Multi-target node hiding method based on permanence

doi:10.11772/j.issn.1001-9081.2024091314

Journal of Computer Applications ›› 2025, Vol. 45 ›› Issue (10): 3203-3213.DOI: 10.11772/j.issn.1001-9081.2024091314

• Data science and technology • Previous Articles

Multi-target node hiding method based on permanence

Le LYU¹, Bohan ZHANG², Junchang JING³, Dong LIU¹^,²^,³()

^1.School of Computer and Information Engineering，Henan Normal University，Xinxiang Henan 453007，China
^2.Henan Provincial Key Laboratory of Artificial Intelligence and Personalized Learning in Education （Henan Normal University），Xinxiang Henan 453007，China
^3.Big Data for Teaching Resources and Education Quality Evaluation Henan Engineering Laboratory （Henan Normal University），Xinxiang Henan 453007，China

Received:2024-09-14 Revised:2024-12-03 Accepted:2024-12-09 Online:2025-01-14 Published:2025-10-10
Contact: Dong LIU
About author:LYU Le， born in 2000， M. S. candidate. His research interests include social network analysis.
ZHANG Bohan， born in 1998， M. S. candidate. His research interests include social network analysis.
JING Junchang， born in 1990， Ph. D.， lecturer. His research interests include social computing， multimedia content analysis.
LIU Dong， born in 1976， Ph. D.， professor. His research interests include education big data mining， social network analysis.
Supported by:
National Natural Science Foundation of China(62072160)

基于持久性的多目标节点隐藏方法

吕乐¹, 张博瀚², 荆军昌³, 刘栋¹^,²^,³()

^1.河南师范大学计算机与信息工程学院，河南新乡 453007
^2.教育人工智能与个性化学习河南省重点实验室（河南师范大学），河南新乡 453007
^3.教学资源与教育质量评估大数据河南省工程实验室（河南师范大学），河南新乡 453007

通讯作者: 刘栋
作者简介:吕乐（2000—），男，河南驻马店人，硕士研究生，主要研究方向：社会网络分析
张博瀚（1998—），男，河南新乡人，硕士研究生，主要研究方向：社会网络分析
荆军昌（1990—），男，河南焦作人，讲师，博士，CCF会员，主要研究方向：社会计算、多媒体内容分析
刘栋（1976—），男，河南新乡人，教授，博士，CCF会员，主要研究方向：教育大数据挖掘、社会网络分析。Email:liudong@htu.edu.cn
基金资助:
国家自然科学基金资助项目(62072160)

Abstract

Abstract:

Although community detection can reveal underlying structural characteristics of the network and relationships between nodes deeply， it also raises privacy leakage issues. Community hiding methods can resist community detection algorithms effectively， thereby achieving privacy protection of network node information. However， most of the traditional community hiding methods only focus on privacy protection of a single target or community in the network， there is a lack of a method that can hide any target set. In order to solve the above problems， a Based on Permanence-loss Maximization for multiple target Nodes Hiding （BPMNH） method was proposed. In the method， the set of target nodes to be hidden was able to be configured freely， and permanence loss maximization scheme was provided according to the network scale adaptively， thereby achieving hiding of multiple target nodes in different communities with minimal network topology disturbance cost. On eight datasets such as Karate， the experimental results show that BPMNH is better than three baseline methods such as Modularity Based Attack （MBA） in terms of hiding effect， network structure and comprehensive deception effect， validating the superiority of the proposed method in multi-target node hiding.

Key words: community hiding, community detection, multiple target nodes, permanence, complex network

摘要：

社区检测尽管能深度揭示网络潜在的结构特征和节点之间的关系，但也产生了隐私泄露问题。社区隐藏方法能够有效对抗社区检测算法，从而实现网络节点信息的隐私保护。然而，传统的社区隐藏方法大多关注网络中的单一目标或单一社区的隐私保护，缺乏一种能够针对任意目标集合进行隐藏的方法。针对上述问题，提出一种持久性损失最大化的多目标节点隐藏（BPMNH）方法。该方法可以自由配置拟隐藏的目标节点集合，并根据网络规模自适应地给出持久性损失最大化方案，从而在最小的网络拓扑扰动代价下，实现不同社区的多个目标节点隐藏。在Karate等8个数据集上，从隐藏效果、网络结构和综合欺骗效果方面与基于模块度的攻击（MBA）等3种基线方法进行对比，实验结果表明BPMNH在多目节点隐藏上均优于对比方法，验证了所提方法的优越性。

关键词: 社区隐藏, 社区检测, 多目标节点, 持久性, 复杂网络

CLC Number:

TP18

Le LYU, Bohan ZHANG, Junchang JING, Dong LIU. Multi-target node hiding method based on permanence[J]. Journal of Computer Applications, 2025, 45(10): 3203-3213.

吕乐, 张博瀚, 荆军昌, 刘栋. 基于持久性的多目标节点隐藏方法[J]. 《计算机应用》唯一官方网站, 2025, 45(10): 3203-3213.

Figures/Tables 13

References 45

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数据集	节点数	边数	数据集描述
Karate	34	78	空手道网络
Dolphins	62	159	海豚社交网络
Polbooks	105	441	美国政治书籍网络
Football	115	616	足球网络
Email-univ	1 133	5 451	大学邮件网络
Power	4 941	6 594	美国电网
Oregon-1	10 670	22 002	自治系统对等信息网络
Tech-pgp	10 680	24 316	安全信息交换网络

数据集	节点数	边数	数据集描述
Karate	34	78	空手道网络
Dolphins	62	159	海豚社交网络
Polbooks	105	441	美国政治书籍网络
Football	115	616	足球网络
Email-univ	1 133	5 451	大学邮件网络
Power	4 941	6 594	美国电网
Oregon-1	10 670	22 002	自治系统对等信息网络
Tech-pgp	10 680	24 316	安全信息交换网络

检测方法	Karate数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	5.0	11.1	11.1	3.3	6.7	22.2	11.1	26.7	13.3	11.1	33.3	33.3	33.3	11.1	33.3	33.3
Lei	0.0	66.7	0.0	0.0	6.7	33.3	66.7	33.3	25.0	66.7	66.6	33.3	43.3	66.7	66.7	33.3
Inf	0.0	0.0	0.0	0.0	1.7	0.0	0.0	0.0	11.7	0.0	0.0	33.3	20.0	33.3	66.7	100.0
Lab	13.3	0.0	0.0	33.3	16.7	0.0	33.3	33.3	31.7	0.0	33.3	33.3	30.0	0.0	33.3	33.3
Walk	3.3	0.0	0.0	0.0	3.3	0.0	0.0	66.7	11.7	0.0	66.7	66.7	41.7	100.0	66.7	66.7
Fast	3.3	0.0	0.0	0.0	20.0	33.3	0.0	33.3	25.0	33.3	33.3	66.7	40.0	66.7	0.0	33.3
平均值	4.2	13.0	1.9	6.1	9.2	14.8	18.5	32.2	19.7	18.5	38.9	44.4	34.7	46.3	44.4	50.0
检测方法	Polbooks数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	1.0	0.0	6.7	15.0	13.5	33.3	33.3	15.0	16.5	20.0	26.7	34.0	36.5	36.7	56.7	57.0
Lei	3.5	0.0	0.0	0.0	7.0	0.0	0.0	20.0	34.5	20.0	0.0	50.0	40.5	20.0	70.0	80.0
Inf	0.0	0.0	0.0	0.0	1.0	0.0	10.0	0.0	4.0	0.0	0.0	10.0	5.5	0.0	40.0	30.0
Lab	8.0	0.0	0.0	0.0	9.0	0.0	0.0	50.0	10.5	0.0	0.0	0.0	25.0	0.0	20.0	50.0
Walk	0.5	10.0	0.0	0.0	2.0	10.0	0.0	10.0	2.0	0.0	0.0	10.0	9.0	10.0	0.0	30.0
Fast	1.0	0.0	20.0	20.0	1.0	0.0	0.0	10.0	8.5	0.0	0.0	40.0	12.5	0.0	0.0	40.0
平均值	2.3	1.7	4.4	5.8	5.6	7.2	7.2	17.5	12.7	6.7	4.4	24.0	21.5	11.1	31.1	47.8
检测方法	Football数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	3.6	18.2	16.7	16.4	7.7	39.4	16.7	63.6	32.7	100.0	33.3	90.9	74.1	100.0	61.1	100.0
Lei	6.4	9.1	0.0	0.0	11.4	45.5	16.7	54.5	36.8	81.8	33.3	90.9	68.2	100.0	33.3	100.0
Inf	27.3	27.3	33.3	27.3	35.5	54.5	50.0	72.7	48.2	100.0	33.3	72.7	76.4	100.0	50.0	81.8
Lab	23.2	9.1	33.3	27.3	47.3	54.5	33.3	81.8	64.1	90.9	33.3	72.7	86.8	100.0	50.0	81.8
Walk	5.5	9.1	0.0	0.0	25.0	63.6	50.0	45.5	66.4	100.0	50.0	81.8	80.5	100.0	66.7	90.9
Fast	41.8	45.5	33.3	54.5	48.6	63.6	33.3	63.6	56.8	90.9	66.7	100.0	72.7	90.9	66.7	72.7
平均值	18.0	19.7	19.4	20.9	29.2	53.5	33.3	63.6	50.8	93.9	41.7	84.8	76.4	98.5	54.6	87.9
检测方法	Dolphins数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	3.3	0.0	16.7	3.3	8.3	0.0	16.7	33.3	15.8	5.6	38.9	35.0	34.2	5.6	61.1	61.7
Lei	0.8	0.0	0.0	0.0	14.2	0.0	16.7	33.3	23.3	0.0	33.3	28.3	45.8	33.3	33.3	66.7
Inf	5.8	0.0	0.0	50.0	15.8	50.0	50.0	16.7	37.5	66.7	33.3	50.0	46.7	16.7	50.0	66.7
Lab	20.8	16.7	33.3	16.7	27.5	50.0	33.3	33.3	34.2	50.0	33.3	33.3	40.0	50.0	50.0	66.7
Walk	8.3	16.7	0.0	0.0	8.3	0.0	50.0	50.0	43.3	16.7	50.0	50.0	39.2	16.7	66.7	16.6
Fast	13.3	16.7	33.3	16.7	20.8	16.7	33.3	33.3	35.0	0.0	66.7	50.0	46.7	50.0	66.7	50.0
平均值	8.7	8.3	13.9	14.4	15.8	19.4	33.3	33.3	31.5	23.1	42.6	41.1	42.1	28.7	54.6	54.7
检测方法	Email-univ数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	30.3	20.9	17.7	25.0	25.3	38.9	28.3	39.0	27.6	46.9	34.5	47.0	41.8	51.6	36.6	58.7
Lei	14.9	28.3	18.6	22.6	18.9	41.6	22.1	32.7	25.7	38.9	29.2	38.9	29.4	42.5	29.2	42.9
Inf	27.1	31.9	24.8	34.5	31.7	53.1	29.2	40.7	38.2	58.4	38.1	72.6	49.7	76.1	43.4	61.1
Lab	37.3	23.9	19.5	48.7	44.8	46.9	48.7	48.7	49.7	46.9	48.7	48.7	48.7	46.0	47.8	48.7
Walk	9.7	15.0	7.1	10.6	21.8	23.0	10.6	17.7	21.1	35.4	21.2	30.1	39.1	49.6	21.2	29.2
Fast	42.1	44.2	46.0	42.5	41.4	46.0	23.9	44.2	43.5	39.8	30.1	45.1	44.2	44.2	35.4	48.7
平均值	26.9	27.4	22.3	30.6	30.6	41.6	27.1	37.2	34.3	44.4	33.6	47.1	42.1	51.7	35.6	48.2
检测方法	Tech-pgp数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	16.5	15.7	21.4	22.8	20.7	17.5	26.6	29.7	23.4	18.4	31.5	33.9	26.0	24.8	37.3	39.0
Lei	14.0	10.3	17.4	17.4	16.3	13.1	23.1	29.5	17.7	19.6	29.7	29.5	18.0	24.3	32.6	33.9
Inf	23.9	78.6	78.6	78.3	23.9	78.5	28.4	78.6	37.4	78.3	58.9	56.3	78.7	28.5	69.5	61.0
Lab	16.6	25.4	14.1	21.2	14.3	27.6	25.6	24.6	14.7	38.3	19.0	26.5	15.4	36.5	25.7	42.3
Walk	18.7	23.2	17.9	16.4	20.3	17.8	24.9	23.8	25.1	23.5	29.2	29.5	23.2	29.6	32.5	33.5
Fast	8.6	18.9	23.9	31.1	25.0	26.3	44.2	36.7	27.7	24.5	39.7	43.5	27.2	33.1	46.1	45.1
平均值	16.4	28.7	28.9	31.2	20.1	30.1	28.8	37.1	24.3	33.8	34.7	36.5	31.4	29.4	40.6	42.5

检测方法	Karate数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	5.0	11.1	11.1	3.3	6.7	22.2	11.1	26.7	13.3	11.1	33.3	33.3	33.3	11.1	33.3	33.3
Lei	0.0	66.7	0.0	0.0	6.7	33.3	66.7	33.3	25.0	66.7	66.6	33.3	43.3	66.7	66.7	33.3
Inf	0.0	0.0	0.0	0.0	1.7	0.0	0.0	0.0	11.7	0.0	0.0	33.3	20.0	33.3	66.7	100.0
Lab	13.3	0.0	0.0	33.3	16.7	0.0	33.3	33.3	31.7	0.0	33.3	33.3	30.0	0.0	33.3	33.3
Walk	3.3	0.0	0.0	0.0	3.3	0.0	0.0	66.7	11.7	0.0	66.7	66.7	41.7	100.0	66.7	66.7
Fast	3.3	0.0	0.0	0.0	20.0	33.3	0.0	33.3	25.0	33.3	33.3	66.7	40.0	66.7	0.0	33.3
平均值	4.2	13.0	1.9	6.1	9.2	14.8	18.5	32.2	19.7	18.5	38.9	44.4	34.7	46.3	44.4	50.0
检测方法	Polbooks数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	1.0	0.0	6.7	15.0	13.5	33.3	33.3	15.0	16.5	20.0	26.7	34.0	36.5	36.7	56.7	57.0
Lei	3.5	0.0	0.0	0.0	7.0	0.0	0.0	20.0	34.5	20.0	0.0	50.0	40.5	20.0	70.0	80.0
Inf	0.0	0.0	0.0	0.0	1.0	0.0	10.0	0.0	4.0	0.0	0.0	10.0	5.5	0.0	40.0	30.0
Lab	8.0	0.0	0.0	0.0	9.0	0.0	0.0	50.0	10.5	0.0	0.0	0.0	25.0	0.0	20.0	50.0
Walk	0.5	10.0	0.0	0.0	2.0	10.0	0.0	10.0	2.0	0.0	0.0	10.0	9.0	10.0	0.0	30.0
Fast	1.0	0.0	20.0	20.0	1.0	0.0	0.0	10.0	8.5	0.0	0.0	40.0	12.5	0.0	0.0	40.0
平均值	2.3	1.7	4.4	5.8	5.6	7.2	7.2	17.5	12.7	6.7	4.4	24.0	21.5	11.1	31.1	47.8
检测方法	Football数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	3.6	18.2	16.7	16.4	7.7	39.4	16.7	63.6	32.7	100.0	33.3	90.9	74.1	100.0	61.1	100.0
Lei	6.4	9.1	0.0	0.0	11.4	45.5	16.7	54.5	36.8	81.8	33.3	90.9	68.2	100.0	33.3	100.0
Inf	27.3	27.3	33.3	27.3	35.5	54.5	50.0	72.7	48.2	100.0	33.3	72.7	76.4	100.0	50.0	81.8
Lab	23.2	9.1	33.3	27.3	47.3	54.5	33.3	81.8	64.1	90.9	33.3	72.7	86.8	100.0	50.0	81.8
Walk	5.5	9.1	0.0	0.0	25.0	63.6	50.0	45.5	66.4	100.0	50.0	81.8	80.5	100.0	66.7	90.9
Fast	41.8	45.5	33.3	54.5	48.6	63.6	33.3	63.6	56.8	90.9	66.7	100.0	72.7	90.9	66.7	72.7
平均值	18.0	19.7	19.4	20.9	29.2	53.5	33.3	63.6	50.8	93.9	41.7	84.8	76.4	98.5	54.6	87.9
检测方法	Dolphins数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	3.3	0.0	16.7	3.3	8.3	0.0	16.7	33.3	15.8	5.6	38.9	35.0	34.2	5.6	61.1	61.7
Lei	0.8	0.0	0.0	0.0	14.2	0.0	16.7	33.3	23.3	0.0	33.3	28.3	45.8	33.3	33.3	66.7
Inf	5.8	0.0	0.0	50.0	15.8	50.0	50.0	16.7	37.5	66.7	33.3	50.0	46.7	16.7	50.0	66.7
Lab	20.8	16.7	33.3	16.7	27.5	50.0	33.3	33.3	34.2	50.0	33.3	33.3	40.0	50.0	50.0	66.7
Walk	8.3	16.7	0.0	0.0	8.3	0.0	50.0	50.0	43.3	16.7	50.0	50.0	39.2	16.7	66.7	16.6
Fast	13.3	16.7	33.3	16.7	20.8	16.7	33.3	33.3	35.0	0.0	66.7	50.0	46.7	50.0	66.7	50.0
平均值	8.7	8.3	13.9	14.4	15.8	19.4	33.3	33.3	31.5	23.1	42.6	41.1	42.1	28.7	54.6	54.7
检测方法	Email-univ数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	30.3	20.9	17.7	25.0	25.3	38.9	28.3	39.0	27.6	46.9	34.5	47.0	41.8	51.6	36.6	58.7
Lei	14.9	28.3	18.6	22.6	18.9	41.6	22.1	32.7	25.7	38.9	29.2	38.9	29.4	42.5	29.2	42.9
Inf	27.1	31.9	24.8	34.5	31.7	53.1	29.2	40.7	38.2	58.4	38.1	72.6	49.7	76.1	43.4	61.1
Lab	37.3	23.9	19.5	48.7	44.8	46.9	48.7	48.7	49.7	46.9	48.7	48.7	48.7	46.0	47.8	48.7
Walk	9.7	15.0	7.1	10.6	21.8	23.0	10.6	17.7	21.1	35.4	21.2	30.1	39.1	49.6	21.2	29.2
Fast	42.1	44.2	46.0	42.5	41.4	46.0	23.9	44.2	43.5	39.8	30.1	45.1	44.2	44.2	35.4	48.7
平均值	26.9	27.4	22.3	30.6	30.6	41.6	27.1	37.2	34.3	44.4	33.6	47.1	42.1	51.7	35.6	48.2
检测方法	Tech-pgp数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	16.5	15.7	21.4	22.8	20.7	17.5	26.6	29.7	23.4	18.4	31.5	33.9	26.0	24.8	37.3	39.0
Lei	14.0	10.3	17.4	17.4	16.3	13.1	23.1	29.5	17.7	19.6	29.7	29.5	18.0	24.3	32.6	33.9
Inf	23.9	78.6	78.6	78.3	23.9	78.5	28.4	78.6	37.4	78.3	58.9	56.3	78.7	28.5	69.5	61.0
Lab	16.6	25.4	14.1	21.2	14.3	27.6	25.6	24.6	14.7	38.3	19.0	26.5	15.4	36.5	25.7	42.3
Walk	18.7	23.2	17.9	16.4	20.3	17.8	24.9	23.8	25.1	23.5	29.2	29.5	23.2	29.6	32.5	33.5
Fast	8.6	18.9	23.9	31.1	25.0	26.3	44.2	36.7	27.7	24.5	39.7	43.5	27.2	33.1	46.1	45.1
平均值	16.4	28.7	28.9	31.2	20.1	30.1	28.8	37.1	24.3	33.8	34.7	36.5	31.4	29.4	40.6	42.5

检测方法	Email-univ数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	33.6	84.5	38.2	84.5	42.7	94.5	53.6	100.0	46.4	98.2	74.5	99.1	61.8	99.1	93.6	100.0
Lei	43.6	92.7	20.0	81.8	21.8	100.0	40.0	100.0	56.4	100.0	63.6	100.0	45.5	100.0	100.0	100.0
Inf	18.2	90.9	45.5	100.0	36.4	100.0	72.7	100.0	36.4	100.0	81.8	100.0	54.5	100.0	90.9	100.0
Lab	36.4	27.3	36.4	36.4	36.4	100.0	36.4	36.4	36.4	100.0	36.4	54.5	36.4	36.4	36.4	36.4
Walk	0.0	45.5	0.0	63.6	36.4	36.4	54.5	100.0	36.4	45.5	36.4	100.0	100.0	45.5	36.4	100.0
Fast	27.3	72.7	72.7	72.7	63.6	90.9	63.6	90.9	72.7	90.9	72.7	100.0	54.5	90.9	72.7	90.9
平均值	26.5	68.9	35.5	73.2	39.5	87.0	53.5	87.9	47.4	89.1	60.9	92.3	58.8	78.6	71.7	87.9
检测方法	Power数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	22.9	34.7	19.4	39.0	24.7	96.3	36.3	78.4	31.0	99.2	49.0	98.4	32.0	98.4	68.6	98.4
Lei	21.8	34.7	19.4	37.1	28.8	94.7	25.7	82.0	34.9	97.1	50.6	96.1	33.5	100.0	64.3	98.0
Inf	95.9	12.2	85.7	89.8	77.6	91.8	81.6	89.8	87.8	93.9	98.0	89.8	83.7	98.0	95.9	83.7
Lab	40.8	91.8	53.1	79.6	51.0	100.0	79.6	91.8	51.0	100.0	87.8	93.9	57.1	95.9	98.0	95.9
Walk	55.1	73.5	63.3	71.4	67.3	77.6	63.3	77.6	65.3	69.4	65.3	67.3	67.3	67.3	65.3	73.5
Fast	14.3	36.7	22.4	44.9	26.5	93.9	36.7	73.5	36.7	98.0	51.0	95.9	49.0	100.0	61.2	95.9
平均值	41.8	47.3	43.9	60.3	46.0	92.4	53.9	82.2	51.1	92.9	66.9	90.2	53.8	93.3	75.5	90.9
检测方法	Tech-pgp数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	4.9	10.2	6.2	13.6	6.6	17.4	7.4	26.8	6.3	38.5	7.0	50.7	7.5	92.3	8.3	76.6
Lei	2.6	14.7	4.2	16.2	2.9	15.5	4.3	32.0	4.8	54.3	7.7	68.2	4.9	92.3	8.9	85.5
Inf	12.3	54.7	2.8	29.2	12.3	17.0	5.7	36.8	48.1	27.4	7.5	71.7	56.6	27.4	47.2	71.7
Lab	1.9	36.8	17.0	31.1	17.0	44.3	13.2	53.8	12.3	80.2	46.2	85.8	12.3	99.1	50.0	79.2
Walk	36.8	3.8	16.0	32.1	20.8	18.9	20.8	35.8	42.5	29.2	40.6	66.0	43.4	97.2	49.1	68.9
Fast	2.8	17.9	2.8	17.0	15.1	52.8	18.9	42.5	13.2	25.5	17.9	48.1	13.2	88.7	41.5	50.0
平均值	10.2	23.0	8.2	23.2	12.4	27.6	11.7	37.9	21.2	42.5	21.2	65.1	23	82.8	34.1	72.0
检测方法	Oregon-1数据集上的异化率
	5%预算				10%预算				15%预算				20%预算
	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH	MBA	nDec	CH-SNMF	BPMNH
Lou	17.0	19.3	17.7	26.8	23.2	28.3	24.3	45.8	27.8	33.0	28.9	52.2	34.2	41.3	33.4	57.4
Lei	13.2	15.3	15.1	28.7	24.9	34.0	24.5	44.7	29.8	36.6	30.4	47.4	35.3	39.4	35.5	58.6
Inf	12.3	15.1	17.0	20.8	55.7	12.3	55.7	54.7	84.0	14.2	55.7	55.7	84.0	17.0	86.8	54.7
Lab	13.2	12.3	12.3	25.5	19.8	19.8	19.8	37.7	27.4	31.1	27.4	44.3	50.0	37.7	47.2	49.1
Walk	11.3	56.6	13.2	16.0	17.0	29.2	21.7	31.1	22.6	42.5	31.1	69.8	28.3	41.5	29.2	55.7
Fast	48.1	25.5	18.9	56.6	21.7	52.8	26.4	51.9	22.6	55.7	50.0	59.4	37.7	56.6	51.9	62.3
平均值	19.2	24.0	15.7	29.1	27.0	29.4	28.7	44.3	35.7	35.5	37.2	54.8	44.9	38.9	47.3	56.3

Multi-target node hiding method based on permanence

基于持久性的多目标节点隐藏方法

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