Interpretation of Symmetric Normalised of Graph Adjacency Matrix?
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I'm trying to follow a blog post about Graph Convolutional Neural Networks. To set up some notation, the above blog post denotes a graph $mathcal{G}$, it's adjacency matrix $A$, and the degree matrix $D$.
A section of that blog post then says:
I understand how an adjacency matrix can be row-normalised with $A_{row} = D^{-1}A$, or column normalised with $A_{col} = AD^{-1}$.
My question: is there some intuitive interpretation of a symmetrically normalized adjacency matrix $A_{sym} = D^{-1/2}AD^{-1/2}$?
graph-theory symmetric-matrices adjacency-matrix
asked Dec 11 '18 at 22:59
aaronsnoswellaaronsnoswell
1649
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add a comment |
$begingroup$
I'm trying to follow a blog post about Graph Convolutional Neural Networks. To set up some notation, the above blog post denotes a graph $mathcal{G}$, it's adjacency matrix $A$, and the degree matrix $D$.
A section of that blog post then says:
I understand how an adjacency matrix can be row-normalised with $A_{row} = D^{-1}A$, or column normalised with $A_{col} = AD^{-1}$.
My question: is there some intuitive interpretation of a symmetrically normalized adjacency matrix $A_{sym} = D^{-1/2}AD^{-1/2}$?
graph-theory symmetric-matrices adjacency-matrix
asked Dec 11 '18 at 22:59
aaronsnoswellaaronsnoswell
1649
$endgroup$
add a comment |
$begingroup$
I'm trying to follow a blog post about Graph Convolutional Neural Networks. To set up some notation, the above blog post denotes a graph $mathcal{G}$, it's adjacency matrix $A$, and the degree matrix $D$.
A section of that blog post then says:
I understand how an adjacency matrix can be row-normalised with $A_{row} = D^{-1}A$, or column normalised with $A_{col} = AD^{-1}$.
My question: is there some intuitive interpretation of a symmetrically normalized adjacency matrix $A_{sym} = D^{-1/2}AD^{-1/2}$?
graph-theory symmetric-matrices adjacency-matrix
asked Dec 11 '18 at 22:59
aaronsnoswellaaronsnoswell
1649
$endgroup$
I'm trying to follow a blog post about Graph Convolutional Neural Networks. To set up some notation, the above blog post denotes a graph $mathcal{G}$, it's adjacency matrix $A$, and the degree matrix $D$.
A section of that blog post then says:
I understand how an adjacency matrix can be row-normalised with $A_{row} = D^{-1}A$, or column normalised with $A_{col} = AD^{-1}$.
My question: is there some intuitive interpretation of a symmetrically normalized adjacency matrix $A_{sym} = D^{-1/2}AD^{-1/2}$?
graph-theory symmetric-matrices adjacency-matrix
graph-theory symmetric-matrices adjacency-matrix
asked Dec 11 '18 at 22:59
aaronsnoswellaaronsnoswell
1649
asked Dec 11 '18 at 22:59
aaronsnoswellaaronsnoswell
1649
asked Dec 11 '18 at 22:59
aaronsnoswellaaronsnoswell
1649
asked Dec 11 '18 at 22:59
aaronsnoswellaaronsnoswell
1649
asked Dec 11 '18 at 22:59
aaronsnoswellaaronsnoswell
1649
1649
add a comment |
add a comment |
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