最大协方差展开回归：一种基于协变量的流形学习新方法用于点云数据
Maximum Covariance Unfolding Regression: A Novel Covariate-based Manifold Learning Approach for Point Cloud Data
AI总结：
本文提出最大协方差展开回归方法，用于学习非结构化点云数据的低维流形，并与协变量建立最高相关性，以支持回归建模和过程优化。
摘要：
点云数据广泛应用于制造应用中的过程检测、建模、监控和优化。最先进的张量回归技术已有效用于分析结构化点云数据，其中均匀网格上的测量可以形成张量。然而，这些技术无法处理通常以流形形式存在的非结构化点云数据。在本文中，我们提出了一种名为最大协方差展开回归（Maximum Covariance Unfolding Regression）的非线性降维方法，该方法能够学习点云的低维（LD）流形，且与解释协变量具有最高相关性。然后，该低维流形用于基于过程变量的回归建模和过程优化。所提出方法的性能随后通过仿真和钢支架制造的案例研究进行了评估，并与基准方法进行了比较。
英文摘要：
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.
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