一种基于非线性表征和质心融合的模糊双中心聚类方法

doi:10.16180/j.cnki.issn1007-7820.2025.07.003

Abstract

Abstract:

In view of the problem of high-precision clustering of non-negative incomplete data, an innovative fuzzy clustering method is proposed in this study. By introducing nonlinear function, case frequency regularization term and knowledge transfer to traditional latent factor model, the model representation ability and data filling accuracy are improved, and a nonlinear latent factor model is formed. Combining sparse self-representation and centroid fusion term, the optimal cluster number is determined automatically while considering the global features, and a fuzzy bicentric clustering model is constructed. The experimental results on real data sets and pictures verify the effectiveness of the fuzzy bicentric clustering method based on nonlinear characterization and centroid fusion in dealing with the clustering problem of non-negative incomplete data.

Key words: incomplete data, nonlinear function, latent factor analysis, instance frequency, centroid fusion, fuzzy clustering, sparse self-representation, knowledge transfer

CLC Number:

TP311.13

ZHAO Dan, SONG Yan. A Fuzzy Double C-Means Clustering Method Based on NonlinearCharacterization and Centroid Fusion[J].Electronic Science and Technology, 2025, 38(7): 15-23.

Figures/Tables 13

Figure 1.

Table 1.

Table 2.

Table 3.

Table 4.

Figure 2.

Table 5.

Table 6.

Table 7.

Performances of imputation algorithms for different data sets with 20% missing rate /%"

数据集	模型	UNLF		NIR		LSCF		NCLF
		M₃	M₄	M₃	M₄	M₃	M₄	M₃	M₄
D₁	F₁	28.22±5.44	55.16±5.47	30.05±5.38	57.12±5.17	31.67±4.33	58.06±5.12	33.16±6.55	60.38±3.98
	F₂	30.45±6.13	58.9±6.45	31.84±4.25	60.09±3.55	33.16±5.78	61.34±8.46	34.67±6.36	61.36±5.70
	F₃	29.16±5.26	59.01±4.36	33.87±1.26	60.58±5.45	36.15±4.74	61.58±3.27	34.59±5.46	62.19±4.22
	F₄	31.89±1.55	60.32±1.85	35.48±1.18	61.23±2.38	37.08±2.11	62.49±1.32	36.92±2.78	63.55±0.64
D₂	F₁	10.43±3.82	58.75±5.15	13.29±1.87	59.63±5.36	14.39±3.72	60.24±1.52	15.69±4.13	62.04±6.03
	F₂	13.15±3.26	59.28±3.21	15.36±2.03	60.93±4.15	16.66±4.65	61.55±3.90	17.36±5.22	64.54±2.33
	F₃	13.79±2.44	58.95±2.56	15.98±1.55	61.26±3.78	17.01±2.47	63.15±6.59	17.84±4.59	66.79±3.56
	F₄	14.36±1.27	60.77±2.10	16.93±0.98	63.77±1.46	17.35±1.96	65.12±1.71	18.33±2.68	66.98±0.72
D₃	F₁	26.09±6.95	50.24±5.88	38.23±2.35	62.08±2.98	41.74±5.72	65.49±6.21	45.57±1.25	67.54±4.67
	F₂	28.61±2.61	51.37±4.51	43.9±2.64	65.36±3.67	45.55±7.49	68.45±2.81	49.48±6.12	69.64±4.56
	F₃	29.16±5.45	50.26±5.47	44.02±3.26	66.28±3.01	46.08±3.26	69.58±4.06	48.16±4.78	71.00±3.66
	F₄	30.33±0.02	52.27±2.34	44.30±1.20	68.148±0.89	47.41±1.02	70.07±0.24	50.12±1.11	73.16±2.42
D₄	F₁	20.58±4.03	51.25±2.82	23.02±3.54	52.24±3.31	24.88±4.69	55.30±8.55	24.17±7.30	56.64±5.01
	F₂	23.95±2.56	54.68±6.68	24.96±2.45	56.52±2.35	25.28±6.80	59.68±2.87	26.58±3.03	58.42±5.93
	F₃	22.16±5.45	55.87±5.69	25.16±4.59	58.77±4.16	26.56±4.03	60.08±1.12	27.16±2.35	59.26±1.13
	F₄	24.06±1.89	57.33±1.72	27.58±3.86	60.53±0.56	28.38±2.98	61.40±1.09	29.40±1.05	62.83±2.17
D₅	F₁	30.89±5.43	58.05±4.08	32.05±4.58	61.06±3.62	33.38±2.70	62.87±6.54	35.182±7.64	63.95±5.46
	F₂	31.82±7.45	60.20±5.22	33.25±3.56	61.17±5.29	34.30±6.45	62.17±6.78	37.56±5.77	64.88±3.19
	F₃	32.09±4.15	60.22±4.16	34.16±5.61	61.56±2.36	35.19±1.26	61.49±3.26	38.19±4.16	66.54±2.09
	F₄	33.48±2.12	61.78±1.72	35.43±1.47	63.74±1.02	36.01±0.78	63.87±2.89	40.84±2.24	68.44±1.07

Table 7.

Table 8.

Performances of imputation algorithms for different data sets with 60% missing rate /%"

数据集	模型	UNLF		NIR		LSCF		NCLF
		M₃	M₄	M₃	M₄	M₃	M₄	M₃	M₄
D₁	F₁	22.60±2.88	53.59±2.82	25.64±4.18	54.13±5.17	27.20±3.13	56.77±4.32	28.47±6.88	58.67±8.56
	F₂	24.71±1.94	55.31±1.77	26.62±2.13	56.97±3.49	30.34±4.55	58.21±4.59	29.82±3.24	59.47±5.48
	F₃	23.49±5.26	54.16±4.23	27.56±4.51	56.99±1.26	31.26±2.33	57.26±2.84	30.08±5.12	60.11±2.16
	F₄	25.86±0.29	56.30±0.00	28.63±0.51	58.93±1.20	32.31±1.91	59.80±2.23	31.12±1.15	61.41±1.77
D₂	F₁	7.05±3.72	48.13±4.08	7.62±4.37	50.09±4.75	9.21±5.67	51.95±4.70	11.79±5.73	54.91±5.82
	F₂	7.95±2.16	49.16±2.26	8.94±1.48	50.49±3.26	8.49±2.16	52.03±2.76	13.26±2.11	56.49±1.00
	F₃	9.73±2.98	50.43±3.83	10.66±3.57	51.08±4.70	10.92±4.82	53.23±5.37	15.39±3.12	57.27±4.30
	F₄	10.59±0.62	52.17±1.61	11.06±1.77	53.96±0.92	11.77±2.67	55.87±2.85	16.06±2.01	58.37±2.84
D₃	F₁	48.59±4.98	70.61±2.25	50.62±5.29	70.99±5.91	51.39±5.74	71.89±6.45	52.79±3.89	72.76±5.08
	F₂	50.88±3.72	72.39±1.31	51.36±6.71	72.57±2.28	52.18±6.99	73.10±5.98	54.67±2.42	75.48±2.85
	F₃	51.26±2.22	71.65±2.27	52.78±1.98	73.92±1.65	51.26±3.71	72.94±1.26	55.45±1.58	74.98±1.65
	F₄	52.30±0.55	73.29±1.43	53.24±1.58	74.67±3.49	53.54±2.09	75.29±1.71	57.77±1.02	76.58±0.31
D₄	F₁	15.71±2.85	47.39±4.55	16.96±5.58	47.88±5.83	17.44±2.61	49.08±4.47	20.76±4.29	53.16±7.18
	F₂	16.82±3.32	50.30±3.46	18.38±2.96	51.85±6.24	19.40±1.52	52.43±7.83	23.57±2.74	66.46±2.17
	F₃	17.12±5.26	48.56±3.26	18.99±2.55	50.26±4.59	20.65±1.36	54.27±2.64	24.98±1.65	67.23±1.98
	F₄	18.51±1.15	51.91±1.77	20.87±0.85	53.77±0.97	21.93±1.55	55.05±1.28	25.77±0.95	68.72±1.45
D₅	F₁	31.73±1.04	60.31±2.21	32.12±3.73	61.14±5.07	34.27±2.96	62.70±1.68	36.97±4.22	65.29±5.67
	F₂	33.27±5.85	61.71±7.94	34.52±5.11	62.13±3.54	35.11±3.92	63.69±2.30	37.96±5.69	66.74±3.58
	F₃	34.59±2.26	60.18±2.49	35.61±3.16	62.46±2.16	36.98±2.11	64.59±3.16	36.15±4.46	67.19±2.16
	F₄	35.73±0.98	62.55±1.92	36.13±1.54	63.23±0.25	37.92±0.63	65.91±1.08	38.32±0.91	68.58±0.79

Table 8.

Figure 3.

Figure 4.

Table 9.

References 20

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数据集	样本数	特征数	类别	编号
Zoo	1 962	9	6	D₁
Abalone	33 416	8	3	D₂
Wine	2 314	13	3	D₃
Wisconsin	569	30	2	D₄
Car evaluation	1 728	6	4	D₅

名称	含有非线性映射	含有频率正则化	含有迁移学习
NIR^[6]	否	是	否
LSCF^[12]	否	否	是
UNLF^[13]	是	否	否
NCLF	是	是	是

数据集	评价指标	UNLF/%	NIR/%	LSCF/%	NCLF/%
D₁	M₁	25.57±0.33	22.05±0.57	19.26±0.23	17.54±0.35
D₁	M₂	28.46±0.78	24.88±1.55	23.17±0.16	20.89±0.24
D₂	M₁	19.36±1.10	18.75±2.62	15.22±0.46	13.65±1.26
D₂	M₂	22.41±2.02	20.88±1.63	17.57±0.87	15.38±0.78
D₃	M₁	15.98±0.68	14.90±1.41	14.37±1.01	11.26±0.25
D₃	M₂	18.66±0.89	17.87±3.25	17.39±0.98	14.21±0.39
D₄	M₁	22.52±1.45	20.90±0.86	18.94±0.62	15.68±0.87
D₄	M₂	25.21±0.88	23.72±1.88	21.47±0.78	18.16±0.12
D₅	M₁	20.26±0.76	17.91±2.06	15.17±0.36	12.39±0.84
D₅	M₂	22.20±0.95	20.09±1.74	17.06±0.11	14.15±0.57

数据集	评价指标	UNLF/%	NIR/%	LSCF/%	NCLF/%
D₁	M₁	27.66±1.26	24.40±2.24	22.30±1.12	19.26±0.23
D₁	M₂	29.12±3.04	26.89±1.35	25.64±1.36	22.13±0.75
D₂	M₁	23.15±1.56	20.15±1.56	19.47±0.78	17.84±1.01
D₂	M₂	25.67±2.98	21.58±2.34	21.36±0.22	19.20±0.65
D₃	M₁	17.02±1.24	15.76±1.57	14.34±0.46	13.26±0.45
D₃	M₂	19.88±2.62	18.43±2.46	16.51±0.55	15.68±0.64
D₄	M₁	25.16±4.58	23.89±1.86	23.09±0.65	21.54±0.97
D₄	M₂	27.63±3.87	27.24±2.35	26.53±0.48	25.85±0.16
D₅	M₁	23.59±4.63	22.83±1.08	20.16±0.36	18.76±0.33
D₅	M₂	25.77±1.64	24.73±2.86	22.19±1.02	20.52±0.87

数据集	评价指标	FCM	FD_SSR	FWFD	CF-FDCM
D₁	M₃	54.72±5.16	57.04±4.08	58.26±3.11	60.82±3.28
D₁	M₄	77.86±2.28	78.03±2.70	77.75±4.54	79.70±3.11
D₂	M₃	58.67±3.45	65.06±3.12	67.25±1.56	69.11±2.16
D₂	M₄	82.77±6.12	84.58±4.86	85.26±4.98	87.89±3.53
D₃	M₃	58.67±8.03	65.06±5.74	66.55±3.65	69.11±4.66
D₃	M₄	57.38±0.78	58.54±1.06	58.98±2.71	60.28±0.95
D₄	M₃	15.65±1.89	17.23±2.22	16.75±1.46	18.54±3.26
D₄	M₄	58.10±4.56	60.21±2.09	59.46±3.12	61.25±1.42
D₅	M₃	57.57±3.35	59.07±3.97	57.16±1.25	60.91±2.13
D₅	M₄	76.06±1.61	76.86±1.26	76.98±1.28	77.21±0.97

A Fuzzy Double C-Means Clustering Method Based on NonlinearCharacterization and Centroid Fusion

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算法	UNLF	NIR	LSCF	NCLF
F₁	76.36±5.46	80.45±5.36	80.05±3.46	82.57±3.58
F₂	75.65±6.02	79.63±6.48	82.13±5.22	83.44±5.73
F₃	78.98±3.56	81.58±3.75	83.69±2.47	86.72±1.48

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