核空间广义均衡模糊C-均值聚类算法

Improvement of general equalization fuzzy C-means clustering and its kernel spaces algorithm

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。

Objective A new general equalization fuzzy C-means clustering algorithm that targets the shortcomings of existing, non-convergent types is proposed and applied in image segmentation. The proposed general equalization fuzzy clustering algorithm is also extended into the Hilbert reproduced kernel space. This approach can improve the universality of this algorithm class. Method The limit expression properties of the Schweizer T-norm are applied to construct the objective function of the new general equalization fuzzy C-means clustering based on the objective function of existing types. The Lagrange muhiplier method is then adopted to obtain iterated formulae of the fuzzy membership and clustering center for the modified general equalization fuzzy C-means clustering. The iterafive expression of the clustering center is modified to further improve the performance of the clustering algorithm. The modified clustering algorithm significantly improves a clustering performance class. Finally, a nonlinear function is adopted to map data samples from the Euclidean space to the high-dimensional feature space of Hilbert. The kernel space general equalization fuzzy C-means clustering algorithm is thus ob- tained. The kernel spaces general equalization fuzzy C-means clustering algorithms can improve the error classification rate of image segmentation by 10% to 30% compared with existing fuzzy compactness and separation （FCS） and fuzzy C-means clustering with local information and kernel metric （KFLICM） algorithms. Result Experimental results of the clustering analysis of Iris data and gray image segmentation indicate that the proposed general equalization fuzzy C-means clustering algorithm is efficient. Its modified algorithm can obtain more satisfactory clustering quality and segmentation effects than existing fuzzy c-means clustering algorithms. Conehtsion The proposed algorithm overcomes the shortcomings of existing general equaliza- tion fuzzy C-means clustering algorithms and improves the clustering performance, which is suitable for complex data analysis.