An Improved Virtual Sample Generation Method Based on Quadrat Density Method and Quantile Regression for Small Sample Size Problem

The gradual realization of automation has caused explosive growth of data and increased the amount of researchable data. However, due to the low probability of occurrence and high difficulty in obtaining, representative data is lacking. One of the effective ways to solve this problem is virtual sample generation (VSG). In this study, a novel VSG method is put forward. The sample squares are divided in the input space according to Dominance Analysis, and the virtual inputs are generated by using the Quadrat Density Method in reverse. The corresponding virtual output is predicted by Gaussian Process Regression. Through Quantile Regression, analyze the correlation between input variables and output variables. The generated virtual samples are screened, and the virtual samples that do not meet the correlation relationship are eliminated. In order to verify the effectiveness of the proposed method, experiments are carried out on two numerical simulations and a real-world application from a cascade reaction process for high-density polyethylene. The results show that the method proposed in this paper is superior to other methods.