Two Twin Extreme Learning Machines for Regression and Their Applications in Industry

In the actual industrial production process, due to the uncertainties and disturbances caused by measurement errors, abnormal events and other factors, the single-value exact prediction models for key indicators usually fail to guarantee high prediction accuracy. The adoption of prediction interval regression can effectively improve this problem. In this paper, two twin extreme learning machines for interval regression, TELMR and K-TELMR, are proposed. Specifically, TELMR aims to find two non-parallel hyperplanes passing through the origin that approach the sample points from the upper and lower bounds, respectively. The regression error is minimized in each hyperplane without exceeding the sample points as much as possible, and slack variables and a penalty term are introduced to balance the underfitting and overfitting problems. K-TELMR is based on TELMR with kernel mapping instead of random mapping, which saves the step of optimizing the number of hidden layer neurons and makes the model further simplified and lightweight. Numerical computation results on several UCI regression problems and a practical industrial regression problem validate the effectiveness of the proposed models.