On bandwidth selection using minimal spanning tree for kernel density estimation

Abstract

The use of kernel density estimation is quite well known in large variety of machine learning applications like classification, clustering, feature selection, etc. One of the major issues in the construction of kernel density estimators is the tuning of bandwidth parameter. Most of the bandwidth selection procedures optimize mean integrated squared or absolute error, which require huge computational time as the size of the data increases. Here, the bandwidth has been taken to be a function of inter-point distances of the data set. It is defined as a function of the length of Euclidean Minimal Spanning Tree of the given sample points. No rigorous theory about the asymptotic properties of the EMST based density estimator has been developed in the literature. Theoretical analysis of the asymptotic properties of the EMST based density estimator has been established and proved that the estimator is asymptotically unbiased to the original density at its every continuity point. Moreover, theoretical analysis has been provided for general kernel. Experiments are conducted using both synthetic and real-life data sets to compare the performance of the EMST bandwidth to those of conventional cross-validation and plug-in bandwidth selectors. It is found that the EMST based estimator achieves the comparative performance, while being simpler and faster than the conventional estimators.