Maximum Covariance Unfolding Regression: A Novel Covariate-based Manifold Learning Approach for Point Cloud Data
This addresses a domain-specific problem in manufacturing for process inspection and optimization, offering a novel method for handling unstructured point cloud data, though it appears incremental as it builds on existing manifold learning approaches.
The paper tackled the problem of analyzing unstructured point cloud data, which existing tensor regression methods cannot handle, by proposing Maximum Covariance Unfolding Regression to learn a low-dimensional manifold correlated with covariates for regression and optimization, with performance evaluated through simulations and a steel bracket manufacturing case study.
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.