Point cloud is a widely used 3D data form, which can be produced by depth sensors, such as Light Detection and Ranging (LIDAR) and RGB-D cameras. Being unordered and irregular, many researchers focused on the feature engineering of the point cloud. Being able to learn complex hierarchical structures, deep learning has achieved great success with images from cameras. Recently, many researchers have adapted it into the applications of the point cloud. In this paper, the recent existing point cloud feature learning methods are classified as point-based and tree-based. The former directly takes the raw point cloud as the input for deep learning. The latter first employs a k-dimensional tree (Kd-tree) structure to represent the point cloud with a regular representation and then feeds these representations into deep learning models. Their advantages and disadvantages are analyzed. The applications related to point cloud feature learning, including 3D object classification, semantic segmentation, and 3D object detection, are introduced, and the datasets and evaluation metrics are also collected. Finally, the future research trend is predicted.

In this article, we present a family of adaptive stochastic optimization methods, which are associated with mirror maps that are widely used to capture the geometry properties of optimization problems during iteration processes. The well-known adaptive moment estimation (Adam)-type algorithm falls into the family when the mirror maps take the form of temporal adaptation. In the context of convex objective functions, we show that with proper step sizes and hyperparameters, the average regret can achieve the convergence rate ${\mathcal { O}}(T^{-(1/2)})$ after T iterations under some standard assumptions. We further improve it to $O(T^{-1}\log T)$ when the objective functions are strongly convex. In the context of smooth objective functions (not necessarily convex), based on properties of the strongly convex differentiable mirror map, our algorithms achieve convergence rates of order ${\mathcal { O}}(T^{-(1/2)})$ up to a logarithmic term, requiring large or increasing hyperparameters that are coincident with practical usage of Adam-type algorithms. Thus, our work gives explanations for the selection of the hyperparameters in Adam-type algorithms’ implementation.