Isolation Kernel Density Estimation

Abstract

This paper shows that adaptive kernel density estimator (KDE) can be derived effectively from Isolation Kernel. Existing adaptive KDEs often employ a data independent kernel such as Gaussian kernel. Therefore, it requires an additional means to adapt its bandwidth locally in a given dataset. Because Isolation Kernel is a data dependent kernel which is derived directly from data, no additional adaptive operation is required. The resultant estimator called IKDE is the only KDE that is fast and adaptive. Existing KDEs are either fast but non-adaptive or adaptive but slow. In addition, using IKDE for anomaly detection, we identify two advantages of IKDE over LOF (Local Outlier Factor), contributing to significantly faster runtime.