Adaptive B-spline Knots Selection Using Multi-Resolution Basis Set

Adaptive B-spline Knots Selection Using Multi-Resolution Basis Set Yuan Yuan, Nan Chen, Shiyu Zhou a Department of Industrial and Systems Engineering, the University of Wisconsin – Madison b Department of Industrial & Systems Engineering, National University of Singapore c Corresponding author. Email: [email protected] ABSTRACT B-splines are commonly used in the Computer Aided Design (CAD) and signal processing to fit complicated functions because they are simple yet flexible. However, how to place the knots appropriately in B-spline curve fitting remains a difficult problem. In this paper, we proposed a two-stage knots placement method to place knots adapting to the curvature structures of the unknown function. At the first stage, we selected a subset of basis functions from the pre-specified multi-resolution basis set using the statistical variable selection method—Lasso. At the second stage, we constructed the vector space spanned by the selected basis functions and identified a concise knots vector that is sufficient to characterize such vector space to fit the unknown function. We demonstrated the effectiveness of the proposed method using numerical studies on multiple representative functions.