Gaussian-kernel c-means clustering algorithms

Partitional clustering is the most used in cluster analysis. In partitional clustering, hard c-means (HCM) (or called k-means) and fuzzy c-means (FCM) are the most known clustering algorithms. However, these HCM and FCM algorithms work worse for data sets in a noisy environment and get inaccuracy when the data set has different shape clusters. For solving these drawbacks in HCM and FCM, Wu and Yang (Pattern Recognit 35:2267–2278, 2002) proposed the alternative c-means clustering with an exponential-type distance that extends HCM and FCM into alternative HCM (AHCM) and alternative FCM (AFCM). In this paper, we construct a more generalization of AHCM and AFCM with Gaussian-kernel c-means clustering, called GK-HCM and GK-FCM. For theoretical behaviors of GK-FCM, we analyze the bordered Hessian matrix and then give the theoretical properties of the GK-FCM algorithm. Some numerical and real data sets are used to compare the proposed GK-HCM and GK-FCM with AHCM and AFCM methods. Experimental results and comparisons actually demonstrate these good aspects of the proposed GK-HCM and GK-FCM algorithms with its effectiveness and usefulness. Finally, we apply the GK-FCM algorithm to MRI segmentation.