鲁棒的交叉熵模糊聚类算法

Robust fuzzy clustering algorithm based on cross entropy

针对模糊C-均值聚类(FCM)算法对噪声敏感、容易收敛到局部极小值的问题,提出一种基于交叉熵的模糊聚类算法。通过引入交叉熵重新定义了传统FCM算法的目标函数,利用交叉熵度量样本隶属度之间的差异性,并采用拉格朗日求解方法和朗伯W函数解决了目标函数的优化问题,此外,分析了样本划分矩阵的分布情况,依据分布特性对噪声样本进行识别。人工数据集合和标准数据集加噪的实验结果表明,该算法提高了传统FCM算法的抗干扰能力,具有更强的鲁棒性,噪声样本识别的准确率较高。

For the problem that the traditional fuzzy C-means clustering(FCM)algorithm is easy to be affected by noise data,this paper proposed a fuzzy clustering algorithm based on the cross entropy.This algorithm introduced the cross entropy to the objective function of FCM algorithm to measure the difference between membership function of data,and used Lagrange method and Lambert W function to solve the optimization problem of the objective function.This algorithm could identify the noise samples according to the characteristics of the sample partition matrix.The experiment results on a synthetic data set and a standard data set with noisy show that the proposed algorithm is more robust and has better clustering results.