JACIII Vol.25 No.6 pp. 989-999
doi: 10.20965/jaciii.2021.p0989


Fuzzy Clustering in Assortative and Disassortative Networks

Ryoichi Kojima*,†, Roberto Legaspi*, and Toshiaki Murofushi**

*KDDI Research, Inc.
2-1-15 Ohara, Fujimino-shi, Saitama 356-8502, Japan

**Department of Mathematical and Computing Science, School of Computing, Tokyo Institute of Technology
2-12-1-W8-49 Ookayama, Meguro-ku, Tokyo 152-8550, Japan

Corresponding author

June 1, 2021
September 8, 2021
November 20, 2021
fuzzy clustering, modularity function, assortative network, disassortative network

Despite the significance of assortativity as a property of networks that paves for the emergence of new structural types, surprisingly, there has been little research done on assortativity. Assortative networks are perhaps among the most prominent examples of complex networks believed to be governed by common phenomena, thereby producing structures far from random. Further, certain vertices possess high centrality and can be regarded as significant and influential vertices that can become cluster centers that connect with high membership to many of the surrounding vertices. We propose a fuzzy clustering method to meaningfully characterize assortative, as well as disassortative, networks by adapting the Bonacichi’s power centrality to seek the high degree centrality vertices to become cluster centers. Moreover, we leverage our novel modularity function to determine the optimal number of clusters, as well as the optimal membership among clusters. However, due to the difficulty of finding real-world assortative network datasets that come with ground truths, we evaluated our method using synthetic data but possibly bearing resemblance to real-world network datasets as they were generated by the Lancichinetti–Fortunato–Radicchi benchmark. Our results show our non-hierarchical method outperforms a known hierarchical fuzzy clustering method, and also performs better than a well-known membership-based modularity function. Our method proved to perform beyond satisfactory for both assortative and disassortative networks.

Cite this article as:
R. Kojima, R. Legaspi, and T. Murofushi, “Fuzzy Clustering in Assortative and Disassortative Networks,” J. Adv. Comput. Intell. Intell. Inform., Vol.25 No.6, pp. 989-999, 2021.
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