Journal
PATTERN ANALYSIS AND APPLICATIONS
Volume 23, Issue 1, Pages 455-466Publisher
SPRINGER
DOI: 10.1007/s10044-019-00783-6
Keywords
Clustering; Data distribution; k-means; Fuzzy c-means (FCM); Fuzzifier; Uniform effect
Categories
Funding
- National Natural Science Foundation of China [71822104, 71501056, 71690235]
- Anhui Science and Technology Major Project [17030901024]
- China Postdoctoral Science Foundation [2017M612072]
- Hong Kong Scholars Program [2017-167]
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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.
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