DBSCAN-like clustering method for various data densities

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) epsilon R-n : i = 1,..., m}. First, we define the parameter MinPts = vertical bar ln vertical bar A vertical bar vertical bar and after that, by using a standard procedure from DBSCAN algorithm, for each a epsilon A we determine radius epsilon(a) of the circle containing MinPts elements from the set.. 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) >... > 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),..., 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.