Learning Theory Problems Involving Gradients

Most learning algorithms are based on data points and function sample values. Motivated by some applications in dimensionality reduction and image processing, the researchers study some mathematical problems for learning algorithms involving gradients. A learning algorithm for implicit surface reconstruction with surface point/normal pairs will be analyzed. Error analysis of Hermite learning algorithms will be conducted by an integral operator approach. This investigation will provide new connections between learning theory and multivariate approximation.