融合标签结构依赖性的标签分布学习

doi:10.13232/j.cnki.jnju.2020.04.010

南京大学学报(自然科学版) ›› 2020, Vol. 56 ›› Issue (4): 524–532.doi: 10.13232/j.cnki.jnju.2020.04.010

融合标签结构依赖性的标签分布学习

黄雨婷¹,徐媛媛¹,张恒汝¹(),闵帆^1,²

^1.西南石油大学计算机科学学院，成都，610500
^2.西南石油大学人工智能研究院，成都，610500

收稿日期:2020-06-20 出版日期:2020-07-30 发布日期:2020-08-06
通讯作者: 张恒汝 E-mail:zhanghrswpu@163.com
基金资助:
国家自然科学基金(61902328);四川省科技厅应用基础研究(2019YJ0314);四川省青年科技创新研究团队项目(2019JDTD0017);四川省大学生创新创业训练计划(S20190615090);西南石油大学本科课程教学改革研究项目(X2018KZ077)

Label distribution learning by exploiting structural label dependency

Yuting Huang¹,Yuanyuan Xu¹,Hengru Zhang¹(),Fan Min^1,²

^1.School of Computer Science，Southwest Petroleum University，Chengdu，610500，China
^2.Institute for Artificial Intelligence，Southwest Petroleum University，Chengdu，610500，China

Received:2020-06-20 Online:2020-07-30 Published:2020-08-06
Contact: Hengru Zhang E-mail:zhanghrswpu@163.com

摘要/Abstract

摘要：

针对现有标签分布学习（Label Distribution Learning，LDL）算法较少考虑标签间关联性的问题，提出一种融合结构化标签依赖性的LDL算法.算法分为扩展、学习和恢复三个阶段：在扩展阶段，结合成对标签之间的关联性，构建结构化标签依赖性；在学习阶段，结合该依赖性，构建学习框架；在恢复阶段，利用最小二乘法求解超定方程组以预测标签分布.与七种常用的标签分布学习算法相比，在八个开放数据集上进行实验，提出的算法在Euclidean距离、S?rensen距离、Squard χ²距离、Kullback?Leibler散度、Intersection相似度和Fidelity相似度六个主流评估指标上明显占优.

关键词: 标签分布学习, 标签扩展, 标签恢复, 标签结构依赖性, 有限存储拟牛顿法

Abstract:

Aiming at the problem that the existing Label Distribution Learning (LDL) algorithms rarely consider the correlation between labels，an LDL algorithm that combines structured label dependencies is proposed. The algorithm is divided into three stages: expansion，learning and recovery. In the expansion stage，the association between the pair of labels is combined to construct a structured label dependency. In the learning stage，combining this dependency，a learning framework is constructed. In the recovery stage，the least square method is used to solve the overdetermined equations to predict the label distribution. Compared with the seven popular label distribution learning algorithms，experiments are conducted on eight open datasets. Our method is obviously superior at Euclidean distance，S?rensen distance，Squard χ² distance，Kullback?Leibler divergence，Intersection similarity and Fidelity similarity.

Key words: label distribution learning, label expansion, label recovery, structural label dependencies, the limited?memory quasi?Newton method

中图分类号:

TP391

黄雨婷,徐媛媛,张恒汝,闵帆. 融合标签结构依赖性的标签分布学习[J]. 南京大学学报(自然科学版), 2020, 56(4): 524–532.

Yuting Huang,Yuanyuan Xu,Hengru Zhang,Fan Min. Label distribution learning by exploiting structural label dependency[J]. Journal of Nanjing University(Natural Sciences), 2020, 56(4): 524–532.

图/表 13

图1

表1

表2

表3

LDL算法的评价指标"

Measure	Formula
Euclidean^[24] ↓	$d i s = ∑ j = 1 c (p j - q j) 2$
S?rensen^[25] ↓	$d i s = ∑ j = 1 c p j - q j ∑ j = 1 c p j + q j$
Squard χ^2[26] ↓	$d i s = ∑ j = 1 c (p j - q j) 2 p j + q j$
Kullback?Leibler (KL)^[13] ↓	$d i s = ∑ j = 1 c p i l n p i d i$
Intersection^[27] ↑	$s i m = m i n (p j - q j)$
Fidelity^[28] ↑	$s i m = ∑ j = 1 c p j q j$

表3

表4

表5

表6

表7

表8

表9

表10

表11

表12

参考文献 28

1	Geng X，Smith?Miles K，Zhou Z H. Facial age estimation by learning from label distributions∥Proceedings of the 24^th AAAI Conference on Artificial Intelligence. Atlanta，GA，USA：AAAI，2010：451-456.
2	Geng X. Label distribution learning. IEEE Transactions on Knowledge and Data Engineering，2016，28(7)：1734-1748.
3	Yang X，Gao B B，Xing C，et al. Deep label distribution learning for apparent age estimation∥Proceedings of the 2015 IEEE International Conference on Computer Vision Workshops. Santiago，Chile：IEEE，2015：102-108.
4	Geng X，Ling M G. Soft video parsing by label distribution learning∥Proceedings of the 31^th AAAI Conference on Artificial Intelligence. San Francisco，CA，USA：AAAI Press，2017：1331-1337.
5	Geng X，Wang Q，Xia Y. Facial age estimation by adaptive label distribution learning∥Proceedings of the 22^nd International Conference on Pattern Recognition. Stockholm，Sweden：IEEE，2014：4465-4470.
6	Geng X，Yin C，Zhou Z H. Facial age estimation by learning from label distributions. IEEE Transactions on Pattern Analysis and Machine Intelligence，2013，35(10)：2401-2412.
7	Zhang M L，Zhang K. Multi?label learning by exploiting label dependency∥Proceedings of the 16^th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Washington DC，USA：ACM，2010：999-1008.
8	Wei B，Kwok J T Y. Multilabel classification with label correlations and missing labels∥Proceedings of the 28^th AAAI Conference on Artificial Intelligence. Québec City,Canada，2014：1680-1686.
9	Huang S J，Zhou Z H. Multi∥label learning by exploiting label correlations locally∥Proceedings of the 26^th AAAI Conference on Artificial Intelligence. Toronto，Canada：AAAI，2012：949-955.
10	Zhou D Y，Zhang X，Zhou Y，et al. Emotion distribution learning from texts∥Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing. Austin，TX，USA：Associa?tion for Computational Linguistics，2016：638-647.
11	Zhang Z X，Wang M，Geng X. Crowd counting in public video surveillance by label distribution learning. Neurocomputing，2015，166：151-163.
12	Jégou H，Douze M，Schmid C. Hamming embedding and weak geometric consistency for large scale image search∥Proceedings of the 10^th European Conference on Computer Vision. Springer Berlin Heidelberg，2008：304-317.
13	Kullback S，Leibler R A. On information and sufficiency. Annals of Mathematical Statistics，1951，22(1)：79-86.
14	Zheng X，Jia X Y，Li W W. Label distribution learning by exploiting sample correlations locally∥Proceedings of the 32^nd AAAI Conference on Artificial Intelligence. New Orleans，LA，USA：AAAI，2018：4556-4563.
15	Berger A L，Pietra V J D，Pietra S A D. A maximum entropy approach to natural language processing. Computational Linguistics，1996，22(1)：39-71.
16	Wang J，Geng X. Classification with label distribution learning∥Proceedings of the 28^th International Joint Conference on Artificial Intelligence. Macao，China：International Joint Conferences on Artificial Intelligence Organization，2019：3712-3718.
17	Jia X Y，Li W W，Liu J Y，et al. Label distribution learning by exploiting label correlations∥Proceedings of the 32^nd AAAI Conference on Artificial Intelligence. New Orleans，LA，USA：AAAI，2018：3310-3317.
18	Xu C D，Geng X. Hierarchical classification based on label distribution learning∥Proceedings of the 33^rd AAAI Conference on Artificial Intelligence. Honolulu，HI，USA：AAAI，2019：5533-5540.
19	Ren T T，Jia X Y，Li W W，et al. Label distribution learning with label correlations via low?rank approximation∥Proceedings of the 28^th International Joint Conference on Artificial Intelligence. Macao，China：International Joint Conferences on Artificial Intelligence Organization，2019：3325-3331.
20	Ren T T，Jia X Y，Li W W，et al. Label distribution learning with label?specific features∥Proceedings of the 28^th International Joint Conference on Artificial Intelligence. Macao，China：International Joint Conferences on Artificial Intelligence Organization，2019：3318-3324.
21	Mencía E L，Park S H，Fürnkranz J. Efficient voting prediction for pairwise multilabel classification. Neurocomputing，2010，73(7-9)：1164-1176.
22	Yuan Y X. A modified BFGS algorithm for unconstrained optimization. IMA Journal of Numerical Analysis，1991，11(3)：325-332.
23	Eisen M B，Spellman P T，Brown P O，et al. Cluster analysis and display of genome?wide expression patterns. The National Academy of Sciences of the United States of America，1998，95(25)：14863-14868.
24	Danielsson P E. Euclidean distance mapping. Computer Graphics and Image Processing，1980，14(3)：227-248.
25	S?renson T. A method of establishing groups of equal amplitudes in plant sociology based on similarity of species content and its application to analyses of the vegetation on Danish commons. Kongelige Danske Videnskabernes Selskab，Biologiske Skrifter，1948，5(4)：1-34.
26	Gavin D G，Oswald W W，Wahl E R，et al. A statistical approach to evaluating distance metrics and analog assignments for pollen records. Quaternary Research，2003，60(3)：356-367.
27	Duda R O，Hart P E，Stork D G. Pattern classification. The 2nd Edition. New York：Wiley?Interscience，2000，654.
28	Cha S H. Comprehensive survey on distance/similarity measures between probability density functions. International Journal of Mathematical Models and Methods in Applied Sciences，2007，1(4)：300-307.
	附录
	本文使用L?BFGS方法对目标函数T(θ)进行求解，对应当前迭代次的特征-标签矩阵的二阶泰勒展开为：

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Notations	Meaning
?^q	q?dimensional input space
Y	The complete set of labels
S	The training set
x_i	The i?th instance
d_i	The label distribution associated with x_i
p_i	The predicted label distribution associated with x_i
x_ir	The r?th feature of x_i
d_ij	The description degree of the j?th label to x_i
θ	The distance?mapping model
X	The instance matrix
D	The label distribution matrix

Dataset	Instance	Feature	Label
Alpha	2465	24	18
Cdc	2465	24	15
Elu	2465	24	14
Diau	2465	24	7
Heat	2465	24	6
Spo	2465	24	6
Cold	2465	24	4
Dtt	2465	24	4

Algorithm	Settings
SD?LDL	λ=0.1
PT?Bayes	极大似然估计
PT?SVM	C=1.0，Γ=0.01
AA?kNN	k=5
AA?BP	n=60
IIS?LLD	-
BFGS?LLD	c₁=10^-4，c₂=0.9
EDL	-

	Euclidean↓	S?rensen↓	Squard χ²↓	KL↓	Intersection↑	Fidelity↑
SD?LDL	0.0236±0.0003(1)	0.0386±0.0003(1)	0.0057±0.0003(1)	0.0056±0.0002(1)	0.9614±0.0005(1)	0.9986±0.0003(1)
PT?Bayes	0.2298±0.0124(8)	0.3485±0.0154(8)	0.3879±0.0277(8)	0.5607±0.0710(8)	0.6515±0.0154(8)	0.8777±0.0100(8)
PT?SVM	0.0276±0.0006(5)	0.0445±0.0009(5)	0.0071±0.0003(5)	0.0071±0.0003(5)	0.9565±0.0009(5)	0.9981±0.0001(5)
AA?kNN	0.0279±0.0006(6)	0.0449±0.0012(6)	0.0073±0.0003(6)	0.0074±0.0004(7)	0.9561±0.0012(6)	0.9980±0.0001(6)
AA?BP	0.0871±0.0070(7)	0.1475±0.0131(7)	0.1399±0.0501(7)	0.0073±0.0058(6)	0.8538±0.0117(7)	0.9839±0.0017(7)
IIS?LLD	0.269±0.0004(4)	0.0429±0.0012(3)	0.0069±0.0004(4)	0.0069±0.0004(4)	0.9571±0.0012(3)	0.9983±0.0011(4)
BFGS?LLD	0.0251±0.0004(2)	0.0408±0.0011(2)	0.0063±0.0008(2)	0.0063±0.0004(2)	0.9574±0.0009(2)	0.9985±0.0011(2)
EDL	0.0260±0.0011(3)	0.0429±0.0022(4)	0.0067±0.0006(3)	0.0068±0.0006(3)	0.9570±0.0022(4)	0.9983±0.0002(3)

	Euclidean↓	S?rensen↓	Squard χ²↓	KL↓	Intersection↑	Fidelity↑
SD?LDL	0.0282±0.0004(1)	0.0428±0.0008(1)	0.0073±0.0005(3)	0.0071±0.0001(2)	0.9572±0.0004(1)	0.9983±0.0003(1)
PT?Bayes	0.2399±0.0103(8)	0.3455±0.0111(8)	3853±0.0210(8)	0.5374±0.0503(8)	0.6545±0.0111(8)	0.8778±0.0075(8)
PT?SVM	0.0298±0.0007(4)	0.0458±0.0012(5)	0.0077±0.0004(5)	0.0076±0.0004(5)	0.9554±0.0012(5)	0.9980±0.0001(5)
AA?kNN	0.0301±0.0009(6)	0.0462±0.0013(6)	0.0080±0.0004(6)	0.0079±0.0004(6)	0.9538±0.0013(6)	0.9980±0.0001(5)
AA?BP	0.0769±0.0081(7)	0.1192±0.0109(7)	0.0842±0.0281(7)	0.0511±0.0121(7)	0.8829±0.0134(7)	0.9879±0.0051(7)
IIS?LLD	0.0290±0.0010(5)	0.0445±0.0015(3)	0.0073±0.0005(4)	0.0072±0.0005(4)	0.9556±0.0015(4)	0.9982±0.0012(4)
BFGS?LLD	0.0284±0.0011(3)	0.0449±0.0016(4)	0.0070±0.0004(1)	0.0070±0.0005(1)	0.9558±0.0016(3)	0.9983±0.0011(2)
EDL	0.0283±0.0006(2)	0.0429±0.0008(2)	0.0072±0.0004(2)	0.0072±0.0004(3)	0.9571±0.0008(2)	0.9982±0.0001(3)

融合标签结构依赖性的标签分布学习

Label distribution learning by exploiting structural label dependency

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图/表 13

参考文献 28

相关文章 15

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	Euclidean↓	S?rensen↓	Squard χ²↓	KL↓	Intersection↑	Fidelity↑
SD?LDL	0.0282±0.0004(1)	0.0423±0.0006(1)	0.0064±0.0005(1)	0.0063±0.0003(1)	0.9577±0.0006(1)	0.9984±0.0003(1)
PT?Bayes	0.2588±0.0203(8)	0.3558±0.0198(8)	0.4081±0.0408(8)	0.6062±0.1030(8)	0.6442±0.0198(8)	0.8689±0.0156(8)
PT?SVM	0.0293±0.0008(3)	0.0438±0.0012(3)	0.0068±0.0005(3)	0.0068±0.0005(3)	0.9562±0.0012(3)	0.9983±0.0002(3)
AA?kNN	0.0297±0.0010(4)	0.0443±0.0014(4)	0.0071±0.0006(5)	0.0071±0.0006(5)	0.9557±0.0014(4)	0.9982±0.0002(4)
AA?BP	0.0733±0.0037(7)	0.1100±0.0048(7)	0.0731±0.0026(7)	0.0481±0.0061(7)	0.8891±0.0064(7)	0.9890±0.0025(7)
IIS?LLD	0.0307±0.0009(5)	0.0472±0.0014(5)	0.0071±0.0004(4)	0.0071±0.0004(4)	0.9528±0.0015(6)	0.9982±0.0035(5)
BFGS?LLD	0.0308±0.0009(6)	0.0475±0.0012(6)	0.0075±0.0004(6)	0.0073±0.0003(6)	0.9552±0.0017(5)	0.9979±0.0009(6)
EDL	0.0289±0.0005(2)	0.0431±0.0008(2)	0.0067±0.0003(2)	0.0067±0.0003(2)	0.9569±0.0007(2)	0.9983±0.0001(2)

	Euclidean↓	S?rensen↓	Squard χ²↓	KL↓	Intersection↑	Fidelity↑
SD?LDL	0.0602±0.0009(5)	0.0660±0.0009(5)	0.0160±0.0015(5)	0.0155±0.0011(5)	0.9340±0.0009(5)	0.9959±0.0008(5)
PT?Bayes	0.4027±0.0183(8)	0.4177±0.0170(8)	0.5280±0.0281(8)	0.8512±0.0772(8)	0.5823±0.0170(8)	0.8230±0.0107(8)
PT?SVM	0.0628±0.0037(6)	0.0686±0.0041(6)	0.0169±0.0018(6)	0.0167±0.0017(6)	0.9314±0.0041(6)	0.9957±0.0004(6)
AA?kNN	0.0567±0.0019(3)	0.0622±0.0022(3)	0.0145±0.0011(3)	0.0145±0.0010(3)	0.9378±0.0022(3)	0.9963±0.0003(3)
AA?BP	0.0802±0.0051(7)	0.0863±0.0059(7)	0.0276±0.0013(7)	0.0291±0.0069(7)	0.9142±0.0067(7)	0.9929±0.0031(7)
IIS?LLD	0.0539±0.0031(2)	0.0593±0.0032(2)	0.0144±0.0014(2)	0.0141±0.0013(2)	0.9407±0.0003(2)	0.9964±0.0036(2)
BFGS?LLD	0.0444±0.0022(1)	0.0476±0.0023(1)	0.0089±0.0008(1)	0.0083±0.0009(1)	0.9513±0.0027(1)	0.9978±0.0031(1)
EDL	0.0597±0.0010(4)	0.0653±0.0010(4)	0.0158±0.0005(4)	0.0155±0.0005(4)	0.9347±0.0010(4)	0.9960±0.0002(4)

	Euclidean↓	S?rensen↓	Squard χ²↓	KL↓	Intersection↑	Fidelity↑
SD?LDL	0.0602±0.0009(1)	0.0607±0.0008(1)	0.0131±0.0012(1)	0.0130±0.0008(1)	0.9393±0.0008(1)	0.9967±0.0008(1)
PT?Bayes	0.4500±0.0231(8)	0.4354±0.0193(8)	0.5450±0.0361(8)	0.8678±0.1198(8)	0.5646±0.0193(8)	0.8180±0.0131(8)
PT?SVM	0.0625±0.0023(3)	0.0627±0.0022(2)	0.0141±0.0010(2)	0.0141±0.0010(2)	0.9373±0.0022(3)	0.9964±0.0003(2)
AA?kNN	0.0624±0.0020(2)	0.0632±0.0018(3)	0.0141±0.0010(2)	0.0141±0.0010(2)	0.9368±0.0018(2)	0.9964±0.0003(2)
AA?BP	0.0793±0.0068(7)	0.0822±0.0071(7)	0.0235±0.0047(7)	0.0246±0.0053(7)	0.9198±0.0061(7)	0.9937±0.0028(7)
IIS?LLD	0.0703±0.0036(5)	0.0692±0.0033(5)	0.0182±0.0016(5)	0.0182±0.0016(5)	0.9309±0.0033(5)	0.9954±0.0042(6)
BFGS?LLD	0.0728±0.0031(6)	0.0791±0.0029(6)	0.0188±0.0016(6)	0.0186±0.0015(6)	0.9304±0.0034(6)	0.9961±0.0048(5)
EDL	0.0629±0.0016(4)	0.0633±0.0017(4)	0.0143±0.0008(4)	0.0143±0.0008(4)	0.9366±0.0017(4)	0.9963±0.0003(4)

	Euclidean↓	S?rensen↓	Squard χ²↓	KL↓	Intersection↑	Fidelity↑
SD?LDL	0.0835±0.0012(2)	0.0860±0.0011(2)	0.0265±0.0014(3)	0.0266±0.0011(3)	0.9140±0.0011(3)	0.9932±0.0006(4)
PT?Bayes	0.4038±0.0162(8)	0.4030±0.0134(8)	0.4972±0.0246(8)	0.7172±0.0840(8)	0.5971±0.0134(8)	0.8342±0.0095(8)
PT?SVM	0.0878±0.0019(5)	0.0893±0.0022(5)	0.0280±0.0015(5)	0.0284±0.0015(5)	0.9107±0.0022(5)	0.9929±0.0004(5)
AA?kNN	0.0879±0.0030(6)	0.0899±0.0024(6)	0.0286±0.0020(6)	0.0286±0.0002(6)	0.9096±0.0034(6)	0.9927±0.0005(6)
AA?BP	0.0979±0.0041(7)	0.1012±0.0038(7)	0.0344±0.0038(7)	0.0359±0.0039(7)	0.8982±0.0037(7)	0.9906±0.0010(7)
IIS?LLD	0.0863±0.0041(4)	0.0861±0.0036(3)	0.0251±0.0036(2)	0.0252±0.0022(2)	0.9139±0.0036(3)	0.9937±0.0005(2)
BFGS?LLD	0.0819±0.0045(1)	0.0833±0.0038(1)	0.0229±0.0019(1)	0.0226±0.0021(1)	0.9168±0.0039(1)	0.9951±0.0007(1)
EDL	0.0843±0.0029(3)	0.0872±0.0029(4)	0.0268±0.0015(4)	0.0269±0.0016(4)	0.9128±0.0028(4)	0.9932±0.0004(3)

	Euclidean↓	S?rensen↓	Squard χ²↓	KL↓	Intersection↑	Fidelity↑
SD?LDL	0.0713±0.0009(1)	0.0619±0.0009(1)	0.0133±0.0019(1)	0.0130±0.0014(1)	0.9381±0.0009(1)	0.9968±0.0014(1)
PT?Bayes	0.5252±0.0224(8)	0.4479±0.0189(8)	0.5873±0.0352(8)	0.9089±0.1042(8)	0.5521±0.0189(8)	0.7991±0.0134(8)
PT?SVM	0.0753±0.0080(4)	0.0654±0.0069(5)	0.0147±0.0033(4)	0.0146±0.0033(4)	0.9346±0.0069(5)	0.9963±0.0008(4)
AA?kNN	0.0724±0.0027(2)	0.0630±0.0024(2)	0.0136±0.0011(2)	0.0136±0.0011(2)	0.9370±0.0024(2)	0.9966±0.0003(3)
AA?BP	0.0838±0.0045(7)	0.0710±0.0027(7)	0178±0.0011(7)	0.0163±0.0030(7)	0.9328±0.0029(7)	0.9952±0.0017(7)
IIS?LLD	0.0767±0.0004(5)	0.0653±0.0034(4)	0.0157±0.0015(6)	0.0155±0.0015(6)	0.9347±0.0034(4)	0.9960±0.0039(6)
BFGS?LLD	0.0745±0.0004(3)	0.0641±0.0035(3)	0.0139±0.0013(3)	0.0143±0.0015(3)	0.9348±0.0035(3)	0.9968±0.0036(2)
EDL	0.0771±0.0018(6)	0.0668±0.0016(6)	0.0154±0.0009(5)	0.0153±0.0009(5)	0.9332±0.0016(6)	0.9961±0.0003(5)

	Euclidean↓	S?rensen↓	Squard χ²↓	KL↓	Intersection↑	Fidelity↑
SD?LDL	0.0495±0.0015(1)	0.0429±0.0013(2)	0.0066±0.0038(2)	0.0063±0.0029(2)	0.9571±0.0013(2)	0.9983±0.0021(3)
PT?Bayes	0.4879±0.0242(8)	0.4156±0.0192(8)	0.5416±0.0438(8)	0.9069±0.1580(8)	0.5844±0.0192(8)	0.8113±0.0186(8)
PT?SVM	0.0516±0.0029(5)	0.0447±0.0024(5)	0.0071±0.0009(6)	0.0071±0.0009(6)	0.9553±0.0024(5)	0.9982±0.0003(5)
AA?kNN	0.0512±0.0019(4)	0.0443±0.0017(4)	0.0071±0.0007(5)	0.0070±0.0007(5)	0.9557±0.0017(4)	0.9982±0.0002(4)
AA?BP	0.0622±0.0032(7)	0.0531±0.0029(7)	0.0097±0.0012(7)	0.0122±0.0037(7)	0.9465±0.0024(7)	0.9969±0.0011(7)
IIS?LLD	0.0535±0.0023(6)	0.0480±0.0023(6)	0.0068±0.0005(3)	0.0068±0.0005(3)	0.9520±0.0023(6)	0.9983±0.0013(2)
BFGS?LLD	0.0495±0.0019(2)	0.0409±0.0017(1)	0.0058±0.0005(1)	0.0054±0.0004(1)	0.9584±0.0023(1)	0.9989±0.0010(1)
EDL	0.0508±0.0022(3)	0.0440±0.0018(3)	0.0069±0.0007(4)	0.0068±0.0008(4)	0.9560±0.0018(3)	0.9982±0.0003(5)

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