0.139 $±$ 0.037	0.476 $±$ 0.014	0.302 $±$ 0.019	0.345 $±$ 0.050	0.785 $±$ 0.027
Medical	0.7	0.168 $±$ 0.005	0.529 $±$ 0.016	0.347 $±$ 0.017	0.462 $±$ 0.040	0.977 $±$ 0.006
Langlog	0.3	0.468 $±$ 0.014	0.716 $±$ 0.017	0.629 $±$ 0.057	0.716 $±$ 0.053	0.689 $±$ 0.025
Langlog	0.7	0.487 $±$ 0.015	0.761 $±$ 0.021	0.625 $±$ 0.050	0.811 $±$ 0.031	0.887 $±$ 0.019
Enron	0.3	0.315 $±$ 0.038	0.500 $±$ 0.056	0.548 $±$ 0.008	0.792 $±$ 0.041	0.835 $±$ 0.041
Enron	0.7	0.349 $±$ 0.038	0.569 $±$ 0.055	0.771 $±$ 0.019	0.948 $±$ 0.015	0.967 $±$ 0.023
Corel5k	0.3	0.538 $±$ 0.001	0.745 $±$ 0.002	0.697 $±$ 0.002	0.825 $±$ 0.001	0.889 $±$ 0.001
Corel5k	0.7	0.549 $±$ 0.001	0.783 $±$ 0.004	0.721 $±$ 0.002	0.889 $±$ 0.004	0.903 $±$ 0.002

表8

表9

图1

图2

图3

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数据集	样本	特征	标签	领域	标签基数
Emotions	593	72	6	music	1.869
Yeast	2417	103	14	biology	4.237
CAL500	502	68	174	music	26.044
Medical	978	1449	45	text	1.245
Langlog	1460	1004	75	images	1.18
Enron	1702	1001	53	text	3.378
Corel5k	5000	499	374	images	3.522

	MLML	LRML	CPLST	BR
Average Precision	0.0455	0.0004	0.0001	0.0001
Macro F₁	0.2273	0.0179	0.0230	0.0230
Rank Loss	0.0015	0.0008	0.0003	0.0003

	MLML	LRML	CPLST	BR
Average Precision	0.0046	0.0054	0.0000	0.0007
Macro F₁	0.0008	0.0007	0.0001	0.0000
Rank Loss	0.0007	0.0016	0.0001	0.0000

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一种基于嵌入式的弱标记分类算法

Label embedding for weak label classification

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