A Novel Semi-Supervised Fuzzy C-Means Clustering Algorithm Using Multiple Fuzzification Coefficients

Clustering is an unsupervised machine learning method with many practical applications that has gathered extensive research interest. It is a technique of dividing data elements into clusters such that elements in the same cluster are similar. Clustering belongs to the group of unsupervised machine learning techniques, meaning that there is no information about the labels of the elements. However, when knowledge of data points is known in advance, it will be beneficial to use a semi-supervised algorithm. Within many clustering techniques available, fuzzy C-means clustering (FCM) is a common one. To make the FCM algorithm a semi-supervised method, it was proposed in the literature to use an auxiliary matrix to adjust the membership grade of the elements to force them into certain clusters during the computation. In this study, instead of using the auxiliary matrix, we proposed to use multiple fuzzification coefficients to implement the semi-supervision component. After deriving the proposed semi-supervised fuzzy C-means clustering algorithm with multiple fuzzification coefficients (sSMC-FCM), we demonstrated the convergence of the algorithm and validated the efficiency of the method through a numerical example.