Bates–Kornfeld signatures#

This family generalizes the kernel-signature idea (HKS/WKS) with a different spectral weighting, giving descriptors that emphasize a complementary part of the spectrum.

Bates signatures and BKS#

The Bates–Kornfeld Signature (BKS) follows the same per-vertex template as the heat and wave signatures —

\[ S(x) = \sum_i g(\lambda_i)\, \phi_i(x)^2 \]

— but with a kernel \(g(\lambda)\) chosen to weight the spectrum differently from the exponential (heat) or Gaussian-in-log-energy (wave) kernels. The compute_bates_signatures entry point produces the family; compute_bks is the signature itself.

bates = sb.compute_bates_signatures(decomp, ...)
bks = sb.compute_bks(decomp, ...)

IBKS — the inverse signature#

The inverse BKS reweights toward the opposite end of the spectrum, trading emphasis between coarse and fine geometry. Using BKS and IBKS together brackets the spectral range a single kernel would otherwise sample only partially.

ibks = sb.compute_ibks(decomp, ...)