Efficient estimation of dynamic density functions with an application to outlier detection

In this paper, we propose a new method to estimate the dynamic density over data streams, named KDE-Track as it is based on a conventional and widely used Kernel Density Estimation (KDE) method. KDE-Track can efficiently estimate the density with linear complexity by using interpolation on a kernel model, which is incrementally updated upon the arrival of streaming data. Both theoretical analysis and experimental validation show that KDE-Track outperforms traditional KDE and a baseline method Cluster-Kernels on estimation accuracy of the complex density structures in data streams, computing time and memory usage. KDE-Track is also demonstrated on timely catching the dynamic density of synthetic and real-world data. In addition, KDE-Track is used to accurately detect outliers in sensor data and compared with two existing methods developed for detecting outliers and cleaning sensor data.