  Point cloud data are widely used in manufacturing applications for process
inspection, modeling, monitoring and optimization. The state-of-art tensor
regression techniques have effectively been used for analysis of structured
point cloud data, where the measurements on a uniform grid can be formed into a
tensor. However, these techniques are not capable of handling unstructured
point cloud data that are often in the form of manifolds. In this paper, we
propose a nonlinear dimension reduction approach named Maximum Covariance
Unfolding Regression that is able to learn the low-dimensional (LD) manifold of
point clouds with the highest correlation with explanatory covariates. This LD
manifold is then used for regression modeling and process optimization based on
process variables. The performance of the proposed method is subsequently
evaluated and compared with benchmark methods through simulations and a case
study of steel bracket manufacturing.
