Gaussian-kernel c-means clustering algorithms

• Published in: Soft computing (Berlin, Germany) Vol. 25; no. 3; pp. 1699 - 1716
• Main Authors: Chang-Chien, Shou-Jen, Nataliani, Yessica, Yang, Miin-Shen
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2021
• Subjects: Artificial Intelligence; Computational Intelligence; Control; Engineering; Focus; Mathematical Logic and Foundations; Mechatronics; Robotics; Hard; means (FCM); means (HCM); Fuzzy; Clustering; MRI segmentation; Gaussian-kernel HCM (GK-HCM); Gaussian-kernel FCM (GK-FCM)
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-020-04924-6

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.