共现邻域关系下的属性约简研究

doi:10.13232/j.cnki.jnju.2021.01.016

南京大学学报(自然科学版) ›› 2021, Vol. 57 ›› Issue (1): 150–159.doi: 10.13232/j.cnki.jnju.2021.01.016

• • 上一篇

共现邻域关系下的属性约简研究

毛振宇¹, 窦慧莉¹(), 宋晶晶¹^,³, 姜泽华¹, 王平心²

^1.江苏科技大学计算机学院，镇江，212003
^2.江苏科技大学理学院，镇江，212003
^3.数据科学与智能应用福建省高校重点实验室，漳州，363000

收稿日期:2020-09-16 出版日期:2021-01-21 发布日期:2021-01-21
通讯作者: 窦慧莉 E-mail:douhuili@163.com
作者简介:E⁃mail：douhuili@163.com
基金资助:
国家自然科学基金(62076111);数据科学与智能应用福建省高校重点实验室开放课题(D1901)

Research on attribute reduction via co⁃occurrence neighborhood relation

Zhenyu Mao¹, Huili Dou¹(), Jingjing Song¹^,³, Zehua Jiang¹, Pingxin Wang²

^1.School of Computer，Jiangsu University of Science and Technology，Zhenjiang，212003，China
^2.School of Science，Jiangsu University of Science and Technology，Zhenjiang，212003，China
^3.Fujian Province University Key Laboratory of Data Science and Intelligent Application，Zhangzhou，363000，China

Received:2020-09-16 Online:2021-01-21 Published:2021-01-21
Contact: Huili Dou E-mail:douhuili@163.com

摘要/Abstract

摘要：

在邻域粗糙集的研究中，往往借助给定的半径来约束样本之间的相似性进而实现邻域信息粒化，需要注意的是，若给定的半径较大，则不同类别的样本将落入同一邻域中，易引起邻域中信息的不精确或不一致.为改善这一问题，已有学者给出了伪标记邻域的策略，然而无论是传统邻域还是伪标记邻域，都仅仅使用样本间的距离来度量样本之间的相似性，忽略了邻域信息粒内部不同样本所对应的邻域之间的结构关系.鉴于此，通过引入邻域距离度量，提出一种共现邻域的信息粒化机制，并构造了新型的共现邻域以及伪标记共现邻域粗糙集模型，在此基础上使用前向贪心搜索策略实现了所构造的两种模型下的约简求解.实验结果表明，与传统邻域关系以及伪标记邻域关系所求得的约简相比，利用共现邻域方法求得的约简能够在不降低分类器准确率的前提下产生更高的约简率.

关键词: 粗糙集, 信息粒化, 邻域关系, 伪标记, 共现邻域

Abstract:

In the research of neighborhood rough set，a radius is generally appointed to restrain the similarities between the samples，which follows that the neighborhood information granulation can be realized. It should be noticed that if the radius is too great，then the samples in different classes may fall into the same neighborhood，and they may result in imprecise or inconsistent information. To alleviate the problem，the strategy of pseudo?label neighborhood has been proposed. Nevertheless，in both traditional neighborhood and pseudo?label neighborhood，the similarities of the samples are only measured by the distances between them，while the structural relationship of neighborhoods related to different samples contained in one neighborhood information granule is ignored. In view of this，through introducing the measure for neighborhood distance，the mechanism of co?occurrence neighborhood information granulation is proposed. Based on such mechanism，co?occurrence neighborhood rough set model and pseudo?label co?occurrence neighborhood rough set model are constructed. Then,the forward greedy searching strategy is employed to obtain the corresponding reducts. The experimental results demonstrate that compared with the reduct based on the neighborhood relation and pseudo?label neighborhood relation，the reduct based on co?occurrence neighborhood may provide the higher reduction ratio while the classification accuracy does not decrease.

Key words: rough set, information granulation, neighborhood relation, pseudo?label, co?occurrence neighborhood

中图分类号:

TP18

毛振宇, 窦慧莉, 宋晶晶, 姜泽华, 王平心. 共现邻域关系下的属性约简研究[J]. 南京大学学报(自然科学版), 2021, 57(1): 150–159.

Zhenyu Mao, Huili Dou, Jingjing Song, Zehua Jiang, Pingxin Wang. Research on attribute reduction via co⁃occurrence neighborhood relation[J]. Journal of Nanjing University(Natural Sciences), 2021, 57(1): 150–159.

图/表 7

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参考文献 21

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ID	数据集	样本数量	属性数	决策数
1	Breast Cancer Wisconsin (Diagnostic)	569	30	2
2	Cardiotocography	2126	21	10
3	Connectionist Bench (Vowel Recognition?Deterding Data)	990	13	11
4	Dermatology	366	34	6
5	Fertility	100	9	2
6	Lymphography	98	18	3
7	Sonar	208	60	2
8	Statlog (Heart)	270	13	2
9	Synthetic Control Chart Time Series	600	60	6
10	Urban Land Cover	675	147	9
11	Vertebral Column	310	6	2
12	Wine	178	13	3

ID	NR (ε=1)	CNR (ε=1)	NR (ε=0.95)	CNR (ε=0.95)	PLNR (ε=1)	PLCNR (ε=1)	PLNR (ε=0.95)	PLCNR (ε=0.95)
均值	0.4173	0.4701	0.4940	0.5712	0.6299	0.6369	0.6571	0.6852
1	0.3153	0.4268	0.4943	0.5907	0.8880	0.8983	0.9007	0.9157
2	0.1043	0.1776	0.2752	0.3595	0.6305	0.5952	0.6143	0.6229
3	0.1300	0.1869	0.1985	0.2854	0.6923	0.6508	0.6954	0.6785
4	0.6474	0.7071	0.7168	0.7694	0.6782	0.7088	0.7591	0.7747
5	0.1789	0.2422	0.2711	0.3878	0.1411	0.1822	0.2078	0.3122
6	0.5472	0.5972	0.5733	0.6356	0.4900	0.5283	0.5220	0.6000
7	0.8128	0.8513	0.8400	0.8810	0.7918	0.8313	0.8082	0.8518
8	0.2108	0.2577	0.3208	0.4123	0.2123	0.2115	0.2708	0.3377
9	0.7935	0.8107	0.8228	0.8557	0.8700	0.8787	0.8797	0.8720
10	0.8790	0.8814	0.9062	0.9276	0.9344	0.9385	0.9429	0.9475
11	0.0133	0.0800	0.0500	0.1417	0.7017	0.6633	0.7133	0.6783
12	0.3754	0.5069	0.4592	0.6077	0.5285	0.5562	0.5715	0.6308

ID	NR (ε=1)	CNR (ε=1)	NR (ε=0.95)	CNR (ε=0.95)	PLNR (ε=1)	PLCNR (ε=1)	PLNR (ε=0.95)	PLCNR (ε=0.95)
均值	0.8361	0.8411	0.8362	0.8363	0.7662	0.7935	0.7635	0.7883
1	0.9621	0.9605	0.9591	0.9554	0.9128	0.9110	0.9157	0.9071
2	0.7628	0.7662	0.7602	0.7665	0.6137	0.6762	0.6078	0.6743
3	0.9545	0.9513	0.9441	0.9354	0.5503	0.6684	0.5676	0.6522
4	0.9212	0.9241	0.9236	0.9191	0.8939	0.9137	0.8704	0.8984
5	0.8615	0.8630	0.8605	0.8630	0.8630	0.8625	0.8580	0.8535
6	0.7596	0.7768	0.7736	0.7786	0.7342	0.7603	0.7384	0.7423
7	0.7797	0.7733	0.7772	0.7704	0.7806	0.7662	0.7655	0.7627
8	0.7709	0.7731	0.7754	0.7681	0.7756	0.7813	0.7644	0.7694
9	0.8294	0.8463	0.8209	0.8268	0.7242	0.7973	0.7319	0.8163
10	0.7191	0.7363	0.7215	0.7301	0.6734	0.6956	0.6749	0.7045
11	0.7650	0.7769	0.7734	0.7853	0.7461	0.7513	0.7429	0.7495
12	0.9479	0.9458	0.9451	0.9368	0.9262	0.9382	0.9241	0.9294

ID	NR (ε=1)	CNR (ε=1)	NR (ε=0.95)	CNR (ε=0.95)	PLNR (ε=1)	PLCNR (ε=1)	PLNR (ε=0.95)	PLCNR (ε=0.95)
均值	0.7643	0.7652	0.7613	0.7603	0.7244	0.7420	0.7203	0.7399
1	0.9504	0.9506	0.9509	0.9517	0.8990	0.9084	0.9031	0.9020
2	0.6951	0.6985	0.6832	0.6907	0.5652	0.5959	0.5600	0.5985
3	0.3133	0.3317	0.3156	0.3390	0.2537	0.3027	0.2627	0.2994
4	0.9224	0.9120	0.9213	0.9046	0.8910	0.8990	0.8595	0.8842
5	0.8800	0.8800	0.8800	0.8800	0.8800	0.8800	0.8800	0.8800
6	0.7542	0.7650	0.7445	0.7533	0.7363	0.7718	0.7313	0.7724
7	0.7145	0.7039	0.7163	0.7043	0.7190	0.7049	0.7152	0.7105
8	0.8000	0.7937	0.7961	0.7781	0.8028	0.8059	0.7972	0.7919
9	0.8448	0.8507	0.8413	0.8336	0.7193	0.7887	0.7286	0.8062
10	0.6782	0.6877	0.6781	0.6942	0.6278	0.6442	0.6201	0.6474
11	0.6715	0.6732	0.6724	0.6747	0.6781	0.6781	0.6785	0.6784
12	0.9477	0.9351	0.9360	0.9200	0.9200	0.9240	0.9079	0.9080

ID	NR (ε=1)	CNR (ε=1)	NR (ε=0.95)	CNR (ε=0.95)	PLNR (ε=1)	PLCNR (ε=1)	PLNR (ε=0.95)	PLCNR (ε=0.95)
均值	0.8678	0.8827	0.8739	0.8808	0.8757	0.8744	0.8710	0.8666
1	0.9701	0.9719	0.9719	0.9701	0.9543	0.9508	0.9595	0.9561
2	0.7799	0.7827	0.7864	0.7973	0.7963	0.7977	0.7930	0.7907
3	0.9646	0.9657	0.9626	0.9636	0.9414	0.9404	0.9293	0.9354
4	0.9564	0.9645	0.9535	0.9509	0.9508	0.9454	0.9537	0.9346
5	0.8800	0.8800	0.8900	0.8900	0.8800	0.8900	0.8900	0.8900
6	0.8053	0.8258	0.8163	0.8253	0.8158	0.8158	0.8153	0.7847
7	0.8367	0.8606	0.8369	0.8609	0.8368	0.8272	0.8225	0.8269
8	0.8111	0.8185	0.8222	0.8407	0.8222	0.8185	0.8148	0.8185
9	0.9333	0.9317	0.9200	0.9150	0.9333	0.9250	0.8983	0.9017
10	0.7363	0.7911	0.7541	0.7556	0.7956	0.8000	0.8059	0.7911
11	0.7742	0.8226	0.8065	0.8226	0.8097	0.8097	0.8097	0.8097
12	0.9660	0.9775	0.9660	0.9773	0.9716	0.9717	0.9602	0.9600

共现邻域关系下的属性约简研究

Research on attribute reduction via co⁃occurrence neighborhood relation

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ID	NR (ε=1)	CNR (ε=1)	NR (ε=0.95)	CNR (ε=0.95)	PLNR (ε=1)	PLCNR (ε=1)	PLNR (ε=0.95)	PLCNR (ε=0.95)
均值	0.7967	0.7992	0.7998	0.8018	0.7986	0.8016	0.8042	0.7973
1	0.9543	0.9561	0.9578	0.9578	0.9526	0.9508	0.9508	0.9490
2	0.7093	0.7084	0.7112	0.7140	0.7121	0.7074	0.7182	0.7084
3	0.3848	0.3879	0.3899	0.4273	0.3778	0.4020	0.4253	0.3828
4	0.9482	0.9591	0.9563	0.9427	0.9591	0.9373	0.9346	0.9372
5	0.8800	0.8800	0.8800	0.8800	0.8800	0.8800	0.8800	0.8800
6	0.8263	0.8163	0.8058	0.8053	0.8274	0.8368	0.8363	0.8374
7	0.7455	0.7595	0.7552	0.7646	0.7746	0.7691	0.7743	0.7646
8	0.8259	0.8333	0.8333	0.8333	0.8259	0.8333	0.8296	0.8370
9	0.9100	0.9100	0.9050	0.9083	0.8833	0.9050	0.8950	0.8933
10	0.7274	0.7274	0.7452	0.7363	0.7407	0.7511	0.7526	0.7363
11	0.6774	0.6806	0.6806	0.6806	0.6839	0.6806	0.6871	0.6806
12	0.9716	0.9719	0.9773	0.9717	0.9659	0.9660	0.9662	0.9605