DBSCAN-like clustering method for various data densities

• Published in: Pattern analysis and applications : PAA Vol. 23; no. 2; pp. 541 - 554
• Main Authors: Scitovski, Rudolf, Sabo, Kristian
• Format: Journal Article
• Language: English
• Published: London Springer London 01.05.2020; Springer Nature B.V
• Subjects: Algorithms; Clustering; Computer Science; Data points; Parameters; Partitions; Pattern Recognition; Theoretical Advances; Incremental algorithm; Various data densities; Clusters merging; DBSCAN; Least Squares distance-like function; Clustering
• ISSN: 1433-7541; 1433-755X
• DOI: 10.1007/s10044-019-00809-z

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 A = { a i ∈ R n : i = 1 , ⋯ , m } . First, we define the parameter M i n P t s = ⌊ ln | A | ⌋ and after that, by using a standard procedure from DBSCAN algorithm, for each a ∈ A we determine radius ϵ a of the circle containing MinPts elements from the set 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 ϵ 1 > ⋯ > ϵ t . Furthermore, for parameters { M i n P t s , ϵ 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 ϵ 1 exist. We follow a similar procedure for other parameters ϵ 2 , ⋯ , ϵ 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.