模糊c-harmonic均值算法在不平衡数据上改进

doi:10.13229/j.cnki.jdxbgxb20190963

摘要/Abstract

摘要：

针对模糊c-harmonic均值算法（FCHM）在不平衡数据集上的聚类效果不理想的问题，提出了一种基于聚类体量约束的模糊c-harmonic均值算法。首先，利用隶属度矩阵定义各个类的体量，用于约束FCHM算法的代价函数，从而构建一个新的代价函数；然后，将该代价函数最小化，得到新的隶属度矩阵和聚类中心的计算公式；最后，在UCI数据集、模拟不平衡数据集及真实机床振动检测不平衡数据集上分别进行实验。实验结果表明，与同类算法相比，本文算法在保持传统算法全局最优性能的同时，在不平衡数据集上也能得到理想的聚类效果。

关键词: 人工智能, 聚类, 模糊c-harmonic均值算法, 全局最优, 不平衡数据

Abstract:

A new fuzzy c-harmonic means clustering algorithm, which is based on cluster volumes constraint, is proposed in this paper to solve the problem of imperfect clustering performance of traditional algorithm for imbalanced data set. Firstly, a quantity is defined by the membership matrix to measure the volume of each cluster, which is then used to construct a new objective function by combining with that of traditional algorithm. Secondly, new membership matrix and cluster center formulas are obtained by minimizing this new objective function. The proposed algorithm was tested on the UCI data sets, simulated imbalanced data sets and actual machine vibration detection imbalanced data sets. Experimental results show that, compared with several peer algorithms, the proposed algorithm achieved good clustering performance for imbalanced data sets while maintaining the global optimal performance of the traditional one.

Key words: artificial intelligence, clustering, fuzzy c-harmonic mean algorithm, global optimality, unbalanced data

中图分类号:

TP391

刘富,梁艺馨,侯涛,宋阳,康冰,刘云. 模糊c-harmonic均值算法在不平衡数据上改进[J]. 吉林大学学报(工学版), 2021, 51(4): 1447-1453.

Fu LIU,Yi-xin LIANG,Tao HOU,Yang SONG,Bing KANG,Yun LIU. Improvement of fuzzy c-harmonic mean algorithm on unbalanced data[J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(4): 1447-1453.

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数据集	样本数量	特征数量	类的个数	样本组成
Iris	150	4	2或3	50，50
Iris	150	4	2或3	50，50，50
Ionosphere	351	34	2	126，225
Pima Indians Diabetes	768	8	2	538，230
Breast Cancer1	683	10	2	458，225
Glass	214	9	2	163，51
Breast Cancer2	569	30	2	212，357
振动数据集	215	48 312	2	159，56

数据集	c	J_opt	本文算法
数据集	c	J_opt	J	E	N	t
Iris	2	152.35	152.37	0.01	16	0.03
			152.37	0.01	14	0.01
			152.37	0.01	18	0.01
			152.37	0.01	14	0.01
			152.37	0.01	15	0.01
	3	78.85	79.12	0.33	39	0.05
			79.12	0.33	30	0.02
			79.12	0.33	25	0.02
			79.12	0.33	37	0.03
			79.12	0.33	30	0.02
Ionosphere	2	2419.4	2420.01	0.03	33	0.09
			2420.01	0.03	44	0.12
			2420.01	0.03	36	0.11
			2420.01	0.03	30	0.06
			2420.01	0.03	53	0.14
Pima Indians Diabetes	2	5.14e6	5.18e6	0.68	43	0.19
			5.18e6	0.68	34	0.12
			5.18e6	0.68	43	0.15
			5.18e6	0.68	36	0.14
			5.18e6	0.68	35	0.13
Breast Cancer1	2	1.93e5	1.93e5	0.00	13	0.05
			1.93e5	0.00	15	0.06
			1.93e5	0.00	18	0.06
			1.93e5	0.00	19	0.06
			1.93e5	0.00	16	0.05

数据集	c	J_opt	GKM			MGKM			本文算法
数据集	c	J_opt	E	N	t	E	N	t	E	N	t
Iris	2	152.35	0.00	1.26e4	0.00	0.00	3.55e4	0.00	0.01	13	0.01
Iris	3	78.85	0.01	1.78e4	0.00	0.00	6.34e4	0.00	0.33	22	0.02
Ionosphere	2	2.42e3	0.00	6.63e4	0.03	0.00	1.90e5	0.05	0.03	16	0.03
Pima Indians Diabetes	2	5.14e6	0.00	3.18e5	0.06	0.00	9.09e5	0.09	0.68	35	0.12
Breast Cancer1	2	1.93e5	0.00	2.42e5	0.05	0.00	7.09e5	0.06	0.00	12	0.04

模拟数据集	FCHM		siibFCM		本文算法
模拟数据集	F- value	G-mean	F- value	G-mean	F- value	G-mean
a	0.8621	0.9839	0.9615	0.9960	0.9950	0.9950
b	0.9639	0.9925	0.6700	0.8961	0.9975	0.9975
c	0.9709	0.9910	0.8772	0.9571	0.9967	0.9967
d	0.9913	0.9965	0.9467	0.9772	0.9937	0.9967
e	0.9930	0.9965	0.9718	0.9854	0.9940	0.9970
f	0.9893	0.9932	0.9748	0.9844	0.9933	0.9943
Glass	0.7961	0.8658	0.7805	0.8659	0.8667	0.8745
Breast Cancer2	0.7112	0.7429	0.8779	0.9030	0.9055	0.9161
Ionosphere	0.6383	0.7099	0.6286	0.7025	0.7749	0.8278