基于自適應(yīng)松弛的魯棒模糊C均值聚類算法

高云龍; 王志豪; 潘金艷; 羅斯哲; 王德鑫

doi:10.11999/JEIT190556

基于自適應(yīng)松弛的魯棒模糊C均值聚類算法

doi: 10.11999/JEIT190556 cstr: 32379.14.JEIT190556

1.
廈門(mén)大學(xué)航空航天學(xué)院廈門(mén) 361102
2.
集美大學(xué)信息工程學(xué)院廈門(mén) 361021

基金項(xiàng)目: 國(guó)家自然科學(xué)基金(61203176)，福建省自然科學(xué)基金(2013J05098, 2016J01756)

詳細(xì)信息

作者簡(jiǎn)介:
高云龍：男，1979年生，副教授，主要研究方向?yàn)闄C(jī)器學(xué)習(xí)、時(shí)間序列分析和生產(chǎn)制造系統(tǒng)優(yōu)化和調(diào)度

王志豪：男，1993年生，碩士生，研究方向?yàn)闄C(jī)器學(xué)習(xí)和模式識(shí)別

潘金艷：女，1978年生，副教授，主要研究方向?yàn)槿斯ぶ悄芎蜋C(jī)器學(xué)習(xí)理論與方法

羅斯哲：男，1995年生，碩士生，研究方向?yàn)槟Ｊ阶R(shí)別和維數(shù)約簡(jiǎn)

通訊作者:
王志豪　zhwang@stu.xmu.edu.cn

中圖分類號(hào): TP391; TP273
計(jì)量
- 文章訪問(wèn)數(shù): 2986
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- PDF下載量: 125
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2019-07-24
- 修回日期: 2020-03-13
- 網(wǎng)絡(luò)出版日期: 2020-04-09
- 刊出日期: 2020-07-23

Robust Fuzzy C-Means Based on Adaptive Relaxation

1.
College of Aeronautics and Astronautics, Xiamen University, Xiamen 361102, China
2.
College of Information Engineering, Jimei University, Xiamen 361021, China

Funds: The National Natural Science Foundation of China (61203176), The Provincial Natural Science Foundation of Fujian Province (2013J05098, 2016J01756)

摘要

摘要:
噪聲是影響聚類結(jié)果的最重要的因素之一，現(xiàn)有的模糊聚類算法主要通過(guò)對(duì)隸屬度約束進(jìn)行松弛的方式來(lái)降低噪聲樣本的影響。這種方式仍然存在兩個(gè)基本問(wèn)題需要解決：第一，如何評(píng)估一個(gè)樣本是噪聲的可能性；第二，如何在抑制噪聲樣本影響力的同時(shí)，保留正常樣本的作用力。針對(duì)這兩問(wèn)題，該文提出了基于自適應(yīng)松弛的魯棒模糊C均值聚類算法(AR-RFCM)。新模型基于K最近鄰的方式(KNN)來(lái)估計(jì)樣本的可靠性，自適應(yīng)地調(diào)整松弛參數(shù)，從而實(shí)現(xiàn)在降低噪聲樣本影響力的同時(shí)，保留可靠樣本的作用力。此外，AR-RFCM利用了C均值聚類模型中隸屬度的稀疏性來(lái)提高可靠樣本的作用力，從而提高數(shù)據(jù)簇的內(nèi)聚程度，進(jìn)而降低噪聲樣本的影響。實(shí)驗(yàn)表明，AR-RFCM不僅在處理噪聲樣本時(shí)具有良好的魯棒性，同時(shí)在25個(gè)UCI 數(shù)據(jù)集實(shí)驗(yàn)中，分類正確率(蘭德指數(shù))平均高于FCM算法7.7864%。
- 噪聲 /
- 聚類 /
- 模糊C均值 /
- 自適應(yīng) /
- 松弛
Abstract:
Noise is one of the most important influences for clustering. Existing fuzzy clustering methods try to reduce the impact of noise by relaxing the constraint condition of membership. But there are still two basic problems to be solved. The first is how to evaluate the probability that a sample point is a noise. The second is how to retain the effect of normal points while suppressing the impact of noise. To solve these two problems, Robust Fuzzy C-Means based on Adaptive Relaxation (AR-RFCM) is proposed. The new model estimates the reliability of sample points by the method of the K-Nearest Neighbor (KNN). It adjusts adaptively the relaxation parameters to reduce the impact of noise, and keeps the effect of reliable sample points at the same time. In addition, AR-RFCM utilizes the sparsity of membership in K-means to improve the effect of reliable sample points. Therefore, the compactness of clusters is improved and the impact of noise is suppressed. Experiments demonstrate that AR-RFCM has a good robustness for noise, and also achieves higher rand index in all 25 UCI data sets, even averagely higher than FCM 7.7864%.
- Noise /
- Clustering /
- Fuzzy C-Means (FCM) /
- Adaptive /
- Relaxation

HTML全文

圖 1 不同聚類算法的隸屬度函數(shù)

下載: 全尺寸圖片幻燈片

圖 2 不同聚類算法的隸屬度函數(shù)

下載: 全尺寸圖片幻燈片

圖 3 不同聚類算法的隸屬度函數(shù)

下載: 全尺寸圖片幻燈片

表 1 各算法求得的隸屬度值

樣本編號(hào)	FCM		PCM		NC		REFCM		FDCM_SSR		AR-RFCM
樣本編號(hào)	C#1	C#2	C#1	C#2	C#1	C#2	C#1	C#2	C#1	C#2	C#1	C#2
1	0.054	0.946	0.015	0.539	0.004	0.332	0	0	0.095	0.905	0	0.984
2	0.008	0.992	0.018	0.546	0.005	0.332	0	0	0.060	0.940	0	0.985
3	0.040	0.960	0.019	0.999	0	1.000	0	0.992	0.090	0.910	0	1.000
4	0.093	0.907	0.018	0.545	0.005	0.332	0	0	0.137	0.863	0	0.985
5	0.055	0.945	0.024	0.552	0.007	0.331	0	0	0.114	0.886	0	0.985
6	0.500	0.500	0.003	0.003	0.001	0.001	0	0	0.500	0.500	0	0
7	0.500	0.500	0.010	0.010	0.004	0.004	0	0	0.500	0.500	0	0
8	0.945	0.055	0.552	0.024	0.331	0.007	0	0	0.886	0.114	0.985	0
9	0.992	0.008	0.546	0.018	0.332	0.005	0	0	0.941	0.059	0.985	0
10	0.960	0.040	0.999	0.019	1.000	0	0.992	0	0.910	0.090	1.000	0
11	0.907	0.093	0.545	0.018	0.332	0.005	0	0	0.863	0.137	0.985	0
12	0.946	0.054	0.539	0.015	0.332	0.004	0	0	0.905	0.095	0.984	0

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表 2 各算法所得的聚類簇中心

	簇中心1	簇中心2
FCM	$\left[ \begin{aligned} & { {\rm{3} }{\rm{.9870} } } \\ & { {\rm{0} }{\rm{.0011} } } \end{aligned} \right]$	$\left[ \begin{aligned}& { {\rm{ - 3} }{\rm{.9870} } } \\ &\ \ \, { {\rm{0} }{\rm{.0011} } } \end{aligned} \right]$
PCM	$\left[ \begin{aligned}& { {\rm{3} }{\rm{.9870} } } \\ & { {\rm{0} }{\rm{.0011} } } \end{aligned} \right]$	$\left[ \begin{aligned}& { {\rm{ - 3} }{\rm{.9870} } } \\ & \ \ \, { {\rm{0} }{\rm{.0011} } } \end{aligned} \right]$
NC	$\left[ \begin{aligned}& { {\rm{3} }{\rm{.9996} } } \\ & { {\rm{0} }{\rm{.0002} } } \end{aligned} \right]$	$\left[ \begin{aligned}& { {\rm{ - 3} }{\rm{.9996} } } \\ & \ \ \, { {\rm{0} }{\rm{.0002} } } \end{aligned} \right]$
REFCM	$\left[ \begin{aligned} & { {\rm{4} }{\rm{.000} }0} \\ & { {\rm{0} }{\rm{.0000} } } \end{aligned} \right]$	$\left[ \begin{aligned}& { {\rm{ - 4} }{\rm{.000} }0} \\ &\ \ \, { {\rm{0} }{\rm{.0000} } } \end{aligned} \right]$
FDCM_SSR	$\left[ \begin{aligned}& { {\rm{3} }{\rm{.4833} } } \\ & { {\rm{1} }{\rm{.6530} } } \end{aligned} \right]$	$\left[ \begin{aligned}& { {\rm{ - 3} }{\rm{.4833} } } \\ &\ \ \, { {\rm{1} }{\rm{.6530} } } \end{aligned} \right]$
AR-RFCM	$\left[ \begin{aligned}& { {\rm{3} }{\rm{.9999} } } \\ & { {\rm{0} }{\rm{.0000} } } \end{aligned} \right]$	$\left[ \begin{aligned}& { {\rm{ - 3} }{\rm{.9999} } } \\ &\ \ \, { {\rm{0} }{\rm{.0000} } } \end{aligned} \right]$

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表 3 噪聲數(shù)據(jù)集信息

	均值	協(xié)方差
簇1	[1　2]	$\left[ {\begin{array}{*{20}{c}}2&{0.2}\\{0.2}&2\end{array}} \right]$
簇2	[–1　–2]	$\left[ {\begin{array}{*{20}{c}}2&0\\0&1\end{array}} \right]$
簇3	[–3　–5]	$\left[ {\begin{array}{*{20}{c}}3&0\\0&1\end{array}} \right]$
噪聲	[–3　5]	$\left[ {\begin{array}{*{20}{c}}{10}&0\\0&2\end{array}} \right]$

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表 4 噪聲數(shù)據(jù)集實(shí)驗(yàn)結(jié)果

	FCM	PCM	NC	REFCM	FDCM_SSR	AR-RFCM
準(zhǔn)確率	0.8683	0.8683	0.8767	0.8583	0.8667	0.8833
精確度	0.6775	0.6775	0.6900	0.6625	0.6750	0.7000
靈敏度	0.9033	0.9033	0.9200	0.8833	0.9000	0.9333
特異度	0.8567	0.8567	0.8622	0.8500	0.8556	0.8667

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表 5 不同聚類算法在UCI數(shù)據(jù)集的聚類結(jié)果的RI(%)

	FCM	PCM	NC	REFCM	FDCM_SSR	AR-RFCM
Ecoli	79.66±0.47	78.60±3.28	78.25±1.11	80.12±1.13	79.83±0.45	88.40±1.62
Auto-mpg	76.23±0	75.21±4.02	77.27±0.46	75.64±0	85.62±0.30	77.64±2.09
Dermatology	83.49±1.18	81.17±3.26	69.82±6.61	81.33±5.49	84.88±1.59	92.55±0
Iris	83.68±0	79.33±7.90	82.27±4.23	85.68±0	87.37±0	85.68±0
Zoo	87.91±1.76	87.56±6.15	88.90±5.82	85.76±5.22	89.78±2.33	96.65±0
Transfusion	53.10±0	55.47±5.59	56.30±3.75	53.16±0	63.90±0.09	63.68±0
Parkinsons	52.19±0	58.86±5.86	64.40±5.31	60.27±7.74	63.12±0.57	73.83±0
Banknote	51.52±0	59.55±9.75	61.32±6.89	59.68±12.12	52.44±1.73	66.32±2.79
Creadit-approval	67.57±0.37	55.78±5.82	64.89±0	53.96±6.53	67.51±0	68.06±0
Breast-cancer	90.53±0	78.42±14.25	86.24±16.97	91.59±0	94.31±0	94.86±0
Wine	95.43±0	73.35±4.57	91.85±6.62	90.36±0	95.43±0	96.40±0.73
Automobile	71.83±0.44	70.81±1.78	72.08±1.62	71.79±0.38	71.99±0.29	74.24±0.29
Messidor Features	50.49±0	50.62±0.35	50.63±0.01	50.86±0	50.65±0.53	51.80±0.61
Fertility	50.00±0	65.74±12.93	50.08±0.18	57.99±6.55	79.13±0.71	78.85±1.75
Seeds	89.92±0	78.70±5.28	88.53±0.52	87.06±0	89.92±0	91.26±0.52
Blance	58.82±4.58	58.49±5.70	62.66±4.69	60.55±5.09	60.56±4.07	65.97±3.54
House Votes	77.52±0	71.46±8.61	75.49±6.07	72.41±6.76	77.86±0	78.90±0
Vowel	67.15±2.47	82.68±1.61	53.52±4.44	82.91±0.94	66.81±1.81	85.47±0.20
Glass	71.31±0.45	69.29±1.19	71.58±0.98	71.07±0.86	71.59±0.39	72.45±0.77
Mammographic	67.96±0	64.00±7.05	67.98±0.04	62.35±6.02	68.55±0	68.11±0
Pima Indians Diabetes	59.07±0	56.23±3.27	52.41±0.13	58.09±0	59.06±0.03	59.18±0.29
Qualitative Bankruptcy	94.53±0	74.58±16.72	97.62±0	94.53±0	94.53±0	97.62±0
Seismic Bumps	51.88±0	71.15±12.53	56.19±10.29	87.70±0	87.69±0.10	87.70±0
Phishing Data	68.72±0.29	60.73±5.18	69.13±0.28	62.71±0	68.93±0.39	69.67±0.09
Yeast	65.83±1.61	72.95±1.21	63.44±2.90	72.95±2.06	66.58±1.58	75.71±0.03

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