基于多维相关性的弱类属属性学习

doi:10.13232/j.cnki.jnju.2023.04.015

南京大学学报(自然科学版) ›› 2023, Vol. 59 ›› Issue (4): 690–704.doi: 10.13232/j.cnki.jnju.2023.04.015

基于多维相关性的弱类属属性学习

王一宾¹^,², 葛文信¹, 程玉胜¹^,²(), 吴海峰¹^,²

^1.安庆师范大学计算机与信息学院，安庆，246133
^2.智能感知与计算安徽省高校重点实验室，安庆，246133

收稿日期:2023-05-24 出版日期:2023-07-31 发布日期:2023-08-18
通讯作者: 程玉胜 E-mail:chengyshaq@163.com
基金资助:
并行与分布处理国防科技重点实验室项目(WDZC202252501);安徽省自然科学基金(2108085MF216)

Weak⁃label⁃specific features learning based on multidimensional correlation

Yibin Wang¹^,², Wenxin Ge¹, Yusheng Cheng¹^,²(), Haifeng Wu¹^,²

^1.School of Computer and Information, Anqing Normal University, Anqing, 246133, China
^2.Key Laboratory of Intelligent Perception and Computing of Anhui Province, Anqing, 246133, China

Received:2023-05-24 Online:2023-07-31 Published:2023-08-18
Contact: Yusheng Cheng E-mail:chengyshaq@163.com

摘要/Abstract

摘要：

传统的多标签学习一般基于完整的标签信息，但随着数据量的增大，很难为每个实例获得完整的标签信息，导致弱标签问题在多标签数据集中广泛存在，严重影响了多标签的分类性能.为了提升相关性能，不少学者在实际分类中考虑特征、标签和实例部分的关联性，却忽略了它们之间的相关性.基于此，提出一种基于多维相关性的弱类属属性学习算法：首先，根据特征和标签之间的相关性，采用余弦相似度计算出标签之间的相关性；其次，根据特征与实例之间的相关性，采用密度峰值聚类获得实例相关性，并从中选择具有监督信息的标签矩阵，与分解希尔伯特矩阵获得的特征相关性结合构建流形正则化；最后，在多个不同缺省率的多标签数据集上进行了大量实验，验证了提出的算法的有效性.

Abstract:

Traditional multi?label learning is generally based on complete label information. However，as the volume of data increases，it is difficult to obtain complete label information for each instance，which leads to the widespread presence of weak labels in multi?label datasets. In turn，the classification performance is seriously affected. Many scholars considered the partial association of features，labels and instances in practical classification，while ignoring the correlation between them.Therefore，this paper proposes a weak?label?specific features learning based on multidimensional correlation. Firstly，the correlation between features and labels is measured according to the cosine similarity. Secondly，based on the correlation between labels and instances，density peak clustering is used to obtain instance correlation，which are combined with feature correlation obtained from decomposing hilbert matrices to construct streamwise regularization. Finally，experiments are conducted on multiple multi?label datasets with different missing rates，and the results verifiy the effectiveness of our algorithm.

Key words: weak?label?specific feature, label correlation, feature correlation, density peaks clustering, instance correlation

中图分类号:

TP181

王一宾, 葛文信, 程玉胜, 吴海峰. 基于多维相关性的弱类属属性学习[J]. 南京大学学报(自然科学版), 2023, 59(4): 690–704.

Yibin Wang, Wenxin Ge, Yusheng Cheng, Haifeng Wu. Weak⁃label⁃specific features learning based on multidimensional correlation[J]. Journal of Nanjing University(Natural Sciences), 2023, 59(4): 690–704.

图/表 11

图1

表1

表2

六种算法在12个数据集上的缺省实验结果（海明损失）"

Datasets	r	GLOCAL	LRMML	MSWL	LSML	JLCLS	WSMDC
Arts	0.1	0.0629±0.0016	0.0538±0.0017	0.0605±0.0011	0.0577±0.0009	0.0582±0.0023	0.0530±0.0010
	0.3	0.0629±0.0017	0.0553±0.0013	0.0608±0.0012	0.0588±0.0008	0.0615±0.0015	0.0536±0.0011
	0.5	0.0629±0.0007	0.0570±0.0016	0.0613±0.0015	0.0608±0.0008	0.0624±0.0007	0.0547±0.0016
	0.7	0.0629±0.0013	0.0607±0.0010	0.0621±0.0006	0.0624±0.0005	0.0629±0.0003	0.0566±0.0013
Birds	0.1	0.0734±0.0195	0.0508±0.0029	0.0674±0.0049	0.0616±0.0033	0.0511±0.0018	0.0485±0.0063
	0.3	0.0557±0.0019	0.0533±0.0031	0.0695±0.0025	0.0653±0.0017	0.0516±0.0057	0.0505±0.0079
	0.5	0.0621±0.0029	0.0533±0.0039	0.0713±0.0049	0.0729±0.0033	0.0554±0.0026	0.0547±0.0050
	0.7	0.0592±0.0060	0.0622±0.0045	0.0726±0.0040	0.0735±0.0030	0.0598±0.0059	0.0558±0.0040
Computers	0.1	0.0499±0.0046	0.0337±0.0007	0.0435±0.0012	0.0392±0.0006	0.0384±0.0025	0.0331±0.0010
	0.3	0.0527±0.0007	0.0346±0.0007	0.0436±0.0013	0.0408±0.0018	0.0444±0.0014	0.0335±0.0016
	0.5	0.0544±0.0009	0.0385±0.0007	0.0449±0.0017	0.0428±0.0011	0.0580±0.0022	0.0344±0.0010
	0.7	0.0558±0.0027	0.0597±0.0012	0.0450±0.0003	0.0450±0.0007	0.0889±0.0036	0.0356±0.0011
Entertainment	0.1	0.0589±0.0089	0.0513±0.0010	0.0648±0.0021	0.0574±0.0021	0.0565±0.0017	0.0501±0.0013
	0.3	0.0670±0.0009	0.0535±0.0011	0.0655±0.0019	0.0596±0.0008	0.0634±0.0025	0.0513±0.0024
	0.5	0.0684±0.0008	0.0570±0.0008	0.0665±0.0006	0.0628±0.0012	0.0757±0.0029	0.0524±0.0015
	0.7	0.0699±0.0063	0.0609±0.0007	0.0657±0.0015	0.0666±0.0015	0.1084±0.0056	0.0558±0.0013
Health	0.1	0.0393±0.0039	0.0330±0.0009	0.0481±0.0013	0.0407±0.0006	0.0351±0.0013	0.0316±0.0015
	0.3	0.0412±0.0009	0.0341±0.0010	0.0489±0.0010	0.0436±0.0007	0.0400±0.0011	0.0326±0.0011
	0.5	0.0426±0.0010	0.0377±0.0006	0.0490±0.0006	0.0473±0.0004	0.0507±0.0018	0.0339±0.0014
	0.7	0.0485±0.0020	0.0563±0.0026	0.0503±0.0010	0.0509±0.0010	0.0811±0.0009	0.0358±0.0009
Image	0.1	0.1947±0.0211	0.2110±0.0122	0.2390±0.0078	0.2427±0.0068	0.2120±0.0064	0.2017±0.0199
	0.3	0.2076±0.0050	0.2110±0.0082	0.2443±0.0108	0.2450±0.0101	0.2153±0.0205	0.2123±0.0180
	0.5	0.2122±0.0043	0.2230±0.0097	0.2433±0.0061	0.2453±0.0132	0.2107±0.0059	0.2140±0.0094
	0.7	0.2514±0.0136	0.2207±0.0157	0.2457±0.0051	0.2467±0.0053	0.2110±0.0062	0.2217±0.0151
Medical	0.1	0.0138±0.0022	0.0114±0.0016	0.0247±0.0023	0.0194±0.0006	0.0108±0.0007	0.0101±0.0012
	0.3	0.0117±0.0009	0.0122±0.0011	0.0253±0.0031	0.0220±0.0015	0.0129±0.0005	0.0154±0.0015
	0.5	0.0132±0.0014	0.0144±0.0011	0.0257±0.0026	0.0249±0.0004	0.0179±0.0022	0.0169±0.0019
	0.7	0.0215±0.0028	0.0262±0.0032	0.0278±0.0002	0.0270±0.0010	0.0442±0.0028	0.0182±0.0014
Recreation	0.1	0.0664±0.0080	0.0538±0.0012	0.0621±0.0010	0.0588±0.0009	0.0600±0.0012	0.0528±0.0009
	0.3	0.0718±0.0015	0.0560±0.0007	0.0629±0.0007	0.0602±0.0016	0.0667±0.0017	0.0541±0.0018
	0.5	0.0747±0.0012	0.0588±0.0007	0.0630±0.0020	0.0618±0.0012	0.0791±0.0015	0.0550±0.0022
	0.7	0.0747±0.0045	0.0625±0.0010	0.0631±0.0015	0.0639±0.0016	0.1106±0.0019	0.0582±0.0011
Reference	0.1	0.0338±0.0045	0.0251±0.0006	0.0330±0.0001	0.0290±0.0002	0.0294±0.0008	0.0244±0.0010
	0.3	0.0380±0.0005	0.0262±0.0004	0.0336±0.0004	0.0303±0.0004	0.0362±0.0011	0.0251±0.0009
	0.5	0.0387±0.0006	0.0305±0.0005	0.0339±0.0009	0.0322±0.0003	0.0514±0.0041	0.0253±0.0008
	0.7	0.0394±0.0031	0.0531±0.0026	0.0344±0.0005	0.0346±0.0004	0.0868±0.0021	0.0265±0.0013
Society	0.1	0.0557±0.0070	0.0515±0.0015	0.0586±0.0024	0.0554±0.0014	0.0555±0.0008	0.0508±0.0019
	0.3	0.0617±0.0010	0.0530±0.0009	0.0609±0.0019	0.0570±0.0013	0.0615±0.0012	0.0515±0.0018
	0.5	0.0632±0.0012	0.0571±0.0013	0.0614±0.0016	0.0595±0.0013	0.0738±0.0022	0.0523±0.0018
	0.7	0.0621±0.0034	0.0816±0.0028	0.0620±0.0013	0.0623±0.0013	0.1046±0.0015	0.0541±0.0019
Science	0.1	0.0340±0.0045	0.0312±0.0009	0.0352±0.0001	0.0341±0.0008	0.0334±0.0006	0.0307±0.0013
	0.3	0.0376±0.0007	0.0318±0.0012	0.0359±0.0007	0.0347±0.0006	0.0383±0.0010	0.0317±0.0009
	0.5	0.0386±0.0009	0.0333±0.0008	0.0356±0.0005	0.0353±0.0003	0.0507±0.0008	0.0322±0.0006
	0.7	0.0390±0.0027	0.0350±0.0007	0.0359±0.0007	0.0361±0.0004	0.0829±0.0026	0.0329±0.0009
Social	0.1	0.0217±0.0039	0.0201±0.0004	0.0292±0.0010	0.0238±0.0003	0.0213±0.0006	0.0195±0.0013
	0.3	0.0247±0.0005	0.0213±0.0005	0.0301±0.0007	0.0256±0.0005	0.0259±0.0010	0.0202±0.0011
	0.5	0.0255±0.0006	0.0249±0.0006	0.0310±0.0009	0.0282±0.0005	0.0389±0.0005	0.0207±0.0011
	0.7	0.0282±0.0028	0.0521±0.0013	0.0322±0.0006	0.0318±0.0003	0.0740±0.0022	0.0212±0.0010

表2

表3

六种算法在12个数据集上的缺省实验结果（平均精度）"

Datasets	r	GLOCAL	LRMML	MSWL	LSML	JLCLS	WSMDC
Arts	0.1	0.6192±0.0118	0.6267±0.0104	0.6167±0.0083	0.6114±0.0064	0.6122±0.0040	0.6381±0.0128
	0.3	0.6123±0.0112	0.6029±0.0114	0.6020±0.0091	0.5772±0.0087	0.6099±0.0116	0.6127±0.0138
	0.5	0.6038±0.0072	0.5736±0.0070	0.5830±0.0126	0.5227±0.0102	0.5851±0.0082	0.5823±0.0089
	0.7	0.5837±0.0071	0.5387±0.0123	0.5499±0.0106	0.4706±0.0083	0.5476±0.0109	0.5411±0.0099
Birds	0.1	0.7562±0.0195	0.7608±0.0029	0.7494±0.0267	0.7590±0.0168	0.7645±0.0109	0.7734±0.0353
	0.3	0.7088±0.0136	0.7533±0.0102	0.7392±0.0287	0.7342±0.0239	0.7268±0.0341	0.7510±0.0176
	0.5	0.6889±0.0082	0.7187±0.0152	0.7169±0.0205	0.7046±0.0447	0.7088±0.0322	0.7328±0.0331
	0.7	0.6657±0.0476	0.6857±0.0144	0.6856±0.0330	0.6893±0.0325	0.6768±0.0485	0.6990±0.0311
Computers	0.1	0.6877±0.0531	0.7042±0.0058	0.6991±0.0073	0.6922±0.0121	0.6926±0.0121	0.7206±0.0158
	0.3	0.6511±0.0077	0.6835±0.0079	0.6815±0.0108	0.6560±0.0135	0.6563±0.0120	0.6956±0.0155
	0.5	0.6373±0.0073	0.6316±0.0103	0.6683±0.0165	0.6166±0.0082	0.6082±0.0106	0.6781±0.0122
	0.7	0.6152±0.0271	0.5699±0.0062	0.6383±0.0143	0.5311±0.0089	0.5411±0.0199	0.6404±0.0165
Entertainment	0.1	0.6823±0.0656	0.6886±0.0048	0.6883±0.0101	0.6792±0.0058	0.6833±0.0115	0.7034±0.0120
	0.3	0.6349±0.0095	0.6680±0.0072	0.6746±0.0112	0.6487±0.0105	0.6451±0.0083	0.6887±0.0170
	0.5	0.6172±0.0121	0.6471±0.0077	0.6547±0.0130	0.6089±0.0087	0.6110±0.0038	0.6623±0.0191
	0.7	0.5766±0.0397	0.6083±0.0077	0.6324±0.0072	0.5452±0.0141	0.5343±0.0147	0.6176±0.0106
Health	0.1	0.7663±0.0485	0.7784±0.0109	0.7756±0.0093	0.7724±0.0068	0.7672±0.0077	0.7954±0.0132
	0.3	0.7331±0.0073	0.7625±0.0081	0.7688±0.0101	0.7438±0.0069	0.7353±0.0094	0.7790±0.0101
	0.5	0.7202±0.0066	0.7273±0.0093	0.7508±0.0113	0.6941±0.0067	0.7002±0.0120	0.7641±0.0111
	0.7	0.6814±0.0263	0.6534±0.0073	0.7239±0.0119	0.6112±0.0088	0.6145±0.0122	0.7327±0.0066
Image	0.1	0.7628±0.0302	0.7259±0.0305	0.7564±0.0232	0.7583±0.0130	0.7507±0.0351	0.7620±0.0350
	0.3	0.7418±0.0079	0.6929±0.0337	0.7451±0.0147	0.7537±0.0259	0.7478±0.0292	0.7534±0.0433
	0.5	0.7370±0.0108	0.7190±0.0402	0.7200±0.0382	0.7411±0.0261	0.7395±0.0237	0.7419±0.0357
	0.7	0.6489±0.0275	0.6674±0.0146	0.6906±0.0402	0.7278±0.0437	0.7271±0.0225	0.7214±0.0329
Medical	0.1	0.8604±0.0384	0.8870±0.0132	0.7246±0.0248	0.8895±0.0111	0.8906±0.0142	0.9076±0.0168
	0.3	0.8776±0.0060	0.8724±0.0102	0.6784±0.2881	0.8626±0.0199	0.8634±0.0110	0.8639±0.0294
	0.5	0.8608±0.0166	0.8320±0.0204	0.6340±0.3233	0.8221±0.0169	0.8194±0.0236	0.8405±0.0331
	0.7	0.7103±0.0772	0.7099±0.0274	0.5066±0.2138	0.7122±0.0148	0.6959±0.0308	0.8030±0.0327
Recreation	0.1	0.6236±0.0703	0.6299±0.0051	0.6311±0.0066	0.6209±0.0069	0.6208±0.0075	0.6512±0.0158
	0.3	0.5721±0.0111	0.6104±0.0074	0.6158±0.0138	0.5804±0.0082	0.5872±0.0122	0.6266±0.0126
	0.5	0.5558±0.0129	0.5740±0.0107	0.5917±0.0040	0.5358±0.0094	0.5448±0.0059	0.5935±0.0195
	0.7	0.5113±0.0384	0.5260±0.0060	0.5673±0.0077	0.4749±0.0157	0.4744±0.0086	0.5392±0.0256
Reference	0.1	0.7061±0.0545	0.7092±0.0067	0.7068±0.0079	0.6986±0.0109	0.6936±0.0089	0.7268±0.0092
	0.3	0.6613±0.0064	0.6822±0.0039	0.6938±0.0125	0.6519±0.0062	0.6536±0.0121	0.7017±0.0174
	0.5	0.6510±0.0064	0.6277±0.0066	0.6748±0.0108	0.5973±0.0092	0.5997±0.0168	0.6755±0.0148
	0.7	0.6151±0.0282	0.5516±0.0085	0.6451±0.0121	0.5101±0.0103	0.5059±0.0099	0.6334±0.0117
Society	0.1	0.6426±0.0676	0.6363±0.0114	0.6363±0.0134	0.6207±0.0107	0.6221±0.0079	0.6490±0.0145
	0.3	0.5860±0.0083	0.6124±0.0100	0.5635±0.1146	0.5904±0.0089	0.5860±0.0129	0.6273±0.0114
	0.5	0.5746±0.0040	0.5760±0.0092	0.5497±0.1160	0.5527±0.0114	0.5532±0.0130	0.6069±0.0145
	0.7	0.5662±0.0295	0.5138±0.0107	0.4769±0.1234	0.4871±0.0094	0.4819±0.0109	0.5725±0.0178
Science	0.1	0.5868±0.0776	0.5943±0.0202	0.5947±0.0044	0.5832±0.0090	0.5803±0.0042	0.6197±0.0171
	0.3	0.5352±0.0098	0.5642±0.0202	0.5354±0.0129	0.5393±0.0048	0.5363±0.0041	0.5837±0.0168
	0.5	0.5138±0.0147	0.5162±0.0137	0.4946±0.1196	0.4733±0.0124	0.4720±0.0053	0.5549±0.0126
	0.7	0.4663±0.0346	0.4652±0.0196	0.4160±0.1600	0.3781±0.0122	0.3871±0.0134	0.4935±0.0181
Social	0.1	0.7696±0.0520	0.7708±0.0076	0.7797±0.0140	0.7583±0.0063	0.7615±0.0109	0.7874±0.0137
	0.3	0.7308±0.0060	0.7470±0.0055	0.7633±0.0073	0.7208±0.0154	0.7198±0.0111	0.7647±0.0098
	0.5	0.7223±0.0070	0.6933±0.0077	0.7511±0.0126	0.6708±0.0081	0.6653±0.0071	0.7458±0.0148
	0.7	0.6780±0.0260	0.6140±0.0060	0.7198±0.0041	0.5752±0.0120	0.5751±0.0161	0.7154±0.0134

表3

表4

六种算法在12个数据集上的缺省实验结果（1?错误率）"

Datasets	r	GLOCAL	LRMML	MSWL	LSML	JLCLS	WSMDC
Arts	0.1	0.4554±0.0127	0.4588±0.0113	0.4596±0.0135	0.4590±0.0090	0.4568±0.0149	0.4392±0.0209
	0.3	0.4641±0.0162	0.4764±0.0083	0.4740±0.0139	0.4910±0.0146	0.4620±0.0156	0.4542±0.0168
	0.5	0.4832±0.0097	0.5058±0.0113	0.4938±0.0125	0.5462±0.0130	0.4866±0.0094	0.4840±0.0114
	0.7	0.5049±0.0105	0.5628±0.0165	0.5310±0.0134	0.5992±0.0099	0.5156±0.0157	0.5224±0.0139
Birds	0.1	0.3055±0.0243	0.2868±0.0110	0.2992±0.0301	0.2884±0.0384	0.2899±0.0327	0.2847±0.0486
	0.3	0.3690±0.0195	0.2884±0.0173	0.3116±0.0489	0.3039±0.0275	0.3163±0.0411	0.2884±0.0308
	0.5	0.3938±0.0101	0.3256±0.0298	0.3411±0.0255	0.3364±0.0711	0.3395±0.0358	0.3163±0.0482
	0.7	0.4035±0.0612	0.3597±0.0372	0.3752±0.0262	0.3473±0.0365	0.3612±0.0604	0.3411±0.0436
Computers	0.1	0.3664±0.0591	0.3498±0.0107	0.3480±0.0157	0.3548±0.0180	0.3550±0.0124	0.3362±0.0184
	0.3	0.4038±0.0095	0.3660±0.0063	0.3636±0.0156	0.3814±0.0152	0.3810±0.0062	0.3486±0.0220
	0.5	0.4223±0.0094	0.4022±0.0158	0.3754±0.0143	0.4196±0.0186	0.4302±0.0162	0.3578±0.0134
	0.7	0.4412±0.0338	0.4684±0.0040	0.4092±0.0188	0.5164±0.0126	0.5028±0.0263	0.3896±0.0255
Entertainment	0.1	0.3935±0.0838	0.3950±0.0060	0.3936±0.0094	0.3972±0.0146	0.3962±0.0188	0.3808±0.0205
	0.3	0.4527±0.0119	0.4166±0.0135	0.4068±0.0173	0.4280±0.0121	0.4296±0.0124	0.3898±0.0249
	0.5	0.4772±0.0191	0.4420±0.0091	0.4344±0.0154	0.4692±0.0109	0.4616±0.0055	0.4124±0.0251
	0.7	0.5327±0.0518	0.4882±0.0106	0.4528±0.0160	0.5360±0.0152	0.5512±0.0197	0.4630±0.0103
Health	0.1	0.2805±0.0610	0.2584±0.0202	0.2666±0.0191	0.2556±0.0138	0.2594±0.0082	0.2412±0.0243
	0.3	0.3174±0.0100	0.2634±0.0173	0.2724±0.0195	0.2770±0.0133	0.2864±0.0178	0.2518±0.0151
	0.5	0.3379±0.0115	0.2928±0.0162	0.2946±0.0148	0.3276±0.0124	0.3166±0.0176	0.2580±0.0181
	0.7	0.3827±0.0369	0.3686±0.0052	0.3210±0.0214	0.4200±0.0139	0.4166±0.0039	0.2828±0.0174
Image	0.1	0.3620±0.0476	0.4267±0.0426	0.3833±0.0462	0.3900±0.0232	0.4000±0.0545	0.3733±0.0684
	0.3	0.3960±0.0185	0.4867±0.0437	0.3900±0.0193	0.3917±0.0405	0.3933±0.0504	0.3867±0.0722
	0.5	0.4020±0.0160	0.4417±0.0601	0.4283±0.0668	0.4033±0.0515	0.4133±0.0389	0.4083±0.0602
	0.7	0.5360±0.0425	0.5033±0.0287	0.4717±0.0632	0.4300±0.0676	0.4250±0.0337	0.4433±0.0588
Medical	0.1	0.1840±0.0581	0.1585±0.0237	0.3766±0.0326	0.1452±0.0088	0.1421±0.0186	0.1298±0.0295
	0.3	0.1480±0.0072	0.1667±0.0287	0.3829±0.3155	0.1616±0.0262	0.1687±0.0184	0.1717±0.0420
	0.5	0.1684±0.0194	0.1963±0.0304	0.4380±0.3594	0.2055±0.0177	0.2117±0.0406	0.2025±0.0414
	0.7	0.3723±0.0924	0.3446±0.0358	0.6116±0.2415	0.3364±0.0188	0.3538±0.0357	0.2300±0.0372
Recreation	0.1	0.4588±0.0908	0.4566±0.0118	0.4492±0.0092	0.4662±0.0106	0.4664±0.0143	0.4376±0.0247
	0.3	0.5195±0.0181	0.4844±0.0154	0.4682±0.0171	0.5046±0.0071	0.4948±0.0188	0.4590±0.0217
	0.5	0.5460±0.0165	0.5258±0.0162	0.4960±0.0061	0.5500±0.0149	0.5374±0.0053	0.4844±0.0277
	0.7	0.5936±0.0500	0.5844±0.0115	0.5212±0.0076	0.6242±0.0215	0.6174±0.0131	0.5518±0.0338
Reference	0.1	0.3673±0.0615	0.3666±0.0103	0.3676±0.0123	0.3718±0.0157	0.3764±0.0137	0.3504±0.0132
	0.3	0.4155±0.0095	0.3854±0.0074	0.3846±0.0179	0.4130±0.0034	0.4148±0.0140	0.3664±0.0238
	0.5	0.4292±0.0089	0.4404±0.0057	0.4014±0.0130	0.4734±0.0113	0.4716±0.0134	0.3850±0.0208
	0.7	0.4741±0.0319	0.5260±0.0116	0.4320±0.0178	0.5738±0.0129	0.5806±0.0113	0.4260±0.0193
Society	0.1	0.3871±0.0802	0.3920±0.0178	0.3978±0.0139	0.4010±0.0127	0.4022±0.0088	0.3778±0.0186
	0.3	0.4495±0.0117	0.4114±0.0175	0.4750±0.1207	0.4290±0.0139	0.4360±0.0310	0.3916±0.0177
	0.5	0.4675±0.0060	0.4420±0.0140	0.4866±0.1214	0.4748±0.0183	0.4676±0.0175	0.4142±0.0159
	0.7	0.4756±0.0380	0.5240±0.0156	0.5678±0.1356	0.5564±0.0159	0.5660±0.0160	0.4490±0.0268
Science	0.1	0.4905±0.0952	0.4934±0.0255	0.4932±0.0070	0.4950±0.0124	0.4954±0.0105	0.4740±0.0250
	0.3	0.5513±0.0124	0.5168±0.0245	0.5512±0.0168	0.5268±0.0080	0.5322±0.0088	0.5008±0.0180
	0.5	0.5799±0.0209	0.5594±0.0168	0.5922±0.1291	0.6022±0.0154	0.5988±0.0112	0.5182±0.0172
	0.7	0.6333±0.0427	0.6192±0.0132	0.6738±0.1672	0.7000±0.0157	0.6926±0.0138	0.5762±0.0251
Social	0.1	0.2865±0.0611	0.2752±0.0124	0.2736±0.0145	0.2814±0.0098	0.2782±0.0195	0.2632±0.0187
	0.3	0.3220±0.0102	0.2944±0.0041	0.2916±0.0115	0.3176±0.0162	0.3144±0.0140	0.2838±0.0130
	0.5	0.3387±0.0116	0.3438±0.0146	0.3024±0.0148	0.3724±0.0137	0.3788±0.0112	0.2934±0.0181
	0.7	0.4135±0.0342	0.4354±0.0062	0.3346±0.0091	0.4832±0.0125	0.4830±0.0219	0.3190±0.0151

表4

表5

六种算法在12个数据集上的缺省实验结果（排序损失）"

Datasets	r	GLOCAL	LRMML	MSWL	LSML	JLCLS	WSMDC
Arts	0.1	0.1466±0.0064	0.1244±0.0045	0.1372±0.0043	0.1539±0.0068	0.1537±0.0044	0.1259±0.0060
	0.3	0.1448±0.0071	0.1464±0.0074	0.1471±0.0037	0.1748±0.0044	0.1452±0.0073	0.1458±0.0079
	0.5	0.1446±0.0058	0.1638±0.0053	0.1643±0.0083	0.2130±0.0075	0.1634±0.0053	0.1666±0.0097
	0.7	0.1466±0.0052	0.1706±0.0038	0.1904±0.0067	0.2441±0.0056	0.1917±0.0067	0.1994±0.0091
Birds	0.1	0.1164±0.0137	0.0933±0.0064	0.1099±0.0166	0.0964±0.0044	0.0945±0.0148	0.0878±0.0179
	0.3	0.1074±0.0060	0.1087±0.0095	0.1101±0.0088	0.1207±0.0155	0.1191±0.0152	0.1088±0.0092
	0.5	0.1200±0.0070	0.1268±0.0099	0.1293±0.0183	0.1406±0.0222	0.1358±0.0170	0.1128±0.0195
	0.7	0.1349±0.0124	0.1568±0.0098	0.1496±0.0280	0.1554±0.0172	0.1637±0.0276	0.1410±0.0117
Computers	0.1	0.1027±0.0259	0.0983±0.0026	0.1035±0.0043	0.1106±0.0071	0.1120±0.0107	0.0828±0.0091
	0.3	0.1305±0.0024	0.1134±0.0042	0.1142±0.0052	0.1344±0.0062	0.1351±0.0052	0.1007±0.0075
	0.5	0.1304±0.0026	0.1505±0.0053	0.1286±0.0118	0.1529±0.0033	0.1582±0.0037	0.1154±0.0094
	0.7	0.1358±0.0031	0.1853±0.0072	0.1475±0.0106	0.1990±0.0058	0.1955±0.0117	0.1382±0.0088
Entertainment	0.1	0.1194±0.0358	0.1730±0.0022	0.1142±0.0085	0.1272±0.0039	0.1268±0.0045	0.1007±0.0039
	0.3	0.1517±0.0034	0.1289±0.0016	0.1236±0.0084	0.1492±0.0080	0.1521±0.0046	0.1164±0.0077
	0.5	0.1562±0.0022	0.1339±0.0036	0.1385±0.0109	0.1738±0.0072	0.1744±0.0072	0.1352±0.0101
	0.7	0.1595±0.0028	0.1553±0.0038	0.1569±0.0049	0.2168±0.0122	0.2231±0.0066	0.1618±0.0072
Health	0.1	0.0647±0.0204	0.0662±0.0030	0.0622±0.0033	0.0743±0.0037	0.0766±0.0039	0.0564±0.0051
	0.3	0.0865±0.0009	0.0808±0.0042	0.0672±0.0025	0.0905±0.0034	0.0936±0.0034	0.0668±0.0023
	0.5	0.0857±0.0020	0.0981±0.0045	0.0793±0.0028	0.1153±0.0062	0.1124±0.0049	0.0752±0.0047
	0.7	0.0841±0.0009	0.1353±0.0034	0.0993±0.0031	0.1525±0.0073	0.1475±0.0082	0.0922±0.0050
Image	0.1	0.2085±0.0278	0.2279±0.0353	0.1992±0.0183	0.1874±0.0143	0.1976±0.0279	0.1897±0.0252
	0.3	0.2294±0.0073	0.2483±0.0357	0.2197±0.0205	0.1989±0.0249	0.2038±0.0260	0.1996±0.0415
	0.5	0.2354±0.0108	0.2310±0.0360	0.2431±0.0329	0.2128±0.0260	0.2086±0.0172	0.2089±0.0299
	0.7	0.2644±0.0132	0.2953±0.0266	0.2765±0.0373	0.2228±0.0429	0.2264±0.0248	0.2264±0.0297
Medical	0.1	0.0239±0.0074	0.0202±0.0062	0.1688±0.0146	0.0227±0.0056	0.0247±0.0037	0.0148±0.0050
	0.3	0.0254±0.0022	0.0282±0.0068	0.1494±0.1934	0.0340±0.0116	0.0349±0.0053	0.0303±0.0099
	0.5	0.0260±0.0035	0.0489±0.0091	0.1914±0.2094	0.0463±0.0100	0.0488±0.0059	0.0387±0.0167
	0.7	0.0375±0.0057	0.0836±0.0099	0.2065±0.1334	0.0818±0.0067	0.0834±0.0103	0.0602±0.0190
Recreation	0.1	0.1513±0.0381	0.1492±0.0040	0.1518±0.0049	0.1604±0.0056	0.1591±0.0058	0.1347±0.0082
	0.3	0.1890±0.0018	0.1584±0.0039	0.1633±0.0058	0.1900±0.0055	0.1866±0.0056	0.1520±0.0082
	0.5	0.1907±0.0052	0.1788±0.0051	0.1762±0.0056	0.2192±0.0080	0.2128±0.0055	0.1790±0.0099
	0.7	0.2038±0.0048	0.1976±0.0034	0.2005±0.0056	0.2504±0.0101	0.2544±0.0051	0.2092±0.0142
Reference	0.1	0.0873±0.0300	0.0943±0.0022	0.0944±0.0024	0.1061±0.0044	0.1072±0.0045	0.0782±0.0046
	0.3	0.1243±0.0047	0.1149±0.0009	0.1040±0.0037	0.1356±0.0070	0.1319±0.0065	0.1012±0.0080
	0.5	0.1184±0.0038	0.1453±0.0068	0.1208±0.0060	0.1597±0.0045	0.1629±0.0154	0.1178±0.0079
	0.7	0.1206±0.0029	0.1852±0.0036	0.1422±0.0070	0.2030±0.0079	0.2036±0.0055	0.1428±0.0089
Society	0.1	0.1434±0.0371	0.1509±0.0061	0.1401±0.0069	0.1676±0.0062	0.1636±0.0058	0.1361±0.0084
	0.3	0.1817±0.0009	0.1706±0.0066	0.2110±0.1214	0.1893±0.0043	0.1912±0.0043	0.1567±0.0051
	0.5	0.1820±0.0025	0.1989±0.0038	0.2254±0.1197	0.2115±0.0076	0.2161±0.0050	0.1715±0.0112
	0.7	0.1860±0.0035	0.2328±0.0061	0.3058±0.1382	0.2467±0.0030	0.2491±0.0044	0.1960±0.0131
Science	0.1	0.1310±0.0372	0.1300±0.0086	0.1285±0.0037	0.1485±0.0075	0.1496±0.0024	0.1105±0.0092
	0.3	0.1652±0.0023	0.1560±0.0094	0.1774±0.0087	0.1733±0.0042	0.1768±0.0030	0.1356±0.0109
	0.5	0.1684±0.0027	0.1795±0.0103	0.2172±0.1121	0.2088±0.0089	0.2094±0.0063	0.1536±0.0058
	0.7	0.1740±0.0026	0.2003±0.0171	0.2873±0.1389	0.2623±0.0087	0.2529±0.0066	0.1920±0.0142
Social	0.1	0.0709±0.0259	0.0746±0.0056	0.0644±0.0058	0.0830±0.0043	0.0839±0.0049	0.0595±0.0074
	0.3	0.0985±0.0010	0.0935±0.0053	0.0757±0.0059	0.1038±0.0052	0.1048±0.0050	0.0723±0.0071
	0.5	0.0957±0.0016	0.1187±0.0036	0.0863±0.0058	0.1257±0.0019	0.1278±0.0035	0.0845±0.0070
	0.7	0.0969±0.0035	0.1565±0.0044	0.1089±0.0062	0.1662±0.0116	0.1672±0.0108	0.1038±0.0088

表5

表6

六种算法在12个数据集上的缺省实验结果（覆盖率）"

Datasets	r	GLOCAL	LRMML	MSWL	LSML	JLCLS	WSMDC
Arts	0.1	0.2168±0.0065	0.2117±0.0086	0.1990±0.0052	0.2292±0.0080	0.2281±0.0083	0.1965±0.0084
	0.3	0.2129±0.0123	0.2207±0.0098	0.2105±0.0052	0.2512±0.0043	0.2177±0.0132	0.2194±0.0112
	0.5	0.2115±0.0073	0.2405±0.0076	0.2314±0.0110	0.2926±0.0063	0.2406±0.0080	0.2434±0.0157
	0.7	0.2123±0.0087	0.2445±0.0044	0.2643±0.0107	0.3259±0.0067	0.2715±0.0072	0.2783±0.0075
Birds	0.1	0.1727±0.0186	0.1447±0.0164	0.1656±0.0205	0.1478±0.0120	0.1478±0.0225	0.1369±0.0248
	0.3	0.1691±0.0063	0.1662±0.0166	0.1616±0.0165	0.1789±0.0157	0.1771±0.0213	0.1647±0.0187
	0.5	0.1786±0.0054	0.1815±0.0161	0.1865±0.0285	0.1985±0.0210	0.1902±0.0125	0.1675±0.0280
	0.7	0.1945±0.0147	0.2140±0.0170	0.2164±0.0354	0.2178±0.0194	0.2189±0.0296	0.1971±0.0172
Computers	0.1	0.1325±0.0327	0.1439±0.0035	0.1308±0.0006	0.1587±0.0105	0.1611±0.0138	0.1238±0.0108
	0.3	0.1680±0.0020	0.1629±0.0041	0.1499±0.0057	0.1889±0.0064	0.1876±0.0096	0.1488±0.0098
	0.5	0.1674±0.0031	0.2055±0.0047	0.1631±0.0145	0.2094±0.0043	0.2144±0.0015	0.1684±0.0119
	0.7	0.1747±0.0042	0.2414±0.0072	0.1878±0.0110	0.2572±0.0074	0.2550±0.0161	0.1954±0.0072
Entertainment	0.1	0.1601±0.0368	0.1615±0.0038	0.1510±0.0082	0.1737±0.0063	0.1734±0.0073	0.1435±0.0052
	0.3	0.1940±0.0024	0.1744±0.0052	0.1627±0.0109	0.1969±0.0083	0.1990±0.0044	0.1618±0.0118
	0.5	0.1976±0.0020	0.1790±0.0065	0.1795±0.0129	0.2223±0.0088	0.2230±0.0091	0.1835±0.0112
	0.7	0.1993±0.0027	0.2024±0.0045	0.2012±0.0041	0.2665±0.0146	0.2727±0.0058	0.2100±0.0090
Health	0.1	0.1145±0.0299	0.1271±0.0029	0.1220±0.0054	0.1368±0.0066	0.1413±0.0072	0.1135±0.0093
	0.3	0.1499±0.0011	0.1463±0.0052	0.1304±0.0045	0.1588±0.0056	0.1605±0.0063	0.1267±0.0066
	0.5	0.1460±0.0044	0.1679±0.0027	0.1464±0.0038	0.1883±0.0089	0.1831±0.0043	0.1398±0.0089
	0.7	0.1405±0.0011	0.2108±0.0053	0.1635±0.0028	0.2270±0.0112	0.2225±0.0120	0.1616±0.0096
Image	0.1	0.2200±0.0256	0.2330±0.0255	0.2110±0.0143	0.2023±0.0133	0.2107±0.0249	0.2053±0.0206
	0.3	0.2408±0.0054	0.2503±0.0230	0.2273±0.0299	0.2110±0.0291	0.2170±0.0335	0.2133±0.0365
	0.5	0.2450±0.0080	0.2370±0.0240	0.2460±0.0248	0.2233±0.0273	0.2203±0.0148	0.2200±0.0261
	0.7	0.2714±0.0118	0.2857±0.0138	0.2703±0.0333	0.2307±0.0311	0.2333±0.0220	0.2320±0.0265
Medical	0.1	0.0347±0.0078	0.0325±0.0087	0.1660±0.0244	0.0363±0.0079	0.0391±0.0066	0.0251±0.0064
	0.3	0.0378±0.0027	0.0428±0.0101	0.1698±0.2055	0.0519±0.0154	0.0519±0.0080	0.0440±0.0147
	0.5	0.0388±0.0043	0.0703±0.0111	0.2120±0.2228	0.0637±0.0121	0.0653±0.0088	0.0556±0.0201
	0.7	0.0526±0.0071	0.1041±0.0131	0.2271±0.1367	0.1015±0.0115	0.1047±0.0120	0.0813±0.0238
Recreation	0.1	0.1927±0.0419	0.1989±0.0062	0.1925±0.0071	0.2126±0.0065	0.2113±0.0097	0.1845±0.0086
	0.3	0.2346±0.0013	0.2086±0.0073	0.2059±0.0051	0.2424±0.0084	0.2393±0.0091	0.2028±0.0087
	0.5	0.2361±0.0054	0.2288±0.0051	0.2186±0.0049	0.2725±0.0067	0.2655±0.0105	0.2317±0.0110
	0.7	0.2481±0.0037	0.2463±0.0043	0.2454±0.0087	0.3021±0.0105	0.3075±0.0060	0.2632±0.0139
Reference	0.1	0.0997±0.0346	0.1186±0.0045	0.1122±0.0041	0.1316±0.0040	0.1331±0.0060	0.1015±0.0059
	0.3	0.1436±0.0065	0.1397±0.0020	0.1219±0.0061	0.1611±0.0090	0.1578±0.0064	0.1258±0.0078
	0.5	0.1510±0.0185	0.1708±0.0071	0.1399±0.0082	0.1853±0.0048	0.1884±0.0170	0.1426±0.0099
	0.7	0.1682±0.0386	0.2108±0.0037	0.1634±0.0098	0.2273±0.0068	0.2277±0.0064	0.1680±0.0094
Society	0.1	0.2227±0.0428	0.2381±0.0083	0.2180±0.0103	0.2556±0.0089	0.2516±0.0045	0.2204±0.0121
	0.3	0.2673±0.0016	0.2590±0.0096	0.2864±0.1100	0.2802±0.0038	0.2824±0.0056	0.2437±0.0078
	0.5	0.2673±0.0034	0.2899±0.0073	0.3022±0.1077	0.3029±0.0098	0.3059±0.0053	0.2599±0.0163
	0.7	0.2680±0.0030	0.3207±0.0083	0.3861±0.1258	0.3352±0.0045	0.3375±0.0055	0.2851±0.0160
Science	0.1	0.1754±0.0385	0.1798±0.0112	0.1711±0.0047	0.2000±0.0043	0.2015±0.0055	0.1557±0.0136
	0.3	0.2114±0.0015	0.2098±0.0131	0.2322±0.0075	0.2303±0.0075	0.2317±0.0066	0.1872±0.0118
	0.5	0.2129±0.0024	0.2344±0.0145	0.2665±0.1147	0.2644±0.0098	0.2672±0.0068	0.2080±0.0062
	0.7	0.2174±0.0024	0.2576±0.0222	0.3393±0.1442	0.3197±0.0108	0.3126±0.0078	0.2497±0.0137
Social	0.1	0.0980±0.0335	0.1081±0.0075	0.0905±0.0067	0.1189±0.0065	0.1186±0.0058	0.0886±0.0108
	0.3	0.1341±0.0014	0.1297±0.0072	0.1056±0.0088	0.1396±0.0047	0.1415±0.0060	0.1039±0.0082
	0.5	0.1305±0.0025	0.1566±0.0056	0.1197±0.0071	0.1636±0.0014	0.1653±0.0045	0.1185±0.0103
	0.7	0.1303±0.0037	0.1958±0.0054	0.1464±0.0076	0.2061±0.0122	0.2051±0.0108	0.1411±0.0105

表6

图2

图3

表7

每个评价指标的弗里德曼检验值FF和临界值"

评价指标	$F F$	临界值
HL	49.1169	2.252
AP	33.6400
OE	28.9474
RL	29.0327
CV	32.0061

表7

图4

参考文献 28

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Datasets	Instances	Features	Labels	Cardinality	Domains
Arts^a	5000	462	26	1.636	Text
Birds^b	645	260	20	1.471	Audio
Computers^a	5000	681	33	1.508	Text
Entertainment^a	5000	640	21	1.640	Text
Health^a	5000	612	32	1.612	Text
Image^c	2000	294	5	1.236	Image
Medical^b	979	1449	45	1.215	Text
Recreation^a	5000	606	22	1.606	Text
Reference^a	5000	793	33	1.793	Text
Society^a	5000	636	27	1.692	Text
Science^a	5000	743	40	1.451	Text
Social^a	5000	1047	39	1.283	Text

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基于多维相关性的弱类属属性学习

Weak⁃label⁃specific features learning based on multidimensional correlation

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