Linear Optimal Transport Subspaces for Point Set Classification

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 hyperparameter 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.