基于信念子簇切割的模糊聚类算法

doi:10.11772/j.issn.1001-9081.2023050610

摘要/Abstract

摘要： 摘要: 信念峰值聚类算法(BPC)是一种基于模糊视角的密度峰值聚类算法(DPC)的新变体，它用模糊数学的观点刻画数据的分布特征与相关性。但BPC算法在信念值的计算上主要基于局部数据点信息，而未考察整个数据集整体的分布和结构，并且原始的分配策略鲁棒性弱。针对以上问题，提出一种基于信念子簇切割的模糊聚类算法(BSCC) ，该算法结合了信念峰值和谱方法。首先，通过局部信念信息将数据集划分为众多高纯度子簇；然后，将子簇视作新样本，通过簇间的相似关系，利用谱方法进行割图聚类，从而耦合了局部信息与全局信息；最后，将子簇内的点分配到子簇所在类簇以完成最终聚类。与BPC算法相比，BSCC在带有多子簇结构的据集上具有明显优势，如在americanflag数据集和car数据集上的准确率分别提高了16.38个百分点和21.35个百分点。一系列的在合成数据集和真实数据集上的聚类实验表明，BSCC在调整兰德系数(ARI)、归一化互信息(NMI)和准确率(ACC)这三个评价指标上整体优于BPC和其他7种聚类算法。

关键词: 聚类分析, 密度峰值聚类, 信念峰值聚类, 谱聚类, 信念子簇, 子簇合并

Abstract: Abstract: Belief Peaks Clustering (BPC) algorithm is a new variant of Density Peaks Clustering (DPC) algorithm based on fuzzy perspective. It uses fuzzy mathematics to describe the distribution characteristics and correlation of data. However, BPC algorithm mainly relies on the information of local data points in the calculation of belief values, instead of investigating the distribution and structure of the whole dataset. Moreover, the robustness of the original allocation strategy is weak. To solve these problems, a fuzzy Clustering algorithm based on Belief Subcluster Cutting (BSCC) was proposed by combining belief peak value and spectral method. Firstly, the dataset was divided into many high-purity subclusters by local belief information. Then, the subcluster was regarded as a new sample, and the spectral method was used for cutting graph clustering through the similarity relationship between clusters, thus coupling local information and global information. Finally, the points in the subcluster were assigned to the class cluster where the subcluster was located to complete the final clustering. Compared with BPC algorithm, BSCC has obvious advantages on datasets with multiple subclusters, such as the accuracy improvement of 16.38 and 21.35 percentage points on the americanflag dataset and car dataset, respectively. A series of clustering experiments on synthetic datasets and real datasets show that BSCC outperforms BPC and the other seven clustering algorithms on the three evaluation indicators of Adjusted Rand Index (ARI), Normalized Mutual Information (NMI) and Accuracy (ACC).

Key words: clustering analysis, density peaks clustering, belief peaks clustering, spectral clustering, belief subcluster, subcluster merging

中图分类号:

TP181

丁雨张瀚霖罗荣孟华. 基于信念子簇切割的模糊聚类算法[J]. 计算机应用, DOI: 10.11772/j.issn.1001-9081.2023050610.

图/表 12

图1 Bel?δ决策图示例

Fig. 1 Example of Bel?δ decision graph

图2 DPC和BPC算法在Jain数据集上的聚类效果对比

Fig. 2 Clustering effect comparison of DPC and BPC on Jain dataset

图3 3个合成数据集

Fig. 3 Three synthetic datasets

图4 BPC算法关于子簇数的纯度变化

Fig. 4 Relation between subcluster number and purity for BPC algorithm

图5 happy数据集的预聚类

Fig. 5 Preclustering of happy dataset

图6 共享最近邻居连接图

Fig. 6 Connection diagram of shared nearest neighbors

表1 数据集详情

Tab. 1 Details of datasets

类型	数据集	样本数	特征数	类别数
合成数据集	Aggregation	788	2	7
	R15	600	2	15
	Spiral	312	2	3
	Flame	240	2	2
	Jain	373	2	2
	circle	299	2	3
	happy	266	2	3
	Compound	499	2	6
	fourlines	600	2	4
	S1	5 000	2	15
真实数据集	Iris	150	4	3
	Car	1 728	6	4
	Seeds	210	7	3
	Pima	768	8	2
	Wine	178	13	3
	heartdisseaseh	294	13	5
	congressEW	435	16	2
	vote	435	16	2
	labo	57	16	2
	mfeat-fou	2 000	76	10
	semeionEW	1 593	256	10
	americanflag	873	892	3
	cactus	919	892	3
	worldmap	935	899	3
	leukemia	72	7 070	2

表2 9种聚类算法在10个合成数据集上的聚类性能

Tab. 2 Clustering performance of nine clustering algorithms on ten synthetic datasets

数据集	评价指标	BSCC	BPC	BPEC	FHC-LDP	DPC-DBFN	LDP-MST	DPC-KNN	DPC	SC
数据集	评价指标	$K$ / $k$	$K$	$K$	$k$	$k$	$d i m$	$k$	$d c$	$k$
Aggregation	ARI	0.995 6	0.781 1	0.687 4	1.000 0	0.992 7	0.995 6	0.995 6	0.754 8	0.978 3
	NMI	0.992 4	0.857 8	0.810 6	1.000 0	0.988 3	0.992 4	0.992 4	0.893 5	0.975 4
	ACC	0.997 5	0.785 5	0.821 1	1.000 0	0.996 2	0.997 5	0.997 5	0.818 5	0.989 8
	Arg-	30/4	15	25	6	30	2	21	2	4
R15	ARI	0.992 8	0.992 8	0.992 8	0.992 8	0.996 4	0.989 1	0.992 8	0.992 8	0.992 8
	NMI	0.994 2	0.994 2	0.994 2	0.994 2	0.997 1	0.991 3	0.994 2	0.994 2	0.994 2
	ACC	0.996 7	0.996 7	0.996 7	0.996 7	0.998 3	0.995 0	0.996 7	0.996 7	0.996 7
	Arg-	25/4	25	15	7	39	2	2	0.1	5
Spiral	ARI	1.000 0	0.235 9	0.007 5	1.000 0	0.148 7	1.000 0	1.000 0	1.000 0	1.000 0
	NMI	1.000 0	0.355 7	0.015 9	1.000 0	0.157 4	1.000 0	1.000 0	1.000 0	1.000 0
	ACC	1.000 0	0.669 9	0.381 4	1.000 0	0.554 5	1.000 0	1.000 0	1.000 0	1.000 0
	Arg-	10/3	50	85	3	4	2	6	2	2
Flame	ARI	1.000 0	1.000 0	0.511 7	1.000 0	0.966 6	0.933 9	1.000 0	0.586 1	0.950 1
	NMI	1.000 0	1.000 0	0.470 0	1.000 0	0.926 9	0.875 2	1.000 0	0.577 3	0.899 1
	ACC	1.000 0	1.000 0	0.858 3	1.000 0	0.991 7	0.983 3	1.000 0	0.883 3	0.987 5
	Arg-	25/3	70	45	7	6	2	4	0.1	4
Jain	ARI	1.000 0	0.662 3	0.537 6	1.000 0	0.800 8	1.000 0	0.757 7	0.714 6	1.000 0
	NMI	1.000 0	0.582 3	0.520 5	1.000 0	0.718 8	1.000 0	0.674 7	0.652 2	1.000 0
	ACC	1.000 0	0.916 9	0.868 6	1.000 0	0.951 7	1.000 0	0.941 0	0.924 9	1.000 0
	Arg-	10/5	10	90	7	43	2	37	0.5	4
circle	ARI	1.000 0	0.510 1	0.230 5	1.000 0	0.460 6	1.000 0	0.187 9	0.214 9	1.000 0
	NMI	1.000 0	0.664 9	0.367 2	1.000 0	0.639 6	1.000 0	0.323 0	0.345 5	1.000 0
	ACC	1.000 0	0.642 1	0.575 3	1.000 0	0.739 1	1.000 0	0.602 0	0.568 6	1.000 0
	Arg-	10/6	100	15	7	17	2	36	0.2	4
happy	ARI	1.000 0	1.000 0	0.526 2	1.000 0	0.522 1	1.000 0	0.717 9	0.601 7	1.000 0
	NMI	1.000 0	1.000 0	0.617 1	1.000 0	0.609 4	1.000 0	0.787 1	0.679 1	1.000 0
	ACC	1.000 0	1.000 0	0.815 8	1.000 0	0.815 8	1.000 0	0.898 5	0.849 6	1.000 0
	Arg-	10/5	45	15	8	2	2	17	0.1	4
Compound	ARI	0.844 3	0.777 5	0.766 6	0.848 3	0.808 7	0.833 8	0.808 7	0.546 0	0.533 7
	NMI	0.897 2	0.811 0	0.798 3	0.855 3	0.838 2	0.852 0	0.850 0	0.736 5	0.724 6
	ACC	0.854 6	0.814 5	0.774 4	0.882 2	0.852 1	0.807 0	0.869 7	0.666 7	0.646 6
	Arg-	45/3	25	15	5	5	2	3	1	21
S1	ARI	0.990 6	0.988 9	0.988 0	0.988 9	0.988 0	0.988 5	0.989 7	0.989 7	0.988 4
	NMI	0.990 3	0.989 0	0.988 6	0.988 9	0.987 8	0.988 7	0.989 6	0.989 6	0.988 8
	ACC	0.995 6	0.994 8	0.994 4	0.994 8	0.994 4	0.994 6	0.995 2	0.995 2	0.994 8
	Arg-	15/37	80	55	43	28	2	13	2	36
fourlines	ARI	1.000 0	0.704 0	1.000 0	1.000 0	0.831 1	1.000 0	0.789 0	0.546 5	1.000 0
	NMI	1.000 0	0.821 2	1.000 0	1.000 0	0.875 6	1.000 0	0.860 5	0.758 7	1.000 0
	ACC	1.000 0	0.745 0	1.000 0	1.000 0	0.933 3	1.000 0	0.855 0	0.650 0	1.000 0
	Arg-	10/7	30	55	9	35	2	5	0.1	6

表2 9种聚类算法在10个合成数据集上的聚类性能

Tab. 2 Clustering performance of nine clustering algorithms on ten synthetic datasets

数据集	评价指标	BSCC	BPC	BPEC	FHC-LDP	DPC-DBFN	LDP-MST	DPC-KNN	DPC	SC
数据集	评价指标	$K$ / $k$	$K$	$K$	$k$	$k$	$d i m$	$k$	$d c$	$k$
Aggregation	ARI	0.995 6	0.781 1	0.687 4	1.000 0	0.992 7	0.995 6	0.995 6	0.754 8	0.978 3
	NMI	0.992 4	0.857 8	0.810 6	1.000 0	0.988 3	0.992 4	0.992 4	0.893 5	0.975 4
	ACC	0.997 5	0.785 5	0.821 1	1.000 0	0.996 2	0.997 5	0.997 5	0.818 5	0.989 8
	Arg-	30/4	15	25	6	30	2	21	2	4
R15	ARI	0.992 8	0.992 8	0.992 8	0.992 8	0.996 4	0.989 1	0.992 8	0.992 8	0.992 8
	NMI	0.994 2	0.994 2	0.994 2	0.994 2	0.997 1	0.991 3	0.994 2	0.994 2	0.994 2
	ACC	0.996 7	0.996 7	0.996 7	0.996 7	0.998 3	0.995 0	0.996 7	0.996 7	0.996 7
	Arg-	25/4	25	15	7	39	2	2	0.1	5
Spiral	ARI	1.000 0	0.235 9	0.007 5	1.000 0	0.148 7	1.000 0	1.000 0	1.000 0	1.000 0
	NMI	1.000 0	0.355 7	0.015 9	1.000 0	0.157 4	1.000 0	1.000 0	1.000 0	1.000 0
	ACC	1.000 0	0.669 9	0.381 4	1.000 0	0.554 5	1.000 0	1.000 0	1.000 0	1.000 0
	Arg-	10/3	50	85	3	4	2	6	2	2
Flame	ARI	1.000 0	1.000 0	0.511 7	1.000 0	0.966 6	0.933 9	1.000 0	0.586 1	0.950 1
	NMI	1.000 0	1.000 0	0.470 0	1.000 0	0.926 9	0.875 2	1.000 0	0.577 3	0.899 1
	ACC	1.000 0	1.000 0	0.858 3	1.000 0	0.991 7	0.983 3	1.000 0	0.883 3	0.987 5
	Arg-	25/3	70	45	7	6	2	4	0.1	4
Jain	ARI	1.000 0	0.662 3	0.537 6	1.000 0	0.800 8	1.000 0	0.757 7	0.714 6	1.000 0
	NMI	1.000 0	0.582 3	0.520 5	1.000 0	0.718 8	1.000 0	0.674 7	0.652 2	1.000 0
	ACC	1.000 0	0.916 9	0.868 6	1.000 0	0.951 7	1.000 0	0.941 0	0.924 9	1.000 0
	Arg-	10/5	10	90	7	43	2	37	0.5	4
circle	ARI	1.000 0	0.510 1	0.230 5	1.000 0	0.460 6	1.000 0	0.187 9	0.214 9	1.000 0
	NMI	1.000 0	0.664 9	0.367 2	1.000 0	0.639 6	1.000 0	0.323 0	0.345 5	1.000 0
	ACC	1.000 0	0.642 1	0.575 3	1.000 0	0.739 1	1.000 0	0.602 0	0.568 6	1.000 0
	Arg-	10/6	100	15	7	17	2	36	0.2	4
happy	ARI	1.000 0	1.000 0	0.526 2	1.000 0	0.522 1	1.000 0	0.717 9	0.601 7	1.000 0
	NMI	1.000 0	1.000 0	0.617 1	1.000 0	0.609 4	1.000 0	0.787 1	0.679 1	1.000 0
	ACC	1.000 0	1.000 0	0.815 8	1.000 0	0.815 8	1.000 0	0.898 5	0.849 6	1.000 0
	Arg-	10/5	45	15	8	2	2	17	0.1	4
Compound	ARI	0.844 3	0.777 5	0.766 6	0.848 3	0.808 7	0.833 8	0.808 7	0.546 0	0.533 7
	NMI	0.897 2	0.811 0	0.798 3	0.855 3	0.838 2	0.852 0	0.850 0	0.736 5	0.724 6
	ACC	0.854 6	0.814 5	0.774 4	0.882 2	0.852 1	0.807 0	0.869 7	0.666 7	0.646 6
	Arg-	45/3	25	15	5	5	2	3	1	21
S1	ARI	0.990 6	0.988 9	0.988 0	0.988 9	0.988 0	0.988 5	0.989 7	0.989 7	0.988 4
	NMI	0.990 3	0.989 0	0.988 6	0.988 9	0.987 8	0.988 7	0.989 6	0.989 6	0.988 8
	ACC	0.995 6	0.994 8	0.994 4	0.994 8	0.994 4	0.994 6	0.995 2	0.995 2	0.994 8
	Arg-	15/37	80	55	43	28	2	13	2	36
fourlines	ARI	1.000 0	0.704 0	1.000 0	1.000 0	0.831 1	1.000 0	0.789 0	0.546 5	1.000 0
	NMI	1.000 0	0.821 2	1.000 0	1.000 0	0.875 6	1.000 0	0.860 5	0.758 7	1.000 0
	ACC	1.000 0	0.745 0	1.000 0	1.000 0	0.933 3	1.000 0	0.855 0	0.650 0	1.000 0
	Arg-	10/7	30	55	9	35	2	5	0.1	6

图7 9种算法在Jain数据集上的聚类结果

Fig. 7 Clustering results of nine algorithms on Jain dataset

图8 9种算法在Aggregation数据集上的聚类结果

Fig. 8 Clustering results of nine algorithms on Aggregation dataset

表3 9种聚类算法在15个真实数据集上的聚类性能

Tab. 3 Clustering performance of nine clustering algorithms on fifteen real-world datasets

数据集	评价指标	BSCC	BPC	BPEC	FHC-LDP	DPC-DBFN	LDP-MST	DPC-KNN	DPC	SC
数据集	评价指标	$K$ / $k$	$K$	$K$	$k$	$k$	$d i m$	$k$	$d c$	$k$
Iris	ARI	0.903 8	0.903 8	0.922 2	0.903 8	0.851 0	0.745 5	0.903 8	0.609 6	0.851 5
	NMI	0.885 1	0.885 1	0.901 1	0.885 1	0.836 6	0.798 0	0.885 1	0.705 1	0.862 2
	ACC	0.966 7	0.966 7	0.973 3	0.966 7	0.946 7	0.900 0	0.966 7	0.813 3	0.946 7
	Arg-	10/4	10	15	9	21	4	2	5	4
Car	ARI	0.429 2	0.181 8	0.117 0	0.147 5	0.153 5	-0.021 3	0.310 9	0.216 5	0.255 0
	NMI	0.295 5	0.220 0	0.170 8	0.123 7	0.101 6	0.161 5	0.249 4	0.328 6	0.255 0
	ACC	0.694 4	0.480 9	0.406 8	0.636 6	0.608 8	0.342 0	0.693 3	0.483 2	0.558 4
	Arg-	25/10	95	35	5	50	5	11	0.1	10
Seeds	ARI	0.797 0	0.789 5	0.715 1	0.728 9	0.766 4	0.570 2	0.766 4	0.744 8	0.826 1
	NMI	0.758 4	0.750 8	0.689 2	0.694 2	0.734 3	0.630 7	0.734 3	0.719 4	0.798 1
	ACC	0.928 6	0.923 8	0.895 2	0.900 0	0.914 3	0.819 0	0.914 3	0.904 8	0.938 1
	Arg-	15/5	30	50	12	2	5	4	0.1	4
Pima	ARI	0.149 7	0.013 1	0.072 0	0.014 3	0.078 5	0.019 6	0.014 3	0.141 2	0.085 3
	NMI	0.092 8	0.003 5	0.044 7	0.004 2	0.043 6	0.013 2	0.004 2	0.459 2	0.049 3
	ACC	0.696 6	0.648 4	0.636 7	0.649 7	0.651 0	0.658 9	0.649 7	0.516 9	0.649 7
	Arg-	45/49	25	40	7	46	4	2	0.1	45
Wine	ARI	0.865 1	0.834 9	0.848 5	0.726 9	0.831 8	0.362 7	0.726 9	0.672 4	0.914 9
	NMI	0.835 2	0.821 5	0.816 0	0.743 5	0.795 3	0.432 7	0.743 5	0.710 4	0.892 6
	ACC	0.955 1	0.943 8	0.949 4	0.904 5	0.943 8	0.713 5	0.904 5	0.882 0	0.971 9
	Arg-	15/20	55	30	17	3	2	17	2	15
heartdisseaseh	ARI	0.206 7	0.042 1	0.172 9	0.344 3	0.159 6	0.178 7	0.168 4	0.123 3	0.134 1
	NMI	0.170 9	0.101 6	0.187 3	0.181 5	0.191 7	0.112 7	0.160 1	0.177 8	0.170 8
	ACC	0.485 7	0.445 6	0.445 6	0.598 6	0.438 8	0.574 8	0.418 4	0.370 7	0.418 4
	Arg-	85/2	90	85	6	13	7	5	0.1	3
congressEW	ARI	0.650 1	0.628 1	0.037 1	0.536 7	0.536 3	0.557 2	0.613 5	0.564 1	0.592 1
	NMI	0.565 1	0.547 7	0.023 2	0.464 3	0.432 9	0.489 2	0.526 5	0.505 9	0.520 4
	ACC	0.903 4	0.896 6	0.600 0	0.866 7	0.866 7	0.873 6	0.892 0	0.875 9	0.885 1
	Arg-	30/3	30	10	23	2	15	4	2	9
vote	ARI	0.650 0	0.620 7	0	0.564 0	0.503 5	0.523 2	0.650 0	0.530 0	0.557 2
	NMI	0.551 6	0.532 1	0	0.475 8	0.463 7	0.441 7	0.544 7	0.459 5	0.489 2
	ACC	0.903 4	0.894 3	0.613 8	0.875 9	0.855 2	0.862 1	0.903 4	0.864 4	0.873 6
	Arg-	65/12	30	10	33	4	14	3	2	25
labo	ARI	0.359 0	0.317 3	0.283 3	0.275 4	0.073 4	0.035 8	0.275 4	0.241 6	0.243 7
	NMI	0.254 3	0.219 3	0.224 8	0.184 8	0.061 8	0.033 8	0.184 8	0.163 5	0.172 9
	ACC	0.807 0	0.789 5	0.771 9	0.771 9	0.649 1	0.614 0	0.771 9	0.754 4	0.754 4
	Arg-	25/6	35	45	12	2	7	24	0.5	39
mfeat-fou	ARI	0.463 5	0.305 7	0.359 0	0.470 8	0.145 0	0.685 5	0.331 9	0.363 1	0.533 0
	NMI	0.657 9	0.523 1	0.482 7	0.610 4	0.371 5	0.765 1	0.523 1	0.509 1	0.666 1
	ACC	0.630 0	0.431 5	0.550 5	0.639 0	0.310 5	0.789 5	0.484 0	0.523 5	0.675 4
	Arg-	10/28	100	50	15	6	50	4	0.5	4
semeionEW	ARI	0.488 2	0.407 7	0.304 0	0.525 9	0.299 7	0.446 7	0.220 2	0.266 2	0.567 0
	NMI	0.637 0	0.579 8	0.409 5	0.646 5	0.442 9	0.637 1	0.406 7	0.426 0	0.671 0
	ACC	0.661 0	0.531 1	0.534 8	0.699 3	0.480 2	0.630 3	0.317 6	0.425 6	0.671 7
	Arg-	15/12	90	70	18	3	15	48	0.2	3
americanflag	ARI	0.220 3	0.014 8	-0.014 3	0.070 1	-0.013 6	-0.020 1	0.028 3	0.077 3	0.011 5
	NMI	0.140 3	0.029 3	0.099 0	0.111 5	0.048 4	0.052 2	0.039 6	0.052 9	0.023 7
	ACC	0.627 7	0.463 9	0.429 6	0.572 7	0.378 0	0.529 2	0.423 8	0.497 1	0.568 7
	Arg-	20/5	25	40	21	6	3	5	2	3
cactus	ARI	0.246 1	0.010 3	0.102 6	0.149 1	0.193 6	0.188 8	0.134 7	0.060 1	0.013 2
	NMI	0.123 9	0.012 7	0.127 5	0.068 7	0.089 1	0.112 3	0.079 7	0.048 9	0.015 9
	ACC	0.706 2	0.664 9	0.526 7	0.638 7	0.669 2	0.707 3	0.697 5	0.551 7	0.666 7
	Arg-	30/5	10	25	11	20	6	2	0.1	6
worldmap	ARI	0.253 7	0.211 9	0.141 6	0.125 6	0.080 1	0.224 4	0.192 4	0.072 1	0.005 8
	NMI	0.142 6	0.109 8	0.042 3	0.129 3	0.021 7	0.120 2	0.083 1	0.038 8	0.012 3
	ACC	0.738 0	0.713 4	0.664 2	0.699 5	0.591 4	0.730 5	0.718 7	0.503 7	0.713 4
	Arg-	60/8	30	15	17	46	5	15	0.1	3
leukemia	ARI	0.547 6	0.395 0	0.268 5	0.381 7	0.159 5	0.292 2	0.347 2	0.105 2	0.117 2
	NMI	0.459 4	0.282 8	0.213 7	0.325 0	0.107 3	0.196 3	0.270 4	0.143 9	0.082 6
	ACC	0.875 0	0.819 4	0.763 9	0.819 4	0.708 3	0.777 8	0.805 6	0.708 3	0.680 6
	Arg-	20/2	10	50	9	43	26	4	1	7

表3 9种聚类算法在15个真实数据集上的聚类性能

Tab. 3 Clustering performance of nine clustering algorithms on fifteen real-world datasets

数据集	评价指标	BSCC	BPC	BPEC	FHC-LDP	DPC-DBFN	LDP-MST	DPC-KNN	DPC	SC
数据集	评价指标	$K$ / $k$	$K$	$K$	$k$	$k$	$d i m$	$k$	$d c$	$k$
Iris	ARI	0.903 8	0.903 8	0.922 2	0.903 8	0.851 0	0.745 5	0.903 8	0.609 6	0.851 5
	NMI	0.885 1	0.885 1	0.901 1	0.885 1	0.836 6	0.798 0	0.885 1	0.705 1	0.862 2
	ACC	0.966 7	0.966 7	0.973 3	0.966 7	0.946 7	0.900 0	0.966 7	0.813 3	0.946 7
	Arg-	10/4	10	15	9	21	4	2	5	4
Car	ARI	0.429 2	0.181 8	0.117 0	0.147 5	0.153 5	-0.021 3	0.310 9	0.216 5	0.255 0
	NMI	0.295 5	0.220 0	0.170 8	0.123 7	0.101 6	0.161 5	0.249 4	0.328 6	0.255 0
	ACC	0.694 4	0.480 9	0.406 8	0.636 6	0.608 8	0.342 0	0.693 3	0.483 2	0.558 4
	Arg-	25/10	95	35	5	50	5	11	0.1	10
Seeds	ARI	0.797 0	0.789 5	0.715 1	0.728 9	0.766 4	0.570 2	0.766 4	0.744 8	0.826 1
	NMI	0.758 4	0.750 8	0.689 2	0.694 2	0.734 3	0.630 7	0.734 3	0.719 4	0.798 1
	ACC	0.928 6	0.923 8	0.895 2	0.900 0	0.914 3	0.819 0	0.914 3	0.904 8	0.938 1
	Arg-	15/5	30	50	12	2	5	4	0.1	4
Pima	ARI	0.149 7	0.013 1	0.072 0	0.014 3	0.078 5	0.019 6	0.014 3	0.141 2	0.085 3
	NMI	0.092 8	0.003 5	0.044 7	0.004 2	0.043 6	0.013 2	0.004 2	0.459 2	0.049 3
	ACC	0.696 6	0.648 4	0.636 7	0.649 7	0.651 0	0.658 9	0.649 7	0.516 9	0.649 7
	Arg-	45/49	25	40	7	46	4	2	0.1	45
Wine	ARI	0.865 1	0.834 9	0.848 5	0.726 9	0.831 8	0.362 7	0.726 9	0.672 4	0.914 9
	NMI	0.835 2	0.821 5	0.816 0	0.743 5	0.795 3	0.432 7	0.743 5	0.710 4	0.892 6
	ACC	0.955 1	0.943 8	0.949 4	0.904 5	0.943 8	0.713 5	0.904 5	0.882 0	0.971 9
	Arg-	15/20	55	30	17	3	2	17	2	15
heartdisseaseh	ARI	0.206 7	0.042 1	0.172 9	0.344 3	0.159 6	0.178 7	0.168 4	0.123 3	0.134 1
	NMI	0.170 9	0.101 6	0.187 3	0.181 5	0.191 7	0.112 7	0.160 1	0.177 8	0.170 8
	ACC	0.485 7	0.445 6	0.445 6	0.598 6	0.438 8	0.574 8	0.418 4	0.370 7	0.418 4
	Arg-	85/2	90	85	6	13	7	5	0.1	3
congressEW	ARI	0.650 1	0.628 1	0.037 1	0.536 7	0.536 3	0.557 2	0.613 5	0.564 1	0.592 1
	NMI	0.565 1	0.547 7	0.023 2	0.464 3	0.432 9	0.489 2	0.526 5	0.505 9	0.520 4
	ACC	0.903 4	0.896 6	0.600 0	0.866 7	0.866 7	0.873 6	0.892 0	0.875 9	0.885 1
	Arg-	30/3	30	10	23	2	15	4	2	9
vote	ARI	0.650 0	0.620 7	0	0.564 0	0.503 5	0.523 2	0.650 0	0.530 0	0.557 2
	NMI	0.551 6	0.532 1	0	0.475 8	0.463 7	0.441 7	0.544 7	0.459 5	0.489 2
	ACC	0.903 4	0.894 3	0.613 8	0.875 9	0.855 2	0.862 1	0.903 4	0.864 4	0.873 6
	Arg-	65/12	30	10	33	4	14	3	2	25
labo	ARI	0.359 0	0.317 3	0.283 3	0.275 4	0.073 4	0.035 8	0.275 4	0.241 6	0.243 7
	NMI	0.254 3	0.219 3	0.224 8	0.184 8	0.061 8	0.033 8	0.184 8	0.163 5	0.172 9
	ACC	0.807 0	0.789 5	0.771 9	0.771 9	0.649 1	0.614 0	0.771 9	0.754 4	0.754 4
	Arg-	25/6	35	45	12	2	7	24	0.5	39
mfeat-fou	ARI	0.463 5	0.305 7	0.359 0	0.470 8	0.145 0	0.685 5	0.331 9	0.363 1	0.533 0
	NMI	0.657 9	0.523 1	0.482 7	0.610 4	0.371 5	0.765 1	0.523 1	0.509 1	0.666 1
	ACC	0.630 0	0.431 5	0.550 5	0.639 0	0.310 5	0.789 5	0.484 0	0.523 5	0.675 4
	Arg-	10/28	100	50	15	6	50	4	0.5	4
semeionEW	ARI	0.488 2	0.407 7	0.304 0	0.525 9	0.299 7	0.446 7	0.220 2	0.266 2	0.567 0
	NMI	0.637 0	0.579 8	0.409 5	0.646 5	0.442 9	0.637 1	0.406 7	0.426 0	0.671 0
	ACC	0.661 0	0.531 1	0.534 8	0.699 3	0.480 2	0.630 3	0.317 6	0.425 6	0.671 7
	Arg-	15/12	90	70	18	3	15	48	0.2	3
americanflag	ARI	0.220 3	0.014 8	-0.014 3	0.070 1	-0.013 6	-0.020 1	0.028 3	0.077 3	0.011 5
	NMI	0.140 3	0.029 3	0.099 0	0.111 5	0.048 4	0.052 2	0.039 6	0.052 9	0.023 7
	ACC	0.627 7	0.463 9	0.429 6	0.572 7	0.378 0	0.529 2	0.423 8	0.497 1	0.568 7
	Arg-	20/5	25	40	21	6	3	5	2	3
cactus	ARI	0.246 1	0.010 3	0.102 6	0.149 1	0.193 6	0.188 8	0.134 7	0.060 1	0.013 2
	NMI	0.123 9	0.012 7	0.127 5	0.068 7	0.089 1	0.112 3	0.079 7	0.048 9	0.015 9
	ACC	0.706 2	0.664 9	0.526 7	0.638 7	0.669 2	0.707 3	0.697 5	0.551 7	0.666 7
	Arg-	30/5	10	25	11	20	6	2	0.1	6
worldmap	ARI	0.253 7	0.211 9	0.141 6	0.125 6	0.080 1	0.224 4	0.192 4	0.072 1	0.005 8
	NMI	0.142 6	0.109 8	0.042 3	0.129 3	0.021 7	0.120 2	0.083 1	0.038 8	0.012 3
	ACC	0.738 0	0.713 4	0.664 2	0.699 5	0.591 4	0.730 5	0.718 7	0.503 7	0.713 4
	Arg-	60/8	30	15	17	46	5	15	0.1	3
leukemia	ARI	0.547 6	0.395 0	0.268 5	0.381 7	0.159 5	0.292 2	0.347 2	0.105 2	0.117 2
	NMI	0.459 4	0.282 8	0.213 7	0.325 0	0.107 3	0.196 3	0.270 4	0.143 9	0.082 6
	ACC	0.875 0	0.819 4	0.763 9	0.819 4	0.708 3	0.777 8	0.805 6	0.708 3	0.680 6
	Arg-	20/2	10	50	9	43	26	4	1	7

图9 BSCC在4个数据集上随最近邻K和k值改变的ACC值变化

Fig. 9 ACC value of BSCC algorithm changing with values of nearest neighbors K and k on four datasets

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