Clustering Based on Density Estimation with Sparse Grids

Benjamin Peherstorfer, Dirk Pflüger, Hans-Joachim Bungartz

Abstract: We present a density-based clustering method. The clusters are determined by splitting a similarity graph of the data into connected components. The splitting is accomplished by removing vertices of the graph at which an estimated density function of the data evaluates to values below a threshold. The density function is approximated on a sparse grid in order to make the method feasible in higher-dimensional settings and scalable in the number of data points. With benchmark examples we show that our method is competitive with other modern clustering methods. Furthermore, we consider a real-world example where we cluster nodes of a finite element model of a Chevrolet pick-up truck with respect to the displacements of the nodes during a frontal crash.