Link prediction in directed network based on high-order self-included collaborative filtering

doi:10.11772/j.issn.1001-9081.2021081484

Journal of Computer Applications ›› 2022, Vol. 42 ›› Issue (10): 3060-3068.DOI: 10.11772/j.issn.1001-9081.2021081484

• Data science and technology • Previous Articles Next Articles

Link prediction in directed network based on high-order self-included collaborative filtering

Guangfu CHEN¹^,², Haibo WANG³, Yanping LIAN¹^,²

^1.School of Mathematics and Computer Science，Wuyi University，Wuyishan Fujian 354300，China
^2.Key Laboratory of Cognitive Computing and Intelligent Information Processing of Fujian Education Institutions （Wuyi University），Wuyishan Fujian 354300，China
^3.College of Information Engineering，Hunan University of Science and Engineering，Yongzhou Hunan 425199，China

Received:2021-08-19 Revised:2021-12-03 Accepted:2021-12-08 Online:2022-01-07 Published:2022-10-10
Contact: Guangfu CHEN
About author:CHEN Guangfu， born in 1979， Ph. D. ， lecturer. His research interests include link prediction， network representation.
CHEN Guangfu， born in 1979， Ph. D. ， lecturer. His research interests include link prediction， network representation.
WANG Haibo， born in 1980， M. S. ， lecturer. His research interests include link prediction.
LIAN Yanping， born in 1981， M. S. ， associate professor. His research interests include machine learning， big data.
Supported by:
Research Foundation for Introduction of Talents of Wuyi University(YJ202017)

基于高阶自包含协同过滤的有向网络链路预测

陈广福¹^,², 王海波³, 连雁平¹^,²

^1.武夷学院数学与计算机学院, 福建武夷山 354300
^2.认知计算与智能信息处理福建省高校重点实验室(武夷学院), 福建武夷山 354300
^3.湖南科技学院信息工程学院, 湖南永州 425199

通讯作者: 陈广福
作者简介:第一联系人：陈广福（1979—），男，江西上饶人，讲师，博士，主要研究方向：链路预测、网络表示cgf21st@163.com
王海波（1980—），男，湖南郴州人，讲师，硕士，主要研究方向：链路预测
连雁平（1981—），男，福建莆田人，副教授，硕士，主要研究方向：机器学习、大数据。
基金资助:
武夷学院引进人才科研启动基金资助项目(YJ202017)

Abstract

Abstract:

Aiming at the problem that most existing directed network link prediction methods only focus on the directed local and reciprocal link information and ignore the directed global structure information， a High-order Self-included Collaborative Filtering （HSCF） link prediction framework was proposed. Firstly， random walk method was used to calculate the high-order similarity matrix to preserve the high-order path information of the directed network. Secondly， an HSCF framework was constructed by combining the high-order similarity matrix with collaborative filtering method. Finally， the proposed framework was integrated with four typical directed structure similarity indices including Directed Common Neighbor （DCN）， Directed Adamic-Adar （DAA）， Directed Resource Allocation （DRA） and potential theory （Bifan）， and four directed network prediction indices HSCF-DCN， HSCF-DAA， HSCF-DRA and HSCF-Bifan were proposed on this basis. Compared with the baseline indices on ten real directed networks， the experimental results show that the AUC （Area Under Curve of Receiver Operating Characteristic （ROC）） values of HSCF-DCN， HSCF-DAA， HSCF-DRA and HSCF-Bifan are increased by an average of 8.16%， 8.85%， 9.64% and 10.33% respectively and the F-score values of them are increased by an average of 66.62%， 68.32%， 68.95% and 76.18% respectively.

Key words: directed complex network, link prediction, collaborative filtering, directed structure, random walk

摘要：

针对大部分现存有向网络链路预测方法仅关注有向局部结构及互惠链接信息而忽略有向全局结构的问题，提出高阶自包含协同过滤(HSCF)链路预测框架。首先，利用随机游走方法计算高阶相似度矩阵去保持有向网络的高阶路径信息；其次，将高阶相似度矩阵与协同过滤方法相融合构建HSCF框架；最后，把所提框架分别与有向共同邻居(DCN)、有向Adamic-Adar(DAA)、有向资源分配(DRA)和势能理论Bifan 4个典型有向结构相似度相融合，并由此提出HSCF-DCN、HSCF-DAA、HSCF-DRA和HSCF-Bifan 4个有向网络预测指标。在10个真实有向网络上的实验结果表明，与基准指标相比，HSCF-DCN、HSCF-DAA、HSCF-DRA和HSCF-Bifan的受试者工作特征（ROC）曲线下方面积（AUC）值分别平均提高了8.16%、8.85%、9.64%和10.33%，且F分数值分别平均提高了66.62%、68.32%、68.95%和76.18%。

关键词: 有向复杂网络, 链路预测, 协同过滤, 有向结构, 随机游走

CLC Number:

TP391

Guangfu CHEN, Haibo WANG, Yanping LIAN. Link prediction in directed network based on high-order self-included collaborative filtering[J]. Journal of Computer Applications, 2022, 42(10): 3060-3068.

陈广福, 王海波, 连雁平. 基于高阶自包含协同过滤的有向网络链路预测[J]. 《计算机应用》唯一官方网站, 2022, 42(10): 3060-3068.

Figures/Tables 9

Fig. 1 Process of calculating high-order transition matrix by any directed network

Tab. 1 Topological feature statistics of 10 real directed networks

网络	$N$	$M$	$k m a x i n$	$k m a x o u t$	平均度	稀疏率
SM	3 084	10 412	121	105	6.753 1	0.001 1
CHE	7 301	65 053	140	52	17.823 4	0.001 2
WPL	10 453	140 501	1 228	423	26.882 7	0.001 3
FIG	2 239	6 452	19	14	2.881 6	0.001 3
AG	6 541	51 127	722	86	15.632 2	0.001 1
CAL	9 664	16 150	199	64	1.671 2	0.000 2
OPE	2 939	30 501	236	37	0.438 6	0.003 5
BA	3 783	24 186	398	90	6.393 3	0.001 7
ODL	2 909	18 241	583	47	12.541 4	0.002 2
WV	7 118	103 675	457	93	29.130 6	0.002 1

Tab. 1 Topological feature statistics of 10 real directed networks

网络	$N$	$M$	$k m a x i n$	$k m a x o u t$	平均度	稀疏率
SM	3 084	10 412	121	105	6.753 1	0.001 1
CHE	7 301	65 053	140	52	17.823 4	0.001 2
WPL	10 453	140 501	1 228	423	26.882 7	0.001 3
FIG	2 239	6 452	19	14	2.881 6	0.001 3
AG	6 541	51 127	722	86	15.632 2	0.001 1
CAL	9 664	16 150	199	64	1.671 2	0.000 2
OPE	2 939	30 501	236	37	0.438 6	0.003 5
BA	3 783	24 186	398	90	6.393 3	0.001 7
ODL	2 909	18 241	583	47	12.541 4	0.002 2
WV	7 118	103 675	457	93	29.130 6	0.002 1

Tab. 2 Comparison of AUC under difference indices

指标	数据集										平均值
指标	SM	FIG	OPE	BA	ODL	AG	WV	CHE	CAL	WPL	平均值
DCN	0.892	0.703	0.969	0.837	0.824	0.878	0.921	0.785	0.692	0.915	0.842
DAA	0.877	0.700	0.970	0.838	0.830	0.881	0.925	0.785	0.655	0.914	0.838
DRA	0.896	0.707	0.972	0.836	0.826	0.879	0.924	0.789	0.700	0.916	0.845
Bifan	0.941	0.980	0.964	0.931	0.947	0.968	0.987	0.903	0.951	0.975	0.955
IWR-DCN	0.922	0.704	0.976	0.868	0.927	0.939	0.953	0.904	0.748	0.948	0.889
IWR-DAA	0.904	0.729	0.977	0.868	0.925	0.940	0.950	0.897	0.707	0.951	0.885
IWR-DRA	0.921	0.724	0.979	0.868	0.925	0.937	0.951	0.902	0.730	0.947	0.888
IWR-Bifan	0.969	0.981	0.978	0.959	0.957	0.974	0.979	0.948	0.971	0.972	0.969
Jaccard	0.891	0.705	0.966	0.824	0.829	0.881	0.927	0.786	0.702	0.916	0.843
HPI	0.894	0.705	0.960	0.821	0.825	0.876	0.918	0.788	0.700	0.915	0.840
LP	0.968	0.797	0.984	0.929	0.918	0.960	0.977	0.914	0.814	0.964	0.923
LO	0.857	0.905	0.941	0.767	0.851	0.840	0.876	0.695	0.874	0.903	0.851
HSCF-DCN	0.992	0.924	0.987	0.960	0.957	0.955	0.924	0.943	0.903	0.951	0.950
HSCF-DAA	0.972	0.918	0.992	0.968	0.958	0.974	0.980	0.960	0.861	0.975	0.956
HSCF-DRA	0.992	0.926	0.996	0.976	0.960	0.977	0.972	0.961	0.896	0.978	0.963
HSCF-Bifan	0.987	0.992	0.963	0.944	0.958	0.969	0.981	0.926	0.996	0.969	0.969

Tab. 3 Comparison of F?score under difference indices

指标	数据集										平均值
指标	SM	FIG	OPE	BA	ODL	AG	WV	CHE	CAL	WPL	平均值
DCN	0.339	0.256	0.342	0.201	0.249	0.200	0.216	0.128	0.156	0.389	0.248
DAA	0.412	0.233	0.654	0.451	0.322	0.201	0.541	0.340	0.156	0.522	0.383
DRA	0.536	0.263	0.674	0.467	0.376	0.517	0.590	0.407	0.308	0.567	0.471
Bifan	0.334	0.554	0.537	0.350	0.344	0.360	0.514	0.201	0.276	0.400	0.387
IWR-DCN	0.560	0.313	0.705	0.595	0.625	0.634	0.664	0.599	0.339	0.646	0.568
IWR-DAA	0.615	0.317	0.708	0.611	0.636	0.664	0.687	0.617	0.369	0.671	0.590
IWR-DRA	0.627	0.372	0.719	0.611	0.636	0.665	0.689	0.623	0.405	0.669	0.602
IWR-Bifan	0.701	0.667	0.794	0.803	0.828	0.706	0.724	0.679	0.617	0.812	0.733
Jaccard	0.686	0.366	0.687	0.547	0.614	0.566	0.536	0.376	0.400	0.644	0.542
HPI	0.694	0.396	0.773	0.587	0.587	0.615	0.570	0.431	0.460	0.671	0.578
LP	0.404	0.354	0.642	0.456	0.350	0.423	0.482	0.331	0.201	0.450	0.409
LO	0.602	0.594	0.685	0.619	0.593	0.592	0.600	0.558	0.582	0.654	0.608
HSCF-DCN	0.711	0.616	0.882	0.879	0.836	0.822	0.791	0.855	0.582	0.865	0.784
HSCF-DAA	0.727	0.626	0.886	0.884	0.843	0.835	0.823	0.862	0.563	0.874	0.792
HSCF-DRA	0.747	0.611	0.888	0.885	0.841	0.832	0.822	0.856	0.593	0.871	0.795
HSCF-Bifan	0.792	0.751	0.879	0.874	0.871	0.833	0.827	0.858	0.721	0.879	0.829

Tab. 4 AUC corresponding to different training dataset rate

数据集	训练集比率	DCN	DAA	DRA	Bifan	IRW-DCN	IRW-DAA	IRW-DRA	IRW-Bifan	Jaccard	HPI	LP	LO	HSCF-DCN	HSCF-DAA	HSCF-DRA	HSCF-Bifan
SM	0.3	0.721	0.701	0.721	0.583	0.716	0.697	0.719	0.756	0.720	0.719	0.859	0.489	0.973	0.940	0.973	0.963
	0.5	0.718	0.701	0.723	0.579	0.717	0.696	0.719	0.756	0.722	0.723	0.858	0.491	0.970	0.937	0.972	0.959
	0.7	0.789	0.770	0.788	0.775	0.816	0.791	0.814	0.896	0.785	0.792	0.920	0.639	0.987	0.962	0.987	0.978
FIG	0.3	0.634	0.633	0.632	0.872	0.618	0.635	0.641	0.892	0.637	0.638	0.729	0.598	0.861	0.869	0.867	0.967
	0.5	0.634	0.635	0.632	0.872	0.615	0.633	0.643	0.896	0.634	0.639	0.722	0.604	0.871	0.883	0.877	0.969
	0.7	0.635	0.636	0.636	0.877	0.623	0.640	0.641	0.890	0.634	0.632	0.721	0.599	0.869	0.877	0.894	0.965
OPE	0.3	0.733	0.725	0.729	0.890	0.873	0.867	0.873	0.971	0.732	0.728	0.921	0.725	0.974	0.972	0.982	0.968
	0.5	0.892	0.893	0.892	0.949	0.956	0.951	0.955	0.978	0.891	0.885	0.971	0.851	0.983	0.984	0.991	0.966
	0.7	0.946	0.943	0.949	0.962	0.971	0.970	0.973	0.979	0.940	0.938	0.980	0.908	0.982	0.986	0.992	0.958
ODL	0.3	0.558	0.548	0.557	0.635	0.626	0.602	0.620	0.762	0.558	0.555	0.613	0.546	0.768	0.739	0.772	0.875
	0.5	0.653	0.652	0.655	0.837	0.773	0.769	0.775	0.910	0.655	0.655	0.775	0.701	0.907	0.906	0.911	0.943
	0.7	0.753	0.750	0.755	0.916	0.873	0.862	0.868	0.944	0.753	0.755	0.869	0.791	0.944	0.944	0.941	0.959
BA	0.3	0.537	0.530	0.537	0.580	0.597	0.593	0.600	0.805	0.536	0.534	0.623	0.477	0.839	0.820	0.853	0.831
	0.5	0.689	0.686	0.684	0.851	0.787	0.786	0.785	0.936	0.680	0.680	0.858	0.668	0.918	0.924	0.940	0.916
	0.7	0.780	0.783	0.782	0.910	0.846	0.844	0.846	0.948	0.773	0.769	0.911	0.738	0.935	0.946	0.960	0.923
AG	0.3	0.610	0.600	0.605	0.787	0.725	0.708	0.722	0.901	0.607	0.605	0.742	0.588	0.921	0.923	0.927	0.949
	0.5	0.734	0.735	0.733	0.921	0.854	0.839	0.849	0.957	0.735	0.733	0.891	0.736	0.960	0.960	0.965	0.961
	0.7	0.820	0.817	0.821	0.952	0.912	0.905	0.907	0.971	0.819	0.819	0.943	0.786	0.963	0.972	0.969	0.967
CAL	0.3	0.624	0.580	0.622	0.724	0.629	0.595	0.634	0.796	0.625	0.622	0.709	0.583	0.838	0.761	0.822	0.932
	0.5	0.624	0.588	0.620	0.717	0.634	0.597	0.631	0.793	0.630	0.620	0.714	0.586	0.815	0.755	0.826	0.936
	0.7	0.625	0.584	0.621	0.723	0.631	0.602	0.635	0.794	0.618	0.621	0.716	0.585	0.810	0.757	0.824	0.939
WV	0.3	0.674	0.673	0.674	0.965	0.786	0.777	0.784	0.970	0.673	0.674	0.880	0.712	0.933	0.942	0.941	0.975
	0.5	0.808	0.812	0.810	0.983	0.889	0.887	0.889	0.976	0.807	0.808	0.952	0.792	0.947	0.967	0.960	0.978
	0.7	0.884	0.880	0.885	0.986	0.929	0.927	0.931	0.977	0.879	0.880	0.973	0.836	0.947	0.974	0.970	0.979
CHE	0.3	0.561	0.559	0.564	0.643	0.661	0.655	0.662	0.814	0.560	0.564	0.669	0.511	0.893	0.888	0.882	0.899
	0.5	0.653	0.657	0.656	0.788	0.797	0.796	0.799	0.915	0.657	0.655	0.823	0.593	0.937	0.931	0.941	0.925
	0.7	0.736	0.726	0.736	0.866	0.865	0.863	0.865	0.942	0.735	0.734	0.880	0.651	0.948	0.948	0.954	0.929
WPL	0.3	0.741	0.736	0.738	0.877	0.830	0.826	0.827	0.938	0.735	0.738	0.851	0.733	0.942	0.941	0.945	0.956
	0.5	0.845	0.833	0.839	0.947	0.896	0.895	0.899	0.966	0.834	0.839	0.923	0.843	0.957	0.964	0.967	0.968
	0.7	0.885	0.884	0.888	0.968	0.930	0.927	0.928	0.971	0.881	0.887	0.952	0.884	0.957	0.964	0.974	0.969

Tab. 4 AUC corresponding to different training dataset rate

数据集	训练集比率	DCN	DAA	DRA	Bifan	IRW-DCN	IRW-DAA	IRW-DRA	IRW-Bifan	Jaccard	HPI	LP	LO	HSCF-DCN	HSCF-DAA	HSCF-DRA	HSCF-Bifan
SM	0.3	0.721	0.701	0.721	0.583	0.716	0.697	0.719	0.756	0.720	0.719	0.859	0.489	0.973	0.940	0.973	0.963
	0.5	0.718	0.701	0.723	0.579	0.717	0.696	0.719	0.756	0.722	0.723	0.858	0.491	0.970	0.937	0.972	0.959
	0.7	0.789	0.770	0.788	0.775	0.816	0.791	0.814	0.896	0.785	0.792	0.920	0.639	0.987	0.962	0.987	0.978
FIG	0.3	0.634	0.633	0.632	0.872	0.618	0.635	0.641	0.892	0.637	0.638	0.729	0.598	0.861	0.869	0.867	0.967
	0.5	0.634	0.635	0.632	0.872	0.615	0.633	0.643	0.896	0.634	0.639	0.722	0.604	0.871	0.883	0.877	0.969
	0.7	0.635	0.636	0.636	0.877	0.623	0.640	0.641	0.890	0.634	0.632	0.721	0.599	0.869	0.877	0.894	0.965
OPE	0.3	0.733	0.725	0.729	0.890	0.873	0.867	0.873	0.971	0.732	0.728	0.921	0.725	0.974	0.972	0.982	0.968
	0.5	0.892	0.893	0.892	0.949	0.956	0.951	0.955	0.978	0.891	0.885	0.971	0.851	0.983	0.984	0.991	0.966
	0.7	0.946	0.943	0.949	0.962	0.971	0.970	0.973	0.979	0.940	0.938	0.980	0.908	0.982	0.986	0.992	0.958
ODL	0.3	0.558	0.548	0.557	0.635	0.626	0.602	0.620	0.762	0.558	0.555	0.613	0.546	0.768	0.739	0.772	0.875
	0.5	0.653	0.652	0.655	0.837	0.773	0.769	0.775	0.910	0.655	0.655	0.775	0.701	0.907	0.906	0.911	0.943
	0.7	0.753	0.750	0.755	0.916	0.873	0.862	0.868	0.944	0.753	0.755	0.869	0.791	0.944	0.944	0.941	0.959
BA	0.3	0.537	0.530	0.537	0.580	0.597	0.593	0.600	0.805	0.536	0.534	0.623	0.477	0.839	0.820	0.853	0.831
	0.5	0.689	0.686	0.684	0.851	0.787	0.786	0.785	0.936	0.680	0.680	0.858	0.668	0.918	0.924	0.940	0.916
	0.7	0.780	0.783	0.782	0.910	0.846	0.844	0.846	0.948	0.773	0.769	0.911	0.738	0.935	0.946	0.960	0.923
AG	0.3	0.610	0.600	0.605	0.787	0.725	0.708	0.722	0.901	0.607	0.605	0.742	0.588	0.921	0.923	0.927	0.949
	0.5	0.734	0.735	0.733	0.921	0.854	0.839	0.849	0.957	0.735	0.733	0.891	0.736	0.960	0.960	0.965	0.961
	0.7	0.820	0.817	0.821	0.952	0.912	0.905	0.907	0.971	0.819	0.819	0.943	0.786	0.963	0.972	0.969	0.967
CAL	0.3	0.624	0.580	0.622	0.724	0.629	0.595	0.634	0.796	0.625	0.622	0.709	0.583	0.838	0.761	0.822	0.932
	0.5	0.624	0.588	0.620	0.717	0.634	0.597	0.631	0.793	0.630	0.620	0.714	0.586	0.815	0.755	0.826	0.936
	0.7	0.625	0.584	0.621	0.723	0.631	0.602	0.635	0.794	0.618	0.621	0.716	0.585	0.810	0.757	0.824	0.939
WV	0.3	0.674	0.673	0.674	0.965	0.786	0.777	0.784	0.970	0.673	0.674	0.880	0.712	0.933	0.942	0.941	0.975
	0.5	0.808	0.812	0.810	0.983	0.889	0.887	0.889	0.976	0.807	0.808	0.952	0.792	0.947	0.967	0.960	0.978
	0.7	0.884	0.880	0.885	0.986	0.929	0.927	0.931	0.977	0.879	0.880	0.973	0.836	0.947	0.974	0.970	0.979
CHE	0.3	0.561	0.559	0.564	0.643	0.661	0.655	0.662	0.814	0.560	0.564	0.669	0.511	0.893	0.888	0.882	0.899
	0.5	0.653	0.657	0.656	0.788	0.797	0.796	0.799	0.915	0.657	0.655	0.823	0.593	0.937	0.931	0.941	0.925
	0.7	0.736	0.726	0.736	0.866	0.865	0.863	0.865	0.942	0.735	0.734	0.880	0.651	0.948	0.948	0.954	0.929
WPL	0.3	0.741	0.736	0.738	0.877	0.830	0.826	0.827	0.938	0.735	0.738	0.851	0.733	0.942	0.941	0.945	0.956
	0.5	0.845	0.833	0.839	0.947	0.896	0.895	0.899	0.966	0.834	0.839	0.923	0.843	0.957	0.964	0.967	0.968
	0.7	0.885	0.884	0.888	0.968	0.930	0.927	0.928	0.971	0.881	0.887	0.952	0.884	0.957	0.964	0.974	0.969

Tab. 5 F?score corresponding todifferent training dataset rate

数据集	训练集比率	DCN	DAA	DRA	Bifan	IRW-DCN	IRW-DAA	IRW-DRA	IRW-Bifan	Jaccard	HPI	LP	LO	HSCF-DCN	HSCF-DAA	HSCF-DRA	HSCF-Bifan
SM	0.3	0.173	0.239	0.295	0.049	0.449	0.284	0.356	0.385	0.449	0.489	0.374	0.475	0.796	0.749	0.777	0.740
	0.5	0.176	0.240	0.296	0.048	0.440	0.275	0.355	0.384	0.451	0.489	0.374	0.475	0.795	0.748	0.779	0.739
	0.7	0.232	0.287	0.358	0.120	0.400	0.456	0.486	0.537	0.540	0.575	0.364	0.520	0.765	0.745	0.768	0.760
FIG	0.3	0.191	0.194	0.198	0.268	0.267	0.217	0.237	0.475	0.249	0.294	0.295	0.495	0.557	0.577	0.561	0.702
	0.5	0.192	0.191	0.195	0.273	0.254	0.232	0.238	0.466	0.247	0.300	0.288	0.496	0.569	0.567	0.554	0.703
	0.7	0.195	0.196	0.199	0.270	0.269	0.242	0.221	0.465	0.246	0.293	0.287	0.495	0.554	0.582	0.564	0.720
OPE	0.3	0.164	0.169	0.237	0.171	0.488	0.516	0.530	0.663	0.336	0.427	0.238	0.565	0.850	0.851	0.857	0.858
	0.5	0.241	0.460	0.475	0.267	0.601	0.621	0.629	0.698	0.492	0.625	0.393	0.635	0.873	0.874	0.877	0.872
	0.7	0.277	0.591	0.577	0.346	0.636	0.649	0.657	0.712	0.564	0.705	0.526	0.666	0.879	0.882	0.884	0.875
ODL	0.3	0.058	0.065	0.088	0.077	0.219	0.193	0.219	0.405	0.138	0.158	0.088	0.496	0.488	0.469	0.500	0.701
	0.5	0.115	0.110	0.168	0.183	0.388	0.396	0.399	0.618	0.310	0.332	0.188	0.557	0.756	0.768	0.765	0.854
	0.7	0.180	0.192	0.237	0.246	0.489	0.503	0.508	0.686	0.460	0.445	0.255	0.594	0.826	0.829	0.827	0.869
BA	0.3	0.032	0.044	0.062	0.061	0.198	0.186	0.195	0.464	0.100	0.110	0.074	0.479	0.738	0.737	0.754	0.769
	0.5	0.111	0.171	0.211	0.174	0.419	0.441	0.446	0.657	0.326	0.383	0.196	0.553	0.854	0.858	0.866	0.859
	0.7	0.159	0.318	0.339	0.240	0.498	0.518	0.523	0.693	0.421	0.500	0.309	0.582	0.867	0.872	0.876	0.865
AG	0.3	0.062	0.087	0.139	0.113	0.356	0.350	0.364	0.562	0.255	0.267	0.103	0.503	0.745	0.753	0.722	0.800
	0.5	0.108	0.201	0.281	0.174	0.501	0.528	0.535	0.660	0.445	0.445	0.204	0.550	0.811	0.814	0.805	0.826
	0.7	0.131	0.334	0.411	0.245	0.579	0.610	0.618	0.692	0.518	0.547	0.282	0.573	0.823	0.827	0.825	0.832

Fig. 2 Comparison of running time

Fig. 3 Curves of AUC varying with parameter α

Fig. 4 Curves of F?score varying with parameterα

References 23

1	李艳丽，周涛. 链路预测中的局部相似性指标［J］. 电子科技大学学报， 2021， 50（3）：422-427. 10.12178/1001-0548.2021062
	LI Y L， ZHOU T. Local similarity index in link prediction［J］. Journal of University of Electronic Science and Technology of China， 2021， 50（3）：422-427. 10.12178/1001-0548.2021062
2	HUANG Z， ZENG D D. A link prediction approach to anomalous email detection［C］// Proceedings of the 2006 IEEE International Conference on Systems， Man， and Cybernetics. Piscataway： IEEE， 2006： 1131-1136. 10.1109/icsmc.2006.384552
3	HUO Z P， HUANG X， HU X. Link prediction with personalized social influence［C］// Proceedings of the 32nd AAAI Conference on Artificial Intelligence. Palo Alto， CA： AAAI Press， 2018： 2289-2296. 10.1609/aaai.v32i1.11892
4	YU S Q， ZHAO M H， FU C B， et al. Target defense against link-prediction-based attacks via evolutionary perturbations［J］. IEEE Transactions on Knowledge and Data Engineering， 2021， 33（2）： 754-767.
5	赵学磊，季新生，刘树新，等. 有向网络链路预测研究进展［J］. 信息工程大学学报， 2019， 20（6）： 658-663， 677.
	ZHAO X L， JI X S， LIU S X， et al. Survey of link prediction for directed network［J］. Journal of Information Engineering University， 2019， 20（6）： 658-663， 677.
6	SCHALL D. Link prediction in directed social networks［J］. Social Network Analysis and Mining， 2014， 4（1）： No.157. 10.1007/s13278-014-0157-9
7	BÜTÜN E， KAYA M. A pattern based supervised link prediction in directed complex networks［J］. Physica A： Statistical Mechanics and its Applications， 2019， 525： 1136-1145. 10.1016/j.physa.2019.04.015
8	ZHANG X， ZHAO C L， WANG X J， et al. Identifying missing and spurious interactions in directed networks［J］. International Journal of Distributed Sensor Networks， 2015， 11（9）： No.507386. 10.1155/2015/507386
9	BÜTÜN E， KAYA M， ALHAJJ R. Extension of neighbor-based link prediction methods for directed， weighted and temporal social networks［J］. Information Sciences， 2018， 463/464： 152-165. 10.1016/j.ins.2018.06.051
10	SHANG K K， SMALL M， YAN W S. Link direction for link prediction［J］. Physica A： Statistical Mechanics and its Applications， 2017， 469： 767-776. 10.1016/j.physa.2016.11.129
11	ZHANG Q M， LÜ L Y， WANG W Q， et al. Potential theory for directed networks［J］. PLoS ONE， 2013， 8（2）： No.e55437. 10.1371/journal.pone.0055437
12	LI J S， PENG J H， LIU S X， et al. Link prediction in directed networks utilizing the role of reciprocal links［J］. IEEE Access， 2020， 8： 28668-28680. 10.1109/access.2020.2972072
13	PECH R， HAO D， LEE Y L， et al. Link prediction via linear optimization［J］. Physica A： Statistical Mechanics and its Applications， 2019， 528： No.121319. 10.1016/j.physa.2019.121319
14	李劲松，彭建华，刘树新，等. 一种基于线性规划的有向网络链路预测方法［J］. 电子与信息学报， 2020， 42（10）： 2394-2402. 10.11999/JEIT190731
	LI J S， PENG J H， LIU S X， et al. A link prediction method in directed networks via linear programming［J］. Journal of Electronics and Information Technology， 2020， 42（10）： 2394-2402. 10.11999/JEIT190731
15	CHEN G F， XU C， WANG J Y， et al. Nonnegative matrix factorization for link prediction in directed complex networks using PageRank and asymmetric link clustering information［J］. Expert Systems with Applications， 2020， 148： No.113290. 10.1016/j.eswa.2020.113290
16	LEE Y L， ZHOU T. Collaborative filtering approach to link prediction［J］. Physica A： Statistical Mechanics and its Applications， 2021， 578： No.126107. 10.1016/j.physa.2021.126107
17	CAO S S， LU W， XU Q K. GraRep： learning graph representations with global structural information［C］// Proceedings of the 24th ACM International Conference on Information and Knowledge Management. New York： ACM， 2015： 891-900. 10.1145/2806416.2806512
18	HANLEY J A， McNEIL B J. The meaning and use of the area under a Receiver Operating Characteristic （ROC） curve［J］. Radiology， 1982， 143（1）： 29-36. 10.1148/radiology.143.1.7063747
19	WANG D S， PEDRESCHI D， SONG C M， et al. Human mobility， social ties， and link prediction［C］// Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York： ACM， 2011： 1100-1108. 10.1145/2020408.2020581
20	KUNEGIS J. The KOBLENZ project［EB/OL］. ［2020-10-10］.. 10.1145/2487788.2488173
21	LESKOVEC J， KREVL A. SNAP datasets： Stanford large network dataset collection［DB/OL］. （2014-06）［2020-10-10］..
22	ROSSI R A， AHMED N K. The network data repository with interactive graph analytics and visualization［C］// Proceedings of the 29th AAAI Conference on Artificial Intelligence. Palo Alto， CA： AAAI Press， 2015：4292-4293. 10.1609/aaai.v29i1.9277
23	YU Y， WANG X X. Link prediction in directed network and its application in microblog［J］. Mathematical Problems in Engineering， 2014， 2014： No.509282. 10.1155/2014/509282

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Link prediction in directed network based on high-order self-included collaborative filtering

基于高阶自包含协同过滤的有向网络链路预测

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