  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.
