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According Constrained clustering via affinity propagation, the inverse of $I+MW$ can be computed in closed form using $$ \begin{bmatrix}A & B \\ 0 & I\end{bmatrix}^{-1} = \begin{bmatrix}A^{-1} & -A^{-1}B \\ 0 & I\end{bmatrix} $$ where $M$ and $W$ are symmetric matrices and $A$ is apparently a $2L\times 2L$ matrix where $L$ is the number of non-zeros entries in the upper triangle of $M$ (discounting the diagonal).

Anyone can explain me how this works ?

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  • $\begingroup$ It could be referring to the particular $M$ and $W$ in the paper ($K$ and $M$). $\endgroup$ – Kasra Dec 19 '16 at 14:10
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You may try $$\begin{pmatrix} A & B \\ 0 & I \end{pmatrix}\begin{pmatrix} W & X \\ Y & Z \end{pmatrix}=\begin{pmatrix} I & 0 \\ 0 & I \end{pmatrix}$$Then expand left hand side and compare terms, find W, X, Y, Z.

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