Fuzzy extensions of the DBScan clustering algorithm

The DBSCAN algorithm is a well-known density based clustering approach particularly useful in spatial data mining for its ability to find objects' groups with heterogeneous shapes and homogeneous local density distributions in the feature space. Furthermore, it can be suitable as scaling down approach to deal with big data for its ability to remove noise. Nevertheless, it suffers for some limitations, mainly the inability to identify clusters with variable density distributions and partially overlapping borders, which is often a characteristics of both scientific data and real-world data. To this end, in this work, we propose three fuzzy extensions of the DBSCAN algorithm to generate clusters with distinct fuzzy density characteristics. The original version of DBSCAN requires two precise parameters (minPts and epsilon) to define locally dense areas which serve as seeds of the clusters. Nevertheless, precise values of both parameters may be not appropriate in all regions of the dataset. In the proposed extensions of DBSCAN, we define soft constraints to model approximate values of the input parameters. The first extension, named Fuzzy Core DBSCAN, relaxes the constraint on the neighbourhood's density to generate clusters with fuzzy core points, i.e. cores with distinct density; the second extension, named Fuzzy Border DBSCAN, relaxes epsilon to allow the generation of clusters with overlapping borders. Finally, the third extension, named Fuzzy DBSCAN subsumes the previous ones, thus allowing to generate clusters with both fuzzy cores and fuzzy overlapping borders. Our proposals are compared w.r.t. state of the art fuzzy clustering methods over real-world datasets.