DBSCAN-like clustering method for various data densities

  • Rudolf ScitovskiEmail author
  • Kristian Sabo
Theoretical advances


In this paper, we propose a modification of the well-known DBSCAN algorithm, which recognizes clusters with various data densities in a given set of data points \({\mathcal {A}}=\{a^i\in {\mathbb {R}}^n:i=1,\dots ,m\}\). First, we define the parameter \(MinPts=\lfloor \ln |{\mathcal {A}}|\rfloor\) and after that, by using a standard procedure from DBSCAN algorithm, for each \(a\in {\mathcal {A}}\) we determine radius \(\epsilon _a\) of the circle containing MinPts elements from the set \({\mathcal {A}}\). We group the set of all these radii into the most appropriate number (t) of clusters by using Least Squares distance-like function applying SymDIRECT or SepDIRECT algorithm. In that way, we obtain parameters \(\epsilon _1>\dots >\epsilon _t\). Furthermore, for parameters \(\{MinPts,\epsilon _1\}\) we construct a partition starting with one cluster and then add new clusters for as long as the isolated groups of at least MinPts data points in some circle with radius \(\epsilon _1\) exist. We follow a similar procedure for other parameters \(\epsilon _2,\dots ,\epsilon _t\). After the implementation of the algorithm, a larger number of clusters appear than can be expected in the optimal partition. Along with defined criteria, some of them are merged by applying a merging process for which a detailed algorithm has been written. Compared to the standard DBSCAN algorithm, we show an obvious advantage for the case of data with various densities.


Clustering DBSCAN Incremental algorithm Various data densities Clusters merging Least Squares distance-like function 



The author would like to thank the referees and the journal editors for their careful reading of the paper and insightful comments that helped us improve the paper. Especially, the author would like to thank Mrs. Katarina Moržan for significantly improving the use of English in the paper. This work was supported by the Croatian Science Foundation through research Grant IP-2016-06-6545 “The optimization and statistical models and methods in recognizing properties of data sets measured with errors” and research Grant IP-2016-06-8350 “Methodological framework for efficient energy management by intelligent data analytics”.


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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsijekOsijekCroatia

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