DDCAL: Evenly Distributing Data into Low Variance Clusters Based on Iterative Feature Scaling

Abstract

This work studies the problem of clustering one-dimensional data points such that they are evenly distributed over a given number of low variance clusters. One application is the visualization of data on choropleth maps or on business process models, but without over-emphasizing outliers. This enables the detection and differentiation of smaller clusters. The problem is tackled based on a heuristic algorithm called DDCAL (1d distribution cluster algorithm) that is based on iterative feature scaling which generates stable results of clusters. The effectiveness of the DDCAL algorithm is shown based on 5 artificial data sets with different distributions and 4 real-world data sets reflecting different use cases. Moreover, the results from DDCAL, by using these data sets, are compared to 11 existing clustering algorithms. The application of the DDCAL algorithm is illustrated through the visualization of pandemic and population data on choropleth maps as well as process mining results on process models.