Online wavelet-based density estimation for non-stationary streaming data

There has been an important emergence of applications in which data arrives in an online time-varying fashion (e.g. computer network traffic, sensor data, web searches, ATM transactions) and it is not feasible to exchange or to store all the arriving data in traditional database systems to operate on it. For this kind of applications, as it is for traditional static database schemes, density estimation is a fundamental block for data analysis. A novel online approach for probability density estimation based on wavelet bases suitable for applications involving rapidly changing streaming data is presented. The proposed approach is based on a recursive formulation of the wavelet-based orthogonal estimator using a sliding window and includes an optimised procedure for reevaluating only relevant scaling and wavelet functions each time new data items arrive. The algorithm is tested and compared using both simulated and real world data.