Function Extrapolation of Noisy Data using Converging Lines
Yiming Zhang, Nam Ho Kim, Chanyoung Park, Raphael T. Haftka · AIAA Modeling and Simulation Technologies Conference · 2016
This paper is focused on extrapolating noisy data to a single inaccessible point using the method of converging lines. Matrix multiplication computation time, which is a twodimensional unimodal and monotonic function of matrix dimensions, was adopted as a test problem. Using the method of converging lines, multi-dimensional extrapolation was first transformed into series of one-dimensional extrapolation towards one point. Onedimensional extrapolation results at the extrapolation point were combined using Bayes method. One-dimensional long-range extrapolation was then performed differently depending on the noise level of the data. For low noise levels, the data pattern was clear using logarithmic transformation and standard polynomial regression was used for fitting it. For significant noise levels, ridge regression was used to reduce overfitting. This paper proposes a new scheme to determine the ridge parameter by minimizing prediction error at training samples. This scheme was evaluated based on manufactured data.