Editing Open Problems:62
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{{Header | {{Header | ||
+ | |title=PCAs | ||
|source=bertinoro14 | |source=bertinoro14 | ||
|who=Andrea Montanari | |who=Andrea Montanari | ||
}} | }} | ||
− | Given a symmetric matrix $A$, we can think of | + | Given a symmetric matrix $A$, we can think of PCA as maximizing $x^\top A x$ subject to $\|x\|=1$. If we also add the condition $x \ge 0$, this problem becomes NP-hard. |
We can define a convex relaxation: | We can define a convex relaxation: | ||
− | \[ \max | + | \[ \max Tr(WA) \text{\ s.t\ } Tr(W) = 1, W \ge 0, W \succceq 0 \] |
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