基于邻域粗糙集和帝王蝶优化的特征选择算法

doi:10.11772/j.issn.1001-9081.2021030497

《计算机应用》唯一官方网站 ›› 2022, Vol. 42 ›› Issue (5): 1355-1366.DOI: 10.11772/j.issn.1001-9081.2021030497

所属专题：人工智能

基于邻域粗糙集和帝王蝶优化的特征选择算法

孙林¹^,²(), 赵婧¹, 徐久成¹^,², 王欣雅¹

^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

收稿日期:2021-04-02 修回日期:2021-09-15 接受日期:2021-09-22 发布日期:2022-06-11 出版日期:2022-05-10
通讯作者: 孙林
作者简介:孙林（1979—），男，河南南阳人，副教授，博士，CCF会员，主要研究方向：粒计算、数据挖掘、机器学习、生物信息学 sunlin@htu.edu.cn
赵婧（1996—），女，河南洛阳人，硕士研究生，主要研究方向：数据挖掘、机器学习
徐久成（1963—），男，河南洛阳人，教授，博士生导师，博士，CCF高级会员，主要研究方向：粒计算、数据挖掘、机器学习
王欣雅（1997—），女，河南平顶山人，硕士研究生，主要研究方向：数据挖掘、机器学习。
基金资助:
国家自然科学基金资助项目(62076089);河南省科技攻关项目(212102210136)

Feature selection algorithm based on neighborhood rough set and monarch butterfly optimization

Lin SUN¹^,²(), Jing ZHAO¹, Jiucheng XU¹^,², Xinya WANG¹

^1.College of Computer and Information Engineering，Henan Normal University，Xinxiang Henan 453007，China
^2.Key Laboratory of Artificial Intelligence and Personalized Learning in Education of Henan Province （Henan Normal University），Xinxiang Henan 453007，China

Received:2021-04-02 Revised:2021-09-15 Accepted:2021-09-22 Online:2022-06-11 Published:2022-05-10
Contact: Lin SUN
About author:SUN Lin， born in 1979，Ph. D.，associate professor. His researchinterests include granular computing，data mining，machine learning，bioinformatics.
ZHAO Jing，born in 1996，M. S. candidate. Her research interestsinclude data mining，machine learning.
XU Jiucheng， born in 1963，Ph. D.，professor. His researchinterests include granular computing，data mining，machine learning.
WANG Xinya， born in 1997，M. S. candidate. Her researchinterests include data mining，machine learning.
Supported by:
National Natural Science Foundation of China(62076089);Key Scientific and Technological Project of Henan Province(212102210136)

摘要/Abstract

摘要：

针对经典的帝王蝶优化（MBO）算法不能很好地处理连续型数据，以及粗糙集模型对于大规模、高维复杂的数据处理能力不足等问题，提出了基于邻域粗糙集（NRS）和MBO的特征选择算法。首先，将局部扰动和群体划分策略与MBO算法结合，并构建传输机制以形成一种二进制MBO（BMBO）算法；其次，引入突变算子增强算法的探索能力，设计了基于突变算子的BMBO（BMBOM）算法；然后，基于NRS的邻域度构造适应度函数，并对初始化的特征子集的适应度值进行评估并排序；最后，使用BMBOM算法通过不断迭代搜索出最优特征子集，并设计了一种元启发式特征选择算法。在基准函数上评估BMBOM算法的优化性能，并在UCI数据集上评价所提出的特征选择算法的分类能力。实验结果表明，在5个基准函数上，BMBOM算法的最优值、最差值、平均值以及标准差明显优于MBO和粒子群优化（PSO）算法；在UCI数据集上，与基于粗糙集的优化特征选择算法、结合粗糙集与优化算法的特征选择算法、结合NRS与优化算法的特征选择算法、基于二进制灰狼优化的特征选择算法相比，所提特征选择算法在分类精度、所选特征数和适应度值这3个指标上表现良好，能够选择特征数少且分类精度高的最优特征子集。

关键词: 帝王蝶优化, 特征选择, 邻域粗糙集, 邻域依赖度, 二进制

Abstract:

The classical Monarch Butterfly Optimization （MBO） algorithm cannot handle continuous data well， and the rough set model cannot sufficiently process large-scale， high-dimensional and complex data. To address these problems， a new feature selection algorithm based on Neighborhood Rough Set （NRS） and MBO was proposed. Firstly， local disturbance， group division strategy and MBO algorithm were combined， and a transmission mechanism was constructed to form a Binary MBO （BMBO） algorithm. Secondly， the mutation operator was introduced to enhance the exploration ability of this algorithm， and a BMBO based on Mutation operator （BMBOM） algorithm was proposed. Then， a fitness function was developed based on the neighborhood dependence degree in NRS， and the fitness values of the initialized feature subsets were evaluated and sorted. Finally， the BMBOM algorithm was used to search the optimal feature subset through continuous iterations， and a meta-heuristic feature selection algorithm was designed. The optimization performance of the BMBOM algorithm was evaluated on benchmark functions， and the classification performance of the proposed feature selection algorithm was evaluated on UCI datasets. Experimental results show that， the proposed BMBOM algorithm is significantly better than MBO and Particle Swarm Optimization （PSO） algorithms in terms of the optimal value， worst value， average value and standard deviation on five benchmark functions. Compared with the optimized feature selection algorithms based on rough set， the feature selection algorithms combining rough set and optimization algorithms， the feature selection algorithms combining NRS and optimization algorithms， the feature selection algorithms based on binary grey wolf optimization， the proposed feature selection algorithm performs well in the three indicators of classification accuracy， the number of selected features and fitness value on UCI datasets， and can select the optimal feature subset with few features and high classification accuracy.

Key words: Monarch Butterfly Optimization (MBO), feature selection, Neighborhood Rough Set (NRS), neighborhood dependence degree, binary

中图分类号:

TP181

孙林, 赵婧, 徐久成, 王欣雅. 基于邻域粗糙集和帝王蝶优化的特征选择算法[J]. 计算机应用, 2022, 42(5): 1355-1366.

Lin SUN, Jing ZHAO, Jiucheng XU, Xinya WANG. Feature selection algorithm based on neighborhood rough set and monarch butterfly optimization[J]. Journal of Computer Applications, 2022, 42(5): 1355-1366.

图/表 20

表1 六个基准函数信息

Tab. 1 Information of six benchmark functions

函数	公式	变量范围
Sphere	$f 1 (x) = ∑ i = 1 d x i 2$	［-5.12，5.12］ ^D
Schwefel2. 22	$f 2 (x) = ∑ i = 1 d x i + ∏ i = 1 d x i$	［-10，10］ ^D
Step	$f 3 (x) = ∑ i = 1 d x i + 0.5 2$	［-100，100］ ^D
Griank	$f 4 (x) = 1 4 000 ∑ i = 1 d x i 2 - ∏ i = 1 d c o s x i / i + 1$	［-600，600］ ^D
Ackley	$f 5 (x) = - 20 e x p - 15 1 d ∑ i = 1 d x i 2 - e x p 1 d ∑ i = 1 d c o s (2 π x i) + 20 + e$	［-30，30］ ^D
Rastrigin	$f 6 (x) = ∑ i = 1 d (x i 2 - 10 c o s (2 π x i) + 10)$	［-5.12，5.12］ ^D

表1 六个基准函数信息

Tab. 1 Information of six benchmark functions

函数	公式	变量范围
Sphere	$f 1 (x) = ∑ i = 1 d x i 2$	［-5.12，5.12］ ^D
Schwefel2. 22	$f 2 (x) = ∑ i = 1 d x i + ∏ i = 1 d x i$	［-10，10］ ^D
Step	$f 3 (x) = ∑ i = 1 d x i + 0.5 2$	［-100，100］ ^D
Griank	$f 4 (x) = 1 4 000 ∑ i = 1 d x i 2 - ∏ i = 1 d c o s x i / i + 1$	［-600，600］ ^D
Ackley	$f 5 (x) = - 20 e x p - 15 1 d ∑ i = 1 d x i 2 - e x p 1 d ∑ i = 1 d c o s (2 π x i) + 20 + e$	［-30，30］ ^D
Rastrigin	$f 6 (x) = ∑ i = 1 d (x i 2 - 10 c o s (2 π x i) + 10)$	［-5.12，5.12］ ^D

表2 三种优化算法在6个基准函数30维上的实验结果

Tab. 2 Experimental results of three optimization algorithms on 30-dimensions of six benchmark functions

函数	算法	最优值	最差值	平均值	标准差	运行时间/s
f₁	PSO	4.23E $+ 01$	6.12E+01	5.09E+01	4.06E+00	18
	MBO	7.90E $- 06$	2.15E+02	6.67E+01	7.92E+01	177
	BMBOM	4.75E-08	8.19E-05	8.66E-06	1.62E-05	516
f₂	PSO	7.76E+03	1.57E+04	1.20E+04	1.99E+03	54
	MBO	3.91E+02	5.06E+04	2.37E+04	1.49E+04	142
	BMBOM	0	1.36E+02	5.72E+01	4.58E+01	430
f₃	PSO	9.33E+03	1.60E+04	1.24E+04	1.63E+03	53
	MBO	0	7.28E+04	2.38E+04	2.71E+04	176
	BMBOM	0	8.28E+02	2.76E+01	1.51E+02	388
f₄	PSO	6.57E+05	1.43E+06	1.15E+06	1.66E+05	28
	MBO	1	6.36E+02	1.80E+02	2.29E+02	175
	BMBOM	1	3.18E+01	2.03E+00	5.62E+00	395
f₅	PSO	4.22E+01	1.35E+02	6.09E+01	2.72E+01	19
	MBO	1.32E-01	8.95E+01	3.46E+01	2.36E+01	138
	BMBOM	1.30E-04	9.65E-03	1.92E-03	2.16E-03	341
f₆	PSO	2.06E+02	2.66E+02	2.50E+02	1.37E+01	54
	MBO	2.32E-05	4.45E+02	1.68E+02	1.45E+02	177
	BMBOM	2.81E-07	1.12E+02	6.34E+00	2.27E+01	363

表2 三种优化算法在6个基准函数30维上的实验结果

Tab. 2 Experimental results of three optimization algorithms on 30-dimensions of six benchmark functions

函数	算法	最优值	最差值	平均值	标准差	运行时间/s
f₁	PSO	4.23E $+ 01$	6.12E+01	5.09E+01	4.06E+00	18
	MBO	7.90E $- 06$	2.15E+02	6.67E+01	7.92E+01	177
	BMBOM	4.75E-08	8.19E-05	8.66E-06	1.62E-05	516
f₂	PSO	7.76E+03	1.57E+04	1.20E+04	1.99E+03	54
	MBO	3.91E+02	5.06E+04	2.37E+04	1.49E+04	142
	BMBOM	0	1.36E+02	5.72E+01	4.58E+01	430
f₃	PSO	9.33E+03	1.60E+04	1.24E+04	1.63E+03	53
	MBO	0	7.28E+04	2.38E+04	2.71E+04	176
	BMBOM	0	8.28E+02	2.76E+01	1.51E+02	388
f₄	PSO	6.57E+05	1.43E+06	1.15E+06	1.66E+05	28
	MBO	1	6.36E+02	1.80E+02	2.29E+02	175
	BMBOM	1	3.18E+01	2.03E+00	5.62E+00	395
f₅	PSO	4.22E+01	1.35E+02	6.09E+01	2.72E+01	19
	MBO	1.32E-01	8.95E+01	3.46E+01	2.36E+01	138
	BMBOM	1.30E-04	9.65E-03	1.92E-03	2.16E-03	341
f₆	PSO	2.06E+02	2.66E+02	2.50E+02	1.37E+01	54
	MBO	2.32E-05	4.45E+02	1.68E+02	1.45E+02	177
	BMBOM	2.81E-07	1.12E+02	6.34E+00	2.27E+01	363

表3 14个UCI数据集信息

Tab. 3 Information of fourteen UCI datasets

序号	名称	特征数	样本数
1	Breastcancer	9	699
2	Congress	16	435
3	Heart	13	270
4	Hepatitis	19	155
5	Ionosphere	34	351
6	Lungcancer	56	32
7	Lymphography	18	148
8	Sonar	60	208
9	Spect	22	267
10	Tic-tac-toe	9	958
11	Vote	16	300
12	Waveform	40	5 000
13	Wine	13	178
14	Zoo	16	101

表4 FSNB与5种基于粗糙集的优化特征选择算法的分类精度实验结果 ( %)

Tab. 4 Experimental results of FSNB and five optimized feature selection algorithms based on rough sets on classification accuracy

数据集	FSNB	ARRSFA	PSORSFS	FSARSR	QCSIA_FS	DQBGOA_MR
Average	94.60	81.34	81.07	80.62	80.82	83.04
Breastcancer	95.67	92.61	92.30	91.28	92.90	94.71
Hepatitis	95.04	83.25	82.10	82.75	82.75	83.75
Ionosphere	95.04	82.02	83.17	83.97	82.06	84.71
Lungcancer	89.15	65.80	69.00	62.42	60.92	69.19
Lymphography	91.62	73.97	73.70	74.13	74.16	75.43
Spect	94.77	78.16	78.48	75.83	77.24	79.07
Tic-tac-toe	95.03	75.62	79.53	78.72	81.73	82.48
Vote	95.03	95.37	95.41	96.32	95.74	95.89
Wine	97.53	72.42	67.64	70.25	71.76	74.24
Zoo	97.14	94.14	89.35	90.55	88.91	90.89

表5 FSNB与5种基于粗糙集的优化特征选择算法的所选特征数实验结果

Tab. 5 Experimental results of FSNB and five optimized feature selection algorithms based on rough set on number of selected features

数据集	FSNB	ARRSFA	PSORSFS	FSARSR	QCSIA_FS	DQBGOA_MR
Average	8.49	7.23	9.02	8.65	7.34	5.92
Breastcancer	5.75	3.70	3.80	4.00	3.50	3.00
Hepatitis	14.65	4.10	6.20	5.60	5.00	3.70
Ionosphere	14.65	4.60	10.20	8.50	6.10	4.10
Lungcancer	6.30	7.90	19.40	17.10	11.60	4.30
Lymphography	14.75	9.50	8.60	7.80	7.80	7.10
Spect	5.00	14.00	15.10	16.10	14.70	14.00
Tic-tac-toe	5.00	7.20	7.40	8.00	7.00	7.00
Vote	5.00	9.50	8.80	9.60	8.10	7.50
Wine	7.20	3.20	3.60	3.60	3.10	3.00
Zoo	6.55	8.60	7.10	6.20	6.50	5.50

表6 FSNB与8种结合粗糙集与优化算法的特征选择算法的分类精度实验结果 ( %)

Tab. 6 Experimental results of FSNB and eight feature selection algorithms combining rough set and optimization algorithm on classification accuracy

数据集	FSNB	GARS	PSORS	ABCRS	FARS	SSORS	CSRS	HSRS	IRRARS
Average	89.70	76.49	78.72	82.57	79.81	83.22	82.59	82.48	85.79
Breastcancer	95.67	87.28	91.05	96.49	92.73	95.39	93.42	97.37	97.99
Congress	77.02	89.66	90.41	91.38	91.38	95.86	93.79	92.79	95.17
Heart	76.98	65.06	66.41	70.15	69.41	71.57	70.15	73.13	75.18
Ionosphere	95.04	79.85	80.40	84.90	80.80	84.70	85.40	84.00	86.07
Lungcancer	89.15	60.00	65.36	69.64	64.60	69.64	70.64	66.00	75.98
Waveform	96.89	74.82	76.82	80.60	77.90	81.90	80.60	80.20	83.25
Zoo	97.14	78.79	80.61	84.85	81.88	83.50	84.12	83.88	86.88

表7 FSNB与8种结合粗糙集与优化算法的特征选择算法所选特征数实验结果

Tab. 7 Experimental results of FSNB and eight feature selection algorithms combining rough set and optimization algorithm on number of selected features

数据集	FSNB	GARS	PSORS	ABCRS	FARS	SSORS	CSRS	HSRS	IRRARS
Average	7.68	710.79	602.76	635.32	619.06	596.46	665.62	585.41	376.36
Breastcancer	5.75	492.10	399.13	399.13	437.57	336.92	399.13	422.20	329.23
Congress	5.05	254.91	219.24	146.16	140.51	151.38	137.90	143.12	135.29
Heart	9.15	140.94	120.69	117.99	120.15	112.59	124.20	116.10	113.67
Ionosphere	14.65	193.75	188.49	133.03	144.96	143.21	132.68	143.21	134.08
Lungcancer	6.30	17.15	13.92	13.86	12.48	11.62	11.52	11.74	11.52
Waveform	6.30	3 815.00	3 225.00	3 600.00	3 435.00	3 385.00	3 805.00	3 220.00	1 880.00
Zoo	6.55	61.71	52.82	37.07	42.72	34.54	48.88	41.51	30.70

表8 FSNB与FSNM在分类精度、适应度值和所选特征数上的实验结果

Tab. 8 Experimental results of FSNM and FSNB on classification accuracy， fitness value and number of selected features

数据集	分类精度/%		适应度值		所选特征数		运行时间/s
数据集	FSNM	FSNB	FSNM	FSNB	FSNM	FSNB	FSNM	FSNB
Average	87.47	91.51	0.274 8	0.231 3	10.45	8.64	251	198
Breastcancer	95.24	95.67	0.370 8	0.342 8	6.25	5.75	119	118
Congress	72.68	77.02	0.208 9	0.209 0	5.00	5.05	55	55
Heart	75.22	76.98	0.401 9	0.408 3	8.15	9.15	33	33
Hepatitis	94.64	95.04	0.277 5	0.272 0	15.40	14.65	1 075	1 073
Ionosphere	94.10	95.04	0.276 1	0.272 0	15.10	14.65	1 074	1 065
Lungcancer	73.77	89.15	0.138 6	0.105 0	11.00	6.30	6	5
Lymphography	84.09	91.62	0.280 7	0.085 1	25.22	14.75	865	45
Sonar	81.87	84.21	0.200 2	0.173 6	17.80	15.55	24	24
Spect	86.96	94.77	0.297 8	0.220 5	6.00	5.00	52	81
Tic-tac-toe	85.62	95.03	0.313 9	0.219 5	6.20	5.00	80	143
Vote	93.51	95.03	0.303 6	0.219 5	8.60	5.00	80	85
Waveform	95.02	96.89	0.236 7	0.221 4	6.50	6.30	18	17
Wine	96.14	97.53	0.300 8	0.261 5	7.95	7.20	21	21
Zoo	95.72	97.14	0.240 2	0.227 9	7.10	6.55	18	16

表9 FSNB与8种结合邻域粗糙集与优化算法的特征选择算法的分类精度实验结果 ( %)

Tab. 9 Experimental results of FSNB and eight feature selection algorithms combining NRS and optimization algorithms on classification accuracy

数据集	FSNB	GANRS	PSONRS	ABCNRS	FANRS	SSONRS	CSNRS	HSNRS	IRRANRS
Average	89.70	79.24	83.34	85.92	81.44	86.23	85.42	86.16	88.57
Breastcancer	95.67	95.18	96.93	97.81	93.42	96.49	95.61	97.37	98.68
Congress	77.02	90.43	97.24	95.86	94.48	96.93	94.48	95.17	96.93
Heart	76.98	66.52	69.10	71.54	70.86	72.91	71.61	75.00	76.80
Ionosphere	95.04	80.58	81.39	86.02	81.98	85.60	86.27	85.49	86.61
Lungcancer	89.15	62.86	68.60	70.22	65.37	71.56	72.59	69.26	79.26
Waveform	96.89	78.92	80.88	83.04	79.42	83.18	82.96	84.99	84.64
Zoo	97.14	80.21	89.22	96.97	84.58	96.97	94.44	95.87	97.06

表10 FSNB与8种结合邻域粗糙集与优化算法的特征选择算法所选特征数实验结果

Tab. 10 Experimental results of FSNB and eight feature selection algorithms combining NRS and optimization algorithms on number of selected features

数据集	FSNB	GANRS	PSONRS	ABCNRS	FANRS	SSONRS	CSNRS	HSNRS	IRRANRS
Average	7.68	685.39	576.52	608.29	583.31	579.51	644.16	563.34	354.53
Breastcancer	5.75	466.23	381.79	359.99	370.82	355.51	389.90	399.55	312.87
Congress	5.05	245.21	206.58	136.81	128.19	140.33	124.85	134.07	124.67
Heart	9.15	124.71	119.53	110.70	105.30	108.86	122.15	112.48	106.22
Ionosphere	14.65	183.68	179.43	124.08	137.45	133.20	123.48	134.96	125.27
Lungcancer	6.30	16.39	13.10	13.19	11.82	10.81	10.63	10.81	11.09
Waveform	6.30	3 702.00	3 085.00	3 478.50	3 289.50	3 276.00	3 692.00	3 112.50	1 773.00
Zoo	6.55	59.52	50.20	34.78	40.05	31.83	46.11	39.04	28.60

表11 FSNB与6种基于二进制灰狼优化的特征选择算法的分类精度实验结果 ( %)

Tab. 11 Experimental results of FSNB and six feature selection algorithms based on binary grey wolf optimizer on classification accuracy

数据集	FSNB	BGWO	ABGWO	ABGWO-V1	ABGWO-V2	ABGWO-V3	ABGWO-V4
Average	91.93	77.61	78.39	78.29	78.04	78.08	78.14
Breastcancer	95.67	80.48	80.58	80.42	80.24	80.59	79.96
Congress	77.02	83.45	84.02	83.32	83.18	83.19	83.57
Ionosphere	95.04	85.95	86.90	86.90	86.91	86.63	86.37
Lymphography	91.62	46.24	47.27	47.27	47.33	47.14	47.55
Sonar	84.21	80.22	81.23	81.23	81.73	81.57	81.17
Spect	94.77	73.31	74.69	74.69	73.95	74.06	73.71
Tic-tac-toe	95.03	77.46	76.15	76.15	75.66	75.75	76.71
Waveform	96.89	81.71	82.38	82.38	81.56	81.74	81.79
Zoo	97.14	89.69	92.28	92.28	91.81	92.09	92.39

表12 FSNB与6种基于二进制灰狼优化的特征选择算法所选特征数实验结果

Tab. 12 Experimental results of FSNB and six feature selection algorithms based on binary grey wolf optimizer on number of selected features

数据集	FSNB	BGWO	ABGWO	ABGWO-V1	ABGWO-V2	ABGWO-V3	ABGWO-V4
Average	8.73	16.62	13.19	12.78	12.53	12.14	12.86
Breastcancer	5.75	5.30	3.80	4.45	3.75	3.95	4.05
Congress	5.05	9.90	8.25	7.75	8.10	7.40	8.50
Ionosphere	14.65	21.00	16.75	15.10	14.00	14.90	15.75
Lymphography	14.75	11.85	8.85	8.65	8.00	7.65	9.00
Sonar	15.55	36.60	30.45	28.20	28.65	27.25	27.85
Spect	5.00	15.45	11.15	11.65	11.85	10.65	11.60
Tic-tac-toe	5.00	6.80	5.90	6.00	5.30	5.35	5.85
Waveform	6.30	31.30	24.35	23.75	24.55	23.05	24.10
Zoo	6.55	11.40	9.20	9.45	8.60	9.10	9.05

表13 FSNB与5种基于粗糙集的优化特征选择算法的统计检验

Tab. 13 Statistical test of FSNB and five optimized feature selection algorithms based on rough set

平均排序						$x F 2$	$F F$
FSNB	ARRSFA	PSORSFS	FSARSR	QCSIA_FS	DQBGOA_MR	$x F 2$	$F F$
1.50	4.20	4.60	4.35	4.25	2.10	25.56	9.41

表13 FSNB与5种基于粗糙集的优化特征选择算法的统计检验

Tab. 13 Statistical test of FSNB and five optimized feature selection algorithms based on rough set

平均排序						$x F 2$	$F F$
FSNB	ARRSFA	PSORSFS	FSARSR	QCSIA_FS	DQBGOA_MR	$x F 2$	$F F$
1.50	4.20	4.60	4.35	4.25	2.10	25.56	9.41

表14 FSNB与8种结合粗糙集与优化算法的特征选择算法的统计检验

Tab. 14 Statistical test of FSNB and eight feature selection algorithms combining rough set and optimization algorithms

平均排序									$x F 2$	$F F$
FSNB	GARS	PSORS	ABCRS	FARS	SSORS	CSRS	HSRS	IRRARS	$x F 2$	$F F$
2.57	8.86	7.71	4.29	6.93	4.07	4.14	4.57	1.86	41.09	16.54

表14 FSNB与8种结合粗糙集与优化算法的特征选择算法的统计检验

Tab. 14 Statistical test of FSNB and eight feature selection algorithms combining rough set and optimization algorithms

平均排序									$x F 2$	$F F$
FSNB	GARS	PSORS	ABCRS	FARS	SSORS	CSRS	HSRS	IRRARS	$x F 2$	$F F$
2.57	8.86	7.71	4.29	6.93	4.07	4.14	4.57	1.86	41.09	16.54

表15 FSNB与8种结合邻域粗糙集与优化算法的特征选择算法的统计检验

Tab. 15 Statistical test of FSNB and eight feature selection algorithms combining NRS and optimization algorithms

平均排序									$x F 2$	$F F$
FSNB	GANRS	PSONRS	ABCNRS	FANRS	SSONRS	CSNRS	HSNRS	IRRANRS	$x F 2$	$F F$
2.86	8.71	6.00	4.21	7.64	3.93	5.29	4.29	2.07	34.77	9.83

表15 FSNB与8种结合邻域粗糙集与优化算法的特征选择算法的统计检验

Tab. 15 Statistical test of FSNB and eight feature selection algorithms combining NRS and optimization algorithms

平均排序									$x F 2$	$F F$
FSNB	GANRS	PSONRS	ABCNRS	FANRS	SSONRS	CSNRS	HSNRS	IRRANRS	$x F 2$	$F F$
2.86	8.71	6.00	4.21	7.64	3.93	5.29	4.29	2.07	34.77	9.83

表16 FSNB与6种基于二进制灰狼优化的特征选择算法的统计检验

Tab. 16 Statistical test of FSNB and six feature selection algorithms based on binary grey wolf optimizer

平均排序							$x F 2$	$F F$
FSNB	BGWO	ABGWO	ABGWO-V1	ABGWO-V2	ABGWO-V3	ABGWO-V4	$x F 2$	$F F$
1.67	5.56	3.28	3.83	4.78	4.67	4.22	18.51	4.17

表16 FSNB与6种基于二进制灰狼优化的特征选择算法的统计检验

Tab. 16 Statistical test of FSNB and six feature selection algorithms based on binary grey wolf optimizer

平均排序							$x F 2$	$F F$
FSNB	BGWO	ABGWO	ABGWO-V1	ABGWO-V2	ABGWO-V3	ABGWO-V4	$x F 2$	$F F$
1.67	5.56	3.28	3.83	4.78	4.67	4.22	18.51	4.17

图1 FSNB与5种基于粗糙集的优化特征选择算法的Bonferroni-Dunn检验结果

Fig. 1 Bonferroni-Dunn test results of FSNB and five optimized feature selection algorithms based on rough set

图2 FSNB与8种结合粗糙集与优化算法的特征选择算法的Bonferroni-Dunn检验结果

Fig. 2 Bonferroni-Dunn test results of FSNB and eight feature selection algorithms based on rough set and optimization algorithms

图3 FSNB与8种结合邻域粗糙集与优化算法的特征选择算法的Bonferroni-Dunn检验结果

Fig. 3 Bonferroni-Dunn test results of FSNB and eight feature selection algorithms based on NRS and optimization algorithms

图4 FSNB与6种基于二进制灰狼优化的特征选择算法的Bonferroni-Dunn检验结果

Fig. 4 Bonferroni-Dunn test results of FSNB and six feature selection algorithms based on binary grey wolf optimizer

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基于邻域粗糙集和帝王蝶优化的特征选择算法

Feature selection algorithm based on neighborhood rough set and monarch butterfly optimization

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