Online kernel density estimation using fuzzy logic

In this paper, a fuzzy method is proposed to estimate kernel density function online. To achieve this goal, Gaussian mixture model is generated by the fuzzy algorithm. Defuzzifier operator is modified to make it suitable for this application. Means and variances of the model are adapted using observed data in each new sample. Then, rule weights are tuned by minimising the expected L₂ risk function of the estimated and true PDFs. In contrast to the existing approaches, our approach does not require fine-tuning parameters for a specific application, specific forms of the target distributions are not assumed, and temporal constraints are not considered on the observed data. The algorithm is simple and easy to use. Simulation results show the capability of the proposed algorithm in online and accurate estimation of kernel density function.