核空间广义均衡模糊C-均值聚类算法

发布时间：2018-03-28 20:57

本文选题：广义均衡模糊C-均值聚类　切入点：核空间　出处：《中国图象图形学报》2017年02期

【摘要】：目的针对现有广义均衡模糊C-均值聚类不收敛问题,提出一种改进广义均衡模糊聚类新算法,并将其推广至再生希尔伯特核空间以便提高该类算法的普适性。方法在现有广义均衡模糊C-均值聚类目标函数的基础上,利用Schweizer T范数极限表达式的性质构造了新的广义均衡模糊C-均值聚类最优化目标函数,然后采用拉格朗日乘子法获取其迭代求解所对应的隶属度和聚类中心表达式,同时对其聚类中心迭代表达式进行修改并得到一类聚类性能显著改善的修正聚类算法;最后利用非线性函数将数据样本映射至高维特征空间获得核空间广义均衡模糊聚类算法。结果对Iris标准文本数据聚类和灰度图像分割测试表明,提出的改进广义均衡模模糊聚类新算法及其修正算法具有良好的分类性能,核空间广义均衡模糊聚类算法对比现有融入类间距离的改进模糊C-均值聚类(FCS)算法和改进再生核空间的模糊局部C-均值聚类(KFLICM)算法能将图像分割的误分率降低10%30%。结论本文算法克服了现有广义均衡模糊C-均值聚类算法的缺陷,同时改善了聚类性能,适合复杂数据聚类分析的需要。
[Abstract]:Aim to solve the problem of non-convergence of generalized equilibrium fuzzy C-means clustering, an improved generalized equilibrium fuzzy clustering algorithm is proposed. It is extended to the reproducing Hilbert kernel space in order to improve the universality of this kind of algorithm. The method is based on the existing generalized equilibrium fuzzy C-means clustering objective function. A new generalized equilibrium fuzzy C-means clustering optimization objective function is constructed by using the properties of the Schweizer T norm limit expression. Then the Lagrange multiplier method is used to obtain the corresponding membership degree and clustering center expression. At the same time, the iterative expression of clustering center is modified and a class of modified clustering algorithm is obtained, which improves the clustering performance significantly. Finally, the kernel space generalized equilibrium fuzzy clustering algorithm is obtained by mapping the data samples to the high dimensional feature space by nonlinear function. Results the Iris standard text data clustering and gray image segmentation test show that, The improved generalized equalization module fuzzy clustering algorithm and its modified algorithm have good classification performance. The kernel space generalized equalization fuzzy clustering algorithm can reduce the error rate of image segmentation by 100% compared with the existing improved fuzzy C-means clustering algorithm (FCSs) which incorporates the distance between clusters and the improved fuzzy local c-means clustering algorithm in the reproducing kernel space. Conclusion this algorithm overcomes the shortcomings of the existing generalized equilibrium fuzzy C-means clustering algorithms. At the same time, the clustering performance is improved, which is suitable for complex data clustering analysis.
【作者单位】：西安邮电大学电子工程学院;
【基金】：国家自然科学基金重点项目(61136002) 陕西省教育厅科学研究计划资助项目(2015JK1654) 陕西省自然科学基金项目(2014JM8331,2014JQ5138,2014JM8307) 研究生创新基金项目(CXL2015-03)~~
【分类号】：TP391.41;TP311.13

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