Mixing
What is a Spectral Graph Convolution?
$begingroup$
I'm reading about Graph Neural Networks and I would like to understand more about first-order and second-order approximations of spectral graph convolution.
What is a Spectral Graph Convolution?
What does a first-order (second-order) approximation of a spectral graph convolution mean? Please, some examples are appreciated.
graph-theory convolution
asked Jan 25 at 8:44
Leo RibeiroLeo Ribeiro
1012
$endgroup$
add a comment |
$begingroup$
I'm reading about Graph Neural Networks and I would like to understand more about first-order and second-order approximations of spectral graph convolution.
What is a Spectral Graph Convolution?
What does a first-order (second-order) approximation of a spectral graph convolution mean? Please, some examples are appreciated.
graph-theory convolution
asked Jan 25 at 8:44
Leo RibeiroLeo Ribeiro
1012
$endgroup$
$begingroup$
Do you know how a circulant matrix $C$ can be diagonalized as $C=Wdiag(hat{C_1}) W^*$ where $W$ is the matrix of the discrete Fourier transform and $hat{C_1}$ is the DFT of the first row of $C$. Then the idea of graph convolution is to generalize by replacing $W$ by the matrix $U$ obtained in diagonalizing the Laplacian $L = UDU^top$ of some initial graph $G$ with $n$ nodes, the vectors of $Bbb{C}^n$ to be convolved being regarded as activations of the nodes of $G$, which is interpreted as telling how the entries of those vectors should be connected
$endgroup$
– reuns
Jan 25 at 9:32
add a comment |
$begingroup$
I'm reading about Graph Neural Networks and I would like to understand more about first-order and second-order approximations of spectral graph convolution.
What is a Spectral Graph Convolution?
What does a first-order (second-order) approximation of a spectral graph convolution mean? Please, some examples are appreciated.
graph-theory convolution
asked Jan 25 at 8:44
Leo RibeiroLeo Ribeiro
1012
$endgroup$
I'm reading about Graph Neural Networks and I would like to understand more about first-order and second-order approximations of spectral graph convolution.
What is a Spectral Graph Convolution?
What does a first-order (second-order) approximation of a spectral graph convolution mean? Please, some examples are appreciated.
graph-theory convolution
graph-theory convolution
asked Jan 25 at 8:44
Leo RibeiroLeo Ribeiro
1012
asked Jan 25 at 8:44
Leo RibeiroLeo Ribeiro
1012
asked Jan 25 at 8:44
Leo RibeiroLeo Ribeiro
1012
asked Jan 25 at 8:44
Leo RibeiroLeo Ribeiro
1012
asked Jan 25 at 8:44
Leo RibeiroLeo Ribeiro
1012
1012
$begingroup$
Do you know how a circulant matrix $C$ can be diagonalized as $C=Wdiag(hat{C_1}) W^*$ where $W$ is the matrix of the discrete Fourier transform and $hat{C_1}$ is the DFT of the first row of $C$. Then the idea of graph convolution is to generalize by replacing $W$ by the matrix $U$ obtained in diagonalizing the Laplacian $L = UDU^top$ of some initial graph $G$ with $n$ nodes, the vectors of $Bbb{C}^n$ to be convolved being regarded as activations of the nodes of $G$, which is interpreted as telling how the entries of those vectors should be connected
$endgroup$
– reuns
Jan 25 at 9:32
add a comment |
$begingroup$
Do you know how a circulant matrix $C$ can be diagonalized as $C=Wdiag(hat{C_1}) W^*$ where $W$ is the matrix of the discrete Fourier transform and $hat{C_1}$ is the DFT of the first row of $C$. Then the idea of graph convolution is to generalize by replacing $W$ by the matrix $U$ obtained in diagonalizing the Laplacian $L = UDU^top$ of some initial graph $G$ with $n$ nodes, the vectors of $Bbb{C}^n$ to be convolved being regarded as activations of the nodes of $G$, which is interpreted as telling how the entries of those vectors should be connected
$endgroup$
– reuns
Jan 25 at 9:32
$begingroup$
Do you know how a circulant matrix $C$ can be diagonalized as $C=Wdiag(hat{C_1}) W^*$ where $W$ is the matrix of the discrete Fourier transform and $hat{C_1}$ is the DFT of the first row of $C$. Then the idea of graph convolution is to generalize by replacing $W$ by the matrix $U$ obtained in diagonalizing the Laplacian $L = UDU^top$ of some initial graph $G$ with $n$ nodes, the vectors of $Bbb{C}^n$ to be convolved being regarded as activations of the nodes of $G$, which is interpreted as telling how the entries of those vectors should be connected
$endgroup$
– reuns
Jan 25 at 9:32
$begingroup$
Do you know how a circulant matrix $C$ can be diagonalized as $C=Wdiag(hat{C_1}) W^*$ where $W$ is the matrix of the discrete Fourier transform and $hat{C_1}$ is the DFT of the first row of $C$. Then the idea of graph convolution is to generalize by replacing $W$ by the matrix $U$ obtained in diagonalizing the Laplacian $L = UDU^top$ of some initial graph $G$ with $n$ nodes, the vectors of $Bbb{C}^n$ to be convolved being regarded as activations of the nodes of $G$, which is interpreted as telling how the entries of those vectors should be connected
$endgroup$
– reuns
Jan 25 at 9:32
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3086884%2fwhat-is-a-spectral-graph-convolution%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3086884%2fwhat-is-a-spectral-graph-convolution%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Do you know how a circulant matrix $C$ can be diagonalized as $C=Wdiag(hat{C_1}) W^*$ where $W$ is the matrix of the discrete Fourier transform and $hat{C_1}$ is the DFT of the first row of $C$. Then the idea of graph convolution is to generalize by replacing $W$ by the matrix $U$ obtained in diagonalizing the Laplacian $L = UDU^top$ of some initial graph $G$ with $n$ nodes, the vectors of $Bbb{C}^n$ to be convolved being regarded as activations of the nodes of $G$, which is interpreted as telling how the entries of those vectors should be connected
$endgroup$
– reuns
Jan 25 at 9:32