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where <math>U</math> is the matrix of eigenvectors of the [[Graph Laplacian|symmetric normalized graph Laplacian]] <math>L^\text{sym}</math>. <math>L^\text{sym}</math> is denoted as:
<math>L^\text{sym} := D^{-\frac{1}{2}} L D^{-\frac{1}{2}} = I - D^{-\frac{1}{2}} A D^{-\frac{1}{2}} = U\Lambda U^{T}</math>
where <math>L</math> is the [[Graph Laplacian|original graph Laplacian]], <math>I</math> is an [[identity matrix]], and <math>\Lambda</math> is a diagonal matrix.
Therefore, based on the [[Graph Fourier Transform|convolution's property]], the convolution of the signal <math>x</math> and a [[Kernel|learnable kernel function]] <math>g</math> is defined as:
<math>g\star x = \mathcal{F^{-1}}(\mathcal{F}(g)\odot \mathcal{F}(x)) = U(U^Tg\odot U^Tx)</math>,
and if we set the learnable kernel function to be a diagonal one <math>g_{\theta}</math>, this operation is further simplified to:
<math>g_{\theta}\star x = Ug_{\theta}U^Tx</math>.
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