Graph Fourier transform

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the graph Fourier transform is a <a href="/facts/Transformation_(function)/Yr2J3o8H">mathematical transform</a> which <a href="/facts/Eigendecomposition_of_a_matrix/a2nfF7hJ">eigendecomposes</a> the <a href="/facts/Laplacian_matrix/Iwea2mm9">Laplacian matrix</a> of a graph into <a href="/facts/Eigenvalues_and_eigenvectors/8TjEoT8u">eigenvalues and eigenvectors</a>. Analogously to the <a href="/facts/Fourier_transform/XXhKJtc8">classical Fourier transform</a>, the eigenvalues represent <a href="/facts/Frequency_domain/pyTVrUSq">frequencies</a> and eigenvectors form what is known as a graph <a href="/facts/Fourier_basis/Bt7jqjY2">Fourier basis</a>.
</p><p>The Graph Fourier transform is important in <a href="/facts/Spectral_graph_theory/tBttgGTh">spectral graph theory</a>. It is widely applied in the recent study of graph structured <a href="/facts/Learning_algorithms/e0w0XJTu">learning algorithms</a>, such as the widely employed <a href="/facts/Convolutional_neural_networks/kHEdnmGU">convolutional networks</a>.
</p>

Graph Fourier transform open-in-new

Graph Fourier transform