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

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.