Abstract: The classical Fuzzy C-Means algorithm（FCM） is based on Euclidean distance function，which can only be used to detect spherical structural clusters.When FCM processes some dataset of high dimension，error probability will be increased.Focusing on above two problems，this paper proposes an improved new algorithm called Fuzzy C-Means based on Mahalanobis distance function（FCM-M），and adds a regulating factor of covariance matrix to each class in objective function.Using the advantage of Mahalanobis distance，FCM-M algorithm effectively solves the shortcomings of FCM algorithm.There are efficient methods to solve singular values problem for finding Eigen value and eigenvectors of a symmetric matrix or computing pseudoinvertion involved in finding the Mahalanobis distance.Experimental results of data clustering and image segmentation illustrate its effectiveness and feasibility.

摘要：

经典的模糊c均值（FCM）算法是基于欧氏距离的，它只适用于球型结构的聚类，且在处理高维的数据集时，分错率增加。针对以上两个问题，提出了一种新的聚类算法（FCM-M），它将马氏距离与模糊c均值相结合，并在目标函数中引进一个协方差矩阵的调节因子，利用马氏距离的优点，有效地解决了FCM算法中的缺陷，并利用特征值、特征矢量及伪逆运算来解决马氏距离中遇到的奇异问题。通过数据聚类和图像分割两组实验，证实了该方法的可行性和有效性。