基于粒子群优化的马氏距离模糊聚类算法

为解决传统模糊聚类迭代算法对初始化敏感，易陷入局部最优及处理高维数据时精度下降的问题，对基于马氏距离的模糊聚类算法(fuzzy c-means algorithm based on Mahalanobis distance,M-FCM)进行优化。将马氏距离代替欧氏距离，通过构造类内紧致度、类间分离度与类间清晰度结合的适应度函数，利用粒子群优化算法(particle swarm optimization,PSO)对马氏距离模糊聚类进行研究，提出了基于粒子群优化的马氏距离模糊聚类算法(Mahalanobis distance fuzzy clustering algorithm based on particle swarm optimization,DPSOM-FCM)，并将此新算法与FCM(fuzzy c-means algorithm)，M-FCM，PSO-FCM，IFPSOFCM(importance for fuzzy clustering algorithm based on particle swarm optimization)算法，在UCI(university of californiairvine)数据库的6个标准数据集上进行实验对比分析。结果表明，DPSOM-FCM算法具有算法收敛性和聚类有效性，并且聚类精确度优于其他算法，对高维数据的聚类识别能力强，即该算法具有全局优化作用。

Mahalanobis distance fuzzy clustering algorithm based on particle-swarm optimization

To solve the problem that traditional fuzzy clustering iteration algorithm is sensitive to initialization, easy to fall into local optimal solution, and the precision of dealing with high dimensional data is degrading, the fuzzy c-means algorithm based on Mahalanobis distance (M-FCM) is optimized. The Euclidean distance is replaced by Mahalanobis distance. Through constructing fitness function of firmness, separation and definition, using particle swarm optimization algorithm (PSO) to study M-FCM, DPSOM-FCM algorithm is proposed. And the algorithm is compared with FCM (fuzzy c-means algorithm), M-FCM, PSO-FCM, IFPSOFCM on six standard data sets from University of California Irvine database. The experimental comparison results show this algorithm is convergent and effective, and clustering accuracy outperforms others. It recognizes high dimensional data clustering well and has global optimization function.