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I am looking at this question. I wonder if I have:

$$\left\|Y-XW\right\|_{\text{F}}^2$$

Does taking derivative w.r.t $W$ yields this?

$$-2X^T(Y-XW)$$

CaTx
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  • Let $\phi(W)=\left|Y-XW\right|_{\text{F}}^2$, write out $\phi(W+H)-\phi(W)$ using the trace and collect linear terms in $H$. – copper.hat Jun 13 '21 at 20:27
  • I have no idea what you mean by swapping positions. – copper.hat Jun 13 '21 at 20:28
  • Also, that is the gradient, not the derivative as such. – copper.hat Jun 13 '21 at 22:14
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    @copper.hat, the original question is about $\left|XW-Y\right|{\text{F}}^2$ and mine is about $\left|Y-XW\right|{\text{F}}^2$. Hence, positions swapped. Also, I made the edit to account for the missing $-2$. – CaTx Jun 13 '21 at 22:22
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    It doesn't matter whether you write $|Y-XW|_F^2$ or $|XW-Y|_F^2$, the gradient is same. – user550103 Jun 14 '21 at 15:14

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