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Operations research, linear programming, control theory, systems theory, optimal control, game theory
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Accepted
How to find $y_u?$
Thanks to this answer.
As $L$ is symmetric,
\begin{align}
\frac{d (E(S, \textbf{y}))}{d y_u} = 0 + y_l^TL^{l,u} + (L^{u,l}y_l)^T + y_u^TL^{u, u} + (L^{u, u}y_u)^T = 0
\\
2 y_l^T L^{L, u} + 2y_u^T L^{ …
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How to find $y_u?$
In the paper Semi-supervised learning by mixed label propagation Wei Tong and Rong Jin define
$S$ as the similarity(adjacency) matrix
$D = \operatorname{diag}(D_1, D_2, \ldots, D_n)$ where $D_i = \sum …