A new mechanism of selecting representative data samples for Parzen windows method

Based on the experimental observations and theoretical analysis, we validate that the significant increase of data samples may not bring about the obvious improvement of estimation performance of Parzen windows method. Thus, in this paper, we discuss a new mechanism of selecting representative data samples for Parzen windows method. An importance degree function is defined to evaluate the importance of data sample. Then, a decision threshold is optimized based on particle swarm optimization (PSO) algorithm. The data samples whose importance degrees are larger than the optimized decision threshold will be selected as the representations to estimate the underlying probability density function (PDF). Finally, the experimental results on the designed datasets obeying Uniform, Normal, Exponential, and Rayleigh distributions show that the estimation of PDF by using the representative data samples can obtain the same estimation errors (the two-tailed t-test with 95% confidence level) compared with the estimation on whole dataset. Meanwhile, the computational complexity of using representative data samples to estimate PDF is decreased evidently.