A1417
Title: A constrained least-squares ghost sample point method for unstructured high-dimensional data
Authors: Kwun Lun Chu - The Hang Seng University of Hong Kong (Hong Kong) [presenting]
Abstract: The constrained least-squares ghost sample points (CLS-GSP) method is introduced, a novel modelling technique for uncovering underlying functions from unstructured, high-dimensional data like point clouds. The method begins with a local approach, fitting the data using a linear combination of radial basis functions. The centres of these basis functions, termed "ghost points," are strategically placed and are independent of the original data points. Furthermore, instead of using a standard least-squares fitting process, a regularization constraint is introduced that forces the local model to precisely interpolate the value at the centre of the neighbourhood. Numerical results demonstrate that this method is effective for solving complex problems, particularly those related to partial differential equations (PDEs).
