Linear optimal transport subspaces for point set classification
This addresses the challenge of modeling unordered and permutation invariant point sets for classification in computer vision and machine learning, with an incremental improvement in handling deformations.
The paper tackles the problem of classifying point sets under spatial deformations, particularly affine deformations, by proposing a framework that uses the Linear Optimal Transport (LOT) transform to create a linear embedding and a nearest-subspace algorithm, achieving competitive accuracies and robustness in out-of-distribution scenarios.
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.