基于公理化模糊子集的改进谱聚类算法

赵小强; 刘晓丽

doi:10.11999/IEIT170904

基于公理化模糊子集的改进谱聚类算法

doi: 10.11999/IEIT170904

赵小强^{1, 2, 3, ,},
刘晓丽¹

1.
兰州理工大学电气工程与信息工程学院兰州 730050
2.
甘肃省工业过程先进控制重点实验室兰州 730050
3.
兰州理工大学国家级电气与控制工程实验教学中心兰州 730050

基金项目: 国家自然科学基金(61763029)，甘肃省基础研究创新群体基金(1506RJIA031)

详细信息

作者简介:
赵小强：男，1969年生，博士生导师，教授，主要研究方向为数据挖掘、故障诊断、图像处理、污水处理、生产调度等

刘晓丽：女，1992年生，硕士生，研究方向为数据挖掘

通讯作者:
赵小强 xqzhao@lut.cn

中图分类号: TP181
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- 被引次数: 0
出版历程
- 收稿日期: 2017-09-25
- 修回日期: 2018-05-02
- 网络出版日期: 2018-05-30
- 刊出日期: 2018-08-01

An Improved Spectral Clustering Algorithm Based on Axiomatic Fuzzy Set

Xiaoqiang ZHAO^{1, 2, 3
, ,},
Xiaoli LIU¹

1.
College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China
2.
Key Laboratory of Gansu Advanced Control for Industrial Processes, Lanzhou 730050, China
3.
National Experimental Teaching Center of Electrical and Control Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Funds: The National Natural Science Foundation of China (61763029), The Gansu Province Basic Research Innovation Group Fund (1506RJIA031)

摘要

摘要: 谱聚类算法通常是采用高斯核作为相似性度量，并利用所有可用的特征来构建具有欧氏距离的相似度矩阵，数据集复杂度会影响其谱聚类性能，因此该文提出一种基于公理化模糊子集(AFS)的改进谱聚类算法。首先结合AFS算法，利用识别特征来衡量更合适的数据成对相似性，生成更强大的亲合矩阵；再有效地利用Nyström采样算法，计算采样点间以及采样点和剩余点间的相似度矩阵去降低计算的复杂度；最后通过在不同数据集以及图像分割上进行实验，证明了提出算法的有效性。
- 亲和矩阵 /
- 谱聚类 /
- 公理化模糊子集 /
- Nyström采样算法
Abstract: Gaussian kernel is usually used as the similarity measure in spectral clustering algorithm, and all the available features are used to construct the similarity matrix with Euclidean distance. The complexity of the data set would affect its spectral clustering performance. Therefore, an improved spectral clustering algorithm based on Axiomatic Fuzzy Set (AFS) is proposed. Firstly, AFS algorithm is combined to measure the similarity of more suitable data by recognizing features, and the stronger affinity matrix is generated. Then Nyström sampling algorithm is used to calculate the similarity matrix between the sampling points and the sampling points and the remaining points to reduce the computational complexity. Finally, the experiment is carried out by using different data sets and image segmentations, the effectiveness of the proposed algorithm are proved.
- Affinity matrix /
- Spectral clustering /
- Axiomatic Fuzzy Set (AFS) /
- Nyström sampling algorithm

HTML全文

图 1 原图

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图 2 谱聚类算法分割结果

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图 3 本文算法分割结果

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表 1 数据集特征

数据集	数据总数	类数	维数
Iris	150	3	4
Heart	270	2	13
Sonar	208	2	60
Wine	178	3	13
Protein	552	8	77
Hepatitis	155	2	19
Segmentation	2310	7	19
Pen digits	10992	10	16

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表 2 数据集的CE(%)

数据集	SC	STSC	AFS	本文算法
Iris	10.71	7.46	9.72	7.63
Heart	20.96	22.13	30.63	12.42
Sonar	44.53	46.83	38.52	33.60
Wine	2.92	2.91	3.54	3.13
Protein	54.70	55.67	55.12	48.87
Hepatitis	30.76	38.73	32.34	23.20
Segmentation	22.08	21.35	31.17	18.63
Pen digits	25.37	24.25	–	22.16

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表 3 数据集的NMI(%)

数据集	SC	STSC	AFS	本文算法
Iris	75.87	78.63	78.06	85.49
Heart	28.54	26.23	18.45	40.33
Sonar	7.32	1.83	15.47	22.38
Wine	89.30	89.34	85.67	87.96
Protein	54.43	48.24	36.62	65.80
Hepatitis	13.75	4.78	3.57	17.42
Segmentation	65.58	66.72	58.56	72.24
Pen digits	60.53	61.48	–	66.52

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表 4 SAR图像分割性能对比表

	谱聚类算法	本文算法
运行时间(S)	30.62	3.27
误分率(%)	9.53	5.34

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表 5 树图像分割性能对比表

	谱聚类算法	本文算法
运行时间(S)	16.39	4.25
误分率(%)	6.87	2.13

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表 6 复杂度分析

	计算步骤	复杂度
	计算矩阵 ${{A}}$	O(n²)
	计算矩阵 ${{B}}$	O(n(N–n))
若矩阵 ${{A}}$正定	对 ${{A}}$矩阵分解	O(n³)
	求解矩阵 ${{p}}$	O(n²(N–n))
	矩阵分解	O(n³)
	求解矩阵 ${{Y}}$	O(n²N)
若矩阵 ${{A}}$非正定	求解矩阵 ${{S}}$	O(n²N)
	对矩阵 ${{S}$对角分解	O(n³)
	求解矩阵 ${{Y}}$	O(n²N)
	K-means算法进行聚类	O(nK²T)

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