Learning from point sets is an essential component in many computer vision
and machine learning applications. Native, unordered, and permutation invariant
set structure space is challenging to model, particularly for point set
classification under spatial deformations. Here we propose a framework for
classifying point sets experiencing certain types of spatial deformations, with
a particular emphasis on datasets featuring affine deformations. Our approach
employs the Linear Optimal Transport (LOT) transform to obtain a linear
embedding of set-structured data. Utilizing the mathematical properties of the
LOT transform, we demonstrate its capacity to accommodate variations in point
sets by constructing a convex data space, effectively simplifying point set
classification problems. Our method, which employs a nearest-subspace algorithm
in the LOT space, demonstrates label efficiency, non-iterative behavior, and
requires no hyper-parameter tuning. It achieves competitive accuracies compared
to state-of-the-art methods across various point set classification tasks.
Furthermore, our approach exhibits robustness in out-of-distribution scenarios
where training and test distributions vary in terms of deformation magnitudes.

通过线性最优传输（LOT）变换构建凸数据空间的方法，对于在空间变形下的点集分类问题具有标签效率、非迭代性和无超参数调整的特点，在各类点集分类任务上取得竞争性的准确率，并在训练和测试分布变化较大的情况下展现出鲁棒性。

点集分类的线性最优传输子空间

Linear optimal transport subspaces for point set classification

Feature learning on point clouds has shown great promise, with the
introduction of effective and generalizable deep learning frameworks such as
pointnet++. Thus far, however, point features have been abstracted in an
independent and isolated manner, ignoring the relative layout of neighboring
points as well as their features. In the present article, we propose to
overcome this limitation by using spectral graph convolution on a local graph,
combined with a novel graph pooling strategy. In our approach, graph
convolution is carried out on a nearest neighbor graph constructed from a
point's neighborhood, such that features are jointly learned. We replace the
standard max pooling step with a recursive clustering and pooling strategy,
devised to aggregate information from within clusters of nodes that are close
to one another in their spectral coordinates, leading to richer overall feature
descriptors. Through extensive experiments on diverse datasets, we show a
consistent demonstrable advantage for the tasks of both point set
classification and segmentation.

本文介绍了一种在点云上进行特征学习的方法，使用基于图卷积的局部图结构和新颖的图池化方法，该方法取得了在点集分类和分割任务中的一致可靠优势。