Objective function of semi-supervised Fuzzy C-Means clustering algorithm

Analyzed here is the physical interpretation of objective function of semi-supervised fuzzy C-means (SS-FCM) algorithm and its coefficient alpha. A conclusion-Stutzpsilas modification to the objective function of Pedrycz is much clearer: unlabeled samples involves in unsupervised learning of FCM, labeled samples involves in unsupervised learning with coefficient (1-a) and participate in supervised learning with a, and when a=1 or 0, the SS-FCM degrades to FCM-is illustrated. The corresponding alternately optimizing algorithm of SS-FCM with fuzzy covariance is provided. The experimental results show that: 1) Modified algorithm has the same semi-supervised role and has much clearer physical interpretation. 2) Using FCM algorithm to assign membership for labeled samples is better than using random number. 3) SS-FCM with fuzzy covariance and a small number of well-selected labeled samples can effectively improve the accuracy and convergence speed.