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A fuzzy clustering method based on topology structure and ϵ-connectedness

Topology is the fundamental mathematical way for describing the shape of objects. Connectedness in topology is used to analyze data by finding clusters and filtering data. The enhanced computational capabilities have made it possible to explore the underlying topological structures of connected components of large data sets, but the main issue is that the connections are not based on crisp criterion like ϵ-connectedness but are fuzzy in nature. This issue is more profound in social and health science datasets where data recording is semi-automated. This paper proposes a new technique which combines the techniques of ϵ-connectedness and fuzzy membership for the purpose of data clustering. The algorithm is tested on various simulated patterns.