Symmetric Sinkhorn normalization converts arbitrary positive smoothing kernels into mass-preserving, spectrum-bounded diffusion operators that approximate heat diffusion at fixed scale.
This equivalence explains the fast convergence in 5 to 10 iterations we observe in practice, which was studied in (Knight et al., 2014)
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Sinkhorn Normalization of Diffusion Kernels
Symmetric Sinkhorn normalization converts arbitrary positive smoothing kernels into mass-preserving, spectrum-bounded diffusion operators that approximate heat diffusion at fixed scale.