Effect of cluster size distribution on clustering: a comparative study of k-means and fuzzy c-means clustering

• Published in: Pattern analysis and applications : PAA Vol. 23; no. 1; pp. 455 - 466
• Main Authors: Zhou, Kaile, Yang, Shanlin
• Format: Journal Article
• Language: English
• Published: London Springer London 01.02.2020; Springer Nature B.V
• Subjects: Cluster analysis; Clustering; Comparative studies; Computer Science; Datasets; Machine learning; Particle size distribution; Pattern Recognition; Theoretical Advances; Vector quantization; means; Uniform effect; Fuzzifier; Data distribution; means (FCM); Fuzzy; Clustering
• ISSN: 1433-7541; 1433-755X
• DOI: 10.1007/s10044-019-00783-6

Data distribution has a significant impact on clustering results. This study focuses on the effect of cluster size distribution on clustering, namely the uniform effect of k -means and fuzzy c -means (FCM) clustering. We first provide some related works of k -means and FCM clustering. Then, the structure decomposition analysis of the objective functions of k -means and FCM is presented. Afterward, extensive experiments on both synthetic two-dimensional and three-dimensional data sets and real-world data sets from the UCI machine learning repository are conducted. The results demonstrate that FCM has stronger uniform effect than k -means clustering. Also, it reveals that the fuzzifier value m  = 2 in FCM, which has been widely adopted in many applications, is not a good choice, particularly for data sets with great variation in cluster sizes. Therefore, for data sets with significant uneven distributions in cluster sizes, a smaller fuzzifier value is preferred for FCM clustering, and k -means clustering is a better choice compared with FCM clustering.