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On rough set based fuzzy clustering for graph data

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Abstract

Data clustering refers to partition the original data set into some subsets such that every vertex belongs to one or more subsets at the same time. For graph data that composed by attribute information of vertices as well as structural information between vertices, how to make an efficient clustering is not an easy thing. In this paper, we propose a novel method of how to partition graph data into some overlapping subgraph data in aspect of rough set theory. At first, we introduce a detailed description about the global similarity measurement of vertices. After that, an objective-function oriented optimization model is constructed in terms of updating fuzzy membership degree and cluster center that based on the theory of rough set. Obviously, the determined cluster is no longer a fuzzy set, but a rough set, that is to say, the cluster is expressed by the upper approximation set and lower approximation set. Finally, eleven real-world graph data and four synthetic graph data are applied to verify the validity of the proposed fuzzy clustering algorithm. The experimental results show that our algorithm is better than existing clustering approach to some extent.

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Notes

  1. Without loss of generality, in this paper we adhere to the hypothesis that \(e_{jj^{\prime }}\in \{0,1\}\) for all \(j, j^{\prime }=1,2,\ldots ,n\). What is more, it should be pointed out that \(e_{jj^{\prime }}=e_{j^{\prime }j}\), that is to say, \({\mathscr {G}}=({\mathscr {X}},{\mathscr {E}})\) is an undirected graph data.

  2. For a special case that \(m=0\), then FCM turns into the famous k-means clustering algorithm.

  3. In fact, the parameter \(\beta\) is not fixed in advance. In Sect. 5, we will discuss the problem that which value of \(\beta\) is the best for certain data set.

  4. http://www.orgnet.com/cases.html.

  5. http://linqs.cs.umd.edu/projects//projects/lbc/index.html.

  6. http://www-personal.umich.edu/~mejn/netdata.

  7. http://dblp.org.

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Acknowledgements

We are hugely grateful to the possible anonymous reviewers for their constructive comments with respect to the original manuscript. What is more, we thank the National Natural Science Foundation of China (Nos. 61966039, 11971065) and the Yunnan Province Education Department Scientific Research Fund Project (No. 2021Y670).

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Authors and Affiliations

  1. School of Mathematics and Computer Sciences, Yunnan Minzu University, Kunming, 650504, People’s Republic of China

    Wenqian He & Shihu Liu

  2. School of Artificial Intelligence, Southwest University, Chongqing, 400715, People’s Republic of China

    Weihua Xu & Wentao Li

  3. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China

    Fusheng Yu

  4. College of Arts and Sciences, Shanghai Maritime University, Shanghai, 201306, People’s Republic of China

    Fang Li

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  1. Wenqian He
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Correspondence to Shihu Liu.

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He, W., Liu, S., Xu, W. et al. On rough set based fuzzy clustering for graph data. Int. J. Mach. Learn. & Cyber. 13, 3463–3490 (2022). https://doi.org/10.1007/s13042-022-01607-6

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