Point cloud is a critically important geometric data structure, and researchers have increasingly focused on and achieved promising results in terms of point cloud processing since PointNet's pioneering work. However, most previous methods only represent the shape of point clouds through coordinates or normal vectors, neglecting the intrinsic geometric and topological properties of this data structure. In this paper, we present an effective point cloud analysis approach which is using topological information. By employing a simplified version of the PointNet++(SSG version), we conduct benchmark experiments on the ModelNet40 dataset to evaluate TPA's performance in the classification task. Our improved method can still directly process point clouds, as the topological invariants ensure the permutation invariance of the input points. Simulation results show that the topological approach based on persistent homology can effectively provide topological structural features and improve the accuracy of the models.
KEYWORDS: Climatology, Data modeling, Design and modelling, Environmental sensing, Process modeling, Modeling, Mathematical optimization, Deep learning, Covariance matrices, Covariance
Climate data is of great essence in various fields of researches. As direct observations are limited by sensing resolution and accuracy, a considerable amount of climate data is generated by theoretical computation. However, current mainstream climate models suffer from either limited accuracy or discrete outputs. In this paper, we propose a method of generating climate data by utilizing the properties of the Gaussian Process and carefully designing its kernel structure. Different from previous work, our model considers both temporal and spatial dimensions as inputs, hence being able to generate continuous predictions on certain areas or time intervals and achieve high accuracy. We conduct experiments on the famous ERA5 dataset and compare our method with classic model. Our model outperforms the classic one in terms of error scores in both spatial and temporal tasks, and comparison of uncertainty growth shows our advantage.
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