New answers tagged matrix-factorization
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Let me re-write the eigen-decomposition as: $S = UDU^{\top}$. Now, consider the QR-decomposition $\sqrt{D}U^{\top} = QR$ where $Q$ is unitary and $R$ is upper triangular. For uniqueness, one has to ensure that $R$ has positive diagonal entries. For negative diagonal values, we can negate the corresponding row of $R$. $\,S=R^{\top}R$ is then the Cholesky ...
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I don't know if this will be helpful to you (since it is a late answer and you already accepted the other answer) but there is a decent literature review of bandwidth minimizing algorithms in https://hal.archives-ouvertes.fr/hal-01166658/document .
I would think the matrix as a graph and collapse each block into a single node, i.e. if two nodes of the ...
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