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Richard Guo added paragraph_No_spurious_local_minima__.tex
over 8 years ago
Commit id: 889a16f620463e64e15ddc0ff30c82fa6a08e6d7
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\paragraph{No spurious local minima} When $\mathbf{A}_0$ is orthogonal, $f(\mathbf{q}, \mathbf{Y})$ has no spurious local minima. In fact, each local minimizer $\hat{\mathbf{q}}$ is sufficient close to a \textit{target} $\mathbf{q}_{\ast}$, which corresponds to a row of $\mathbf{X}_0$ by $\mathbf{q}_{\ast}^T \mathbf{Y} = \alpha \mathbf{e}_i^T \mathbf{X}_0$. $\mathbf{q}_{\ast}$ can be obtained from $\hat{\mathbf{q}}$ by rounding.
