TreeKDE: clustering multivariate data based on decision tree and using one-dimensional kernel density estimation

Abstract

In this paper, we present an algorithm for clustering multidimensional data, which we named TreeKDE. It is based on a tree structure decision associated with the optimization of the one-dimensional kernel density estimator function constructed from the orthogonal projections of the data on the coordinate axes. Among the main features of the proposed algorithm, we highlight the automatic determination of the number of clusters and their insertion in a rectangular region. Comparative numerical experiments are presented to illustrate the performance of the proposed algorithm and the results indicate that the TreeKDE is efficient and competitive when compared to other algorithms from the literature. Features such as simplicity and efficiency make the proposed algorithm an attractive and promising research field, which can be used as a basis for its improvement, and also for the development of new clustering algorithms based on the association between decision tree and kernel density estimator.

Keywords:

• Decision tree
• kernel density estimation
• Gaussian kernel
• clustering data
• optimization method

Notes

1 In order to simplify the notation we represent the multidimensional and improper integrals with a single integral symbol.

Additional information

Funding

This work was partially supported by CAPES, CNPq, and Fundação Araucária, Brazil.