Algorithm A.1.

function HarmonicAlignment $(X,Y,\mathcal{K},t,\ell )={\mathrm{\Phi }}_t^{(X,Y)}$

Input:		Data sets	(X,Y)
		Kernel parameters	$\mathcal{K}=\left\{{\mathcal{K}}^{(X)},{\mathcal{K}}^{(Y)}\right\}$
		Alignment diffusion time	t
		Alignment band count	$\ell$
Output:		Aligned diffusion map	Φt(X, Y)
1:	for Z=X,Y do
2:	${\mathcal{G}}^{(Z)}\leftarrow \left\{W^{(Z)},{\mathcal{L}}^{(Z)},D^{(Z)}\right\}\leftarrow \text{GaussKernelGraph}\left(Z,{\mathcal{K}}^{(Z)}\right)$			▷ Alg. A.2
3:	$\mathrm{\Psi }(Z),{\mathrm{\Lambda }}^{(Z)}\leftarrow \mathrm{SVD}\left(I-{\mathcal{L}}^{(Z)}\right)$			▷ Graph Fourier basis
4:	end for
5:	${{\mathrm{\Phi }}_t}^{(X,Y)}\leftarrow \mathrm{Align}\left(\left\{{\mathrm{\Psi }}^{(X)},{\mathrm{\Lambda }}^{(X)},D^{(X)}\right\},\left\{{\mathrm{\Psi }}^{(Y)},{\mathrm{\Lambda }}^{(Y)},D^{(Y)}\right\},t,\ell \right)$			▷ Alg. A.3
6:	return ${{\mathrm{\Phi }}_t}^{(X,Y)}$