A Novel Fuzzy Clustering Method Based on Topological Connected Component

With the development of fuzzy set theory, the clustering methods widely used in various fields can be divided into hard clustering methods and fuzzy clustering methods. Fuzzy clustering methods use the membership function with values in the interval [0, 1] to describe fuzzy concepts, which is different from the idea of “non-0 is 1” in hard clustering methods, so they are more suitable for some real datasets. In this article, we introduce a novel fuzzy clustering method called fuzzy connected clustering (FCC), which is based on the idea of topological connected components. According to the basic view of topology, FCC directly considers the location characteristics between objects, unlike the common clustering methods that need artificial conditions, such as distance scale, cluster center, fuzzy similar matrix, etc. We use topological knowledge to derive FCC through a series of strict logical reasoning, and design a new algorithm, FCC algorithm. Furthermore, we propose a method of constructing “partial order” to express the clustering results of FCC intuitively. Combining with the application examples of FCC, we not only demonstrate the FCC's high interpretability in dealing with real-world problems, but also compare FCC with the commonly used fuzzy clustering method FEMCM. Moreover, we also try to use a benchmark dataset to show how well the FCC deals with real problems related to fuzzy concepts. Finally, we further discuss the extensions and limitations of FCC, and give some basic directions to effectively address these limitations, as well as prospects for future work related to this novel clustering method FCC.