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[skip-ci] Update README.md
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fradav committed Nov 16, 2023
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2 changes: 1 addition & 1 deletion README.md
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Expand Up @@ -181,7 +181,7 @@ if pls enabled :

**Comment** When there isn’t any missing data, stages $2.1$ and $2.2$ could be replaced by $w_{k}=\frac{X_{k-1}^{T} y_{k-1}}{\left\|X_{k-1}^{T} y_{k-1}\right\|}$ and $2.3$ by $t_{k}=X_{k-1}w_{k}$

To get $W$ so that $T=XW$ we compute : $$\mathbf{W}=\mathbf{W}^{*}\left(\widetilde{\mathbf{P}} \mathbf{W}^{*}\right)^{-1}$$
To get $W$ so that $T=XW$ we compute : $$\mathbf{W}=\mathbf{W}^{*}\left(\widetilde{\mathbf{P}} \mathbf{W}^{\*}\right)^{-1}$$

where $\widetilde{\mathbf{P}}_{K \times p}=\mathbf{t}\left[p_{1}, \ldots, p_{K}\right]$ and $\mathbf{W}^{*}_{p \times K} = [w_1, \ldots, w_K]$

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2 changes: 1 addition & 1 deletion README.qmd
Original file line number Diff line number Diff line change
Expand Up @@ -181,7 +181,7 @@ if pls enabled :
**Comment** When there isn’t any missing data, stages $2.1$ and $2.2$ could be replaced by $w_{k}=\frac{X_{k-1}^{T} y_{k-1}}{\left\|X_{k-1}^{T} y_{k-1}\right\|}$ and $2.3$ by $t_{k}=X_{k-1}w_{k}$

To get $W$ so that $T=XW$ we compute :
$$\mathbf{W}=\mathbf{W}^{*}\left(\widetilde{\mathbf{P}} \mathbf{W}^{*}\right)^{-1}$$
$$\mathbf{W}=\mathbf{W}^{*}\left(\widetilde{\mathbf{P}} \mathbf{W}^{\*}\right)^{-1}$$

where $\widetilde{\mathbf{P}}_{K \times p}=\mathbf{t}\left[p_{1}, \ldots, p_{K}\right]$ and $\mathbf{W}^{*}_{p \times K} = [w_1, \ldots, w_K]$

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