Abstract: The Fuzzy C-Means clustering (FCM) algorithm has the defects of being sensitive to initial clustering center,being susceptible to noise point interference and poor robustness in solving the problem of speech underdetermined mixing matrix estimation. An improved WEighted FCM algorithm based on evolutionary programming (WE-FCM) was proposed to eliminate the defects. Firstly, the powerful search ability of Evolutionary Programming (EP) algorithm was used to optimize FCM for obtaining FCM algorithm based on EP (EP-FCM), in order to obtain a better initial clustering center. Then, the Local Outlier Factor (LOF) algorithm was used to perform weighting to reduce the effects of noise points. The simulation experiment results show that, the normalized mean square error value and the deviation angle value of the proposed algorithm were both much smaller than those of the classical K-means clustering, K-Hough, FCM algorithm based on Genetic Algorithm (GAFCM) and FCM algorithm based on Find Density Peaks (FDP-FCM) when the number of source signals were 3 and 4. The experimental results show that, the proposed algorithm significantly improves the robustness of FCM algorithm and the accuracy of mixing matrix estimation.

Key words: Fuzzy C-Means clustering (FCM) algorithm, Evolutionary Programming (EP) algorithm, Local Outlier Factor (LOF) algorithm, weighting, mixing matrix estimation

摘要： 语音欠定混合矩阵估计问题中，针对模糊C均值聚类(FCM)算法对初始聚类中心敏感、易受噪声点干扰、鲁棒性差的缺陷，提出一种基于加权的进化规划与FCM相结合的改进算法(WE-FCM)。首先，利用进化规划(EP)算法强大的搜索能力优化FCM得到基于进化规划的FCM算法(EP-FCM)，以获得较佳的初始聚类中心；然后，利用局部离群点检测(LOF)算法对EP-FCM加权以降低噪声点的影响。通过仿真实验得出，所提算法在源信号数为3路和4路时归一化均方误差值与偏离角度值均远小于经典的K均值聚类(K-means)算法、K-Hough、基于遗传算法的FCM算法(GAFCM)和基于密度峰值的FCM算法(FDP-FCM)。实验结果表明，所提算法明显提高了FCM算法的鲁棒性和混合矩阵的估计精度。

关键词: 模糊C均值聚类算法, 进化规划算法, 局部离群点检测算法, 加权, 混合矩阵估计