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Learning Submanifolds for Subsequent Inference on Random Dot Product Graphs, Part 1: Theory

arXiv · AI, language, vision and robotics · article · Sep 16, 2026 · UTC

We propose a framework for restricted inference on random dot product graphs whose latent positions lie on an unknown low-dimensional support manifold. For general decision problems, we propose semisupervised decision rules that use auxiliary data to learn the support manifold. Specifically, our rules use the Isomap manifold learning procedure to construct a low-dimensional Euclidean representation of the observed graph, in which space an isometrically invariant function maps configurations of points to actions. We study the behavior of the proposed rules as the quantity of auxiliary data samp

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