Algorithm A.2.

function GaussKernelGraph $(X,ϵ)=\{W,D,ℒ\}$

Apply a Gaussian kernel to a dataset and compute the corresponding graph matrices.

Input:		Dataset	$X=\left\{{\overrightarrow{x}}_1,\dots ,{\overrightarrow{x}}_N:x\in \chi \right\}\subseteq {ℝ}^d$
		Bandwidth function	$\sigma :X\mapsto ℝ$
Output:		Kernel matrix	W
		Degree matrix	D
		Normalized Laplacian	$ℒ$
1:	for i = 1, N do
2:	D(i, j) ← 0
3:	for j = 1, N do
4:	$W(i,j)\leftarrow \frac{1}{2}\left(\exp \left(\frac{-{\Vert {\overrightarrow{x}}_i-{\overrightarrow{x}}_j\Vert }_2^2}{2ϵ\left(x_i\right)}\right)+\exp \left(\frac{-{\Vert {\overrightarrow{x}}_i-{\overrightarrow{x}}_j\Vert }_2^2}{2ϵ\left(x_j\right)}\right)\right)$			▷ Symmetric kernel
5:	D(i, i) ← D(i, i) + W(i, j)			▷ Degrees
6:	end for
7:	end for
8:	$ℒ\leftarrow I-D^{-1/2}W{D}^{-1/2}$			▷ Normalized graph Laplacian
9:	return $\{W,D,ℒ\}$