Maximum Covariance Unfolding: A Novel Covariate-Based Manifold Learning Approach for Point Cloud Regression

Point cloud data are widely used in manufacturing applications for process inspection, modeling, monitoring and optimization. An important body of literature focuses on process optimization for quality improvement by modeling the connection between process variables and point clouds. The state-of-the-art regression techniques often have the assumption that the point cloud space is globally Euclidean. However, these techniques are not capable of handling point clouds with complex shapes in the form of manifolds. The state-of-the-art manifold learning approaches also fail to consider the covariate information during their learning. In this paper, we propose a nonlinear dimension reduction approach named Maximum Covariance Unfolding that is able to learn the low-dimensional (LD) manifold of point clouds with the highest correlation with explanatory covariates in the form of process variables. 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.