ANTLER: Bayesian Nonlinear Tensor Learning and Modeler for Unstructured, Varying-Size Point Cloud Data

Unstructured point clouds with varying sizes are increasingly acquired in a variety of environments through laser triangulation or Light Detection and Ranging (LiDAR). Predicting a scalar response based on unstructured point clouds is a common problem that arises in a wide variety of applications. The current literature relies on several pre-processing steps such as structured subsampling and feature extraction to analyze the point cloud data. Those techniques lead to quantization artifacts and do not consider the relationship between the regression response and the point cloud during pre-processing. Therefore, we propose a general and holistic "Bayesian Nonlinear Tensor Learning and Modeler" (ANTLER) to model the relationship of unstructured, varying-size point cloud data with a scalar or multivariate response. The proposed ANTLER simultaneously optimizes a nonlinear tensor dimensionality reduction and a nonlinear regression model with a 3D point cloud input and a scalar or multivariate response. ANTLER has the ability to consider the complex data representation, high-dimensionality,and inconsistent size of the 3D point cloud data.