Full Rotation Hyper-ellipsoid Multivariate Adaptive Bandwidth Kernel Density Estimator

Adaptive bandwidth kernel density estimators (AB-KDEs) have received attention from the academic community due to an analytical promise of increased performance over classical estimators. However, the field is fragmented, and there exists no comprehensive comparison of the existing state-of-the-art AB-KDEs. We provide a comparison of some state-of-the-art and classical AB-KDE methods as well as a computational framework. We also present a novel implementation of a full principal axes rotation hyper-ellipsoid variant of the k-Nearest Neighbours algorithm and a Gaussian extension to K-NN. The extensive experimental results show the fixed bandwidth rule-of-thumb methods achieve satisfactory results. Further, the balloon estimators are shown to be superior in the higher dimensional spaces, with higher modes or data on non-linear manifolds. The sample point estimators show utility when data are scarce in low dimensions. The empirical results show that our full rotation hyper-ellipsoid estimator and our Gaussian K-NN are state-of-the-art and will have a significant positive impact on data analysis algorithms. Especially algorithms which depend upon underlying density estimates on “complex” higher-dimensional data.