Dynamic prediction of multivariate functional data based on Functional Kernel Partial Least Squares. (August 2022) - Qian, Qingting
Abstract: With the flourishment of sensing technology, a huge mass of functional data can be acquired to describe the manufacturing process and predict the product quality. But these data simultaneously bring in modeling challenges of multi-type data, high-dimensional variables, data irregularity, and complex correlations. To address these challenges, this work proposes the Functional Kernel Partial Least Squares (FKPLS) methodology, which is a function-on-function regression. The FKPLS method first smooths the discrete sequences to continuous functions via functional data analysis (FDA) to retain the dynamic characteristics of variables, and then relies on basis function expansion to estimate the regression coefficient functions in order to avoid the ill-posed problem in directly estimating the functional eigenequation. An artificial dataset and a real-world steelmaking process are used to validate the effectiveness of the FKPLS method. The results demonstrate lower mean relative prediction error of the FKPLS method than the traditional methods, which is no more than 0.36% on simulation data and no more than 14.88% on industrial data. As the regression coefficients are functions, the FKPLS method is also effective in predicting dynamic mapping between predictors and responses. Highlights: Provide a function-on-function regression method for multivariate functional data. Retain the dynamic characteristics of functional data by functional data analysis. Solve the eigenequation of functional data through basis function expansion. Deal with problems of high dimensions, data irregularity, and nonlinear correlation. Accurately predict the carbon concentration of steel during the steelmaking process.