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Richard Guo added subsection_Non_convex_optimization_formulation__.tex
over 8 years ago
Commit id: 2331c1d15ed08b3c0a679ec873f15ae162f8c886
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\subsection{Non-convex optimization formulation}
Since $\mathbf{A_0}$ is complete, the row space of $\mathbf{Y}$ is equivalent to the row space of $\mathbf{X}_0$. By the result from \cite{spielman2013exact}, under the generative model, rows of $\mathbf{X}_0$ corresponds to the $n$ sparsest vectors in the row space. Once $\mathbf{X}_0$ is recovered, $\mathbf{A}_0$ could be solved from least square $\mathbf{A}_0 = \mathbf{Y} \mathbf{X}_0 (\mathbf{X}_0 \mathbf{X}_0^T)^{-1}$.
