An Undersampling Method Based on Spatial Distance and Output Change for Computational Cost Reduction of Regression Models of Engineering Data

Excessive computational cost is one of the main reasons limiting the application of regression analysis in engineering data mining. In this article, an undersampling method is proposed to screen the important samples from the initial dataset, aiming to save the computation cost by reducing the size of the training samples. A cost function is constructed by the weighted sum of the sample distance in the input space and the output change around each sample, and the weights of the above two terms are derived by the Lagrange multiplier method. A modified simulated annealing algorithm is designed to minimize the cost function to obtain the optimal undersampling results. The experiments on mathematical functions and engineering cases show that the proposed method outperforms the other methods in terms of regression accuracy and can save a great computational cost in regression analysis. The proposed undersampling method is applied to the data modeling of a shield machine, in which the Earth pressure is predicted by four operation parameters. The results indicate that the proposed method performs best in most experiments. The undersampling of training samples greatly reduces the computation time by 99.10%, but the prediction accuracy is only reduced by less than 10.00%. Considering the limited computing resources of engineering equipment and the need for rapid response, the proposed undersampling method provides a solution for the engineering application of regression analysis.