Researchers Paulina Hoyos and Yeari Vigder propose incorporating symmetries directly into affinity kernels for spectral embedding, addressing a limitation of standard methods that treat symmetry-related data points as unrelated. They prove that graph Laplacians built from invariant kernels converge to differential operators on the quotient space, yielding improved convergence rates as effective dimension drops. Validation on datasets with SO(2) or SO(3) symmetry confirms the approach recovers intrinsic geometry where standard methods fail.
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