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[DOCS] Fixed NDCG formula issues #22090

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[DOCS] Fixed NDCG formula issues #22090

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[DOCS] Fixed NDCG formula issues
yueguoguo Aug 13, 2018
d0f814f
[DOC] Update NDCG formula and wiki link
yueguoguo Aug 20, 2018
f87cf61
[DOCS] Restore "-1" used in the upper bound
yueguoguo Aug 20, 2018
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4 changes: 2 additions & 2 deletions docs/mllib-evaluation-metrics.md
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Expand Up @@ -461,11 +461,11 @@ $$rel_D(r) = \begin{cases}1 & \text{if $r \in D$}, \\ 0 & \text{otherwise}.\end{
<tr>
<td>Normalized Discounted Cumulative Gain</td>
<td>
$NDCG(k)=\frac{1}{M} \sum_{i=0}^{M-1} {\frac{1}{IDCG(D_i, k)}\sum_{j=0}^{n-1}
$NDCG(k)=\frac{1}{M} \sum_{i=0}^{M-1} {\frac{1}{IDCG(D_i, k)}\sum_{j=1}^{n}
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@srowen srowen Aug 16, 2018

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We do need to fix this, but, this makes the subscripts incorrect for R_i(j). I think the expression should change to ln(j+2) in the next line; this is what the code does. For consistency I'd do the same below too.

\frac{rel_{D_i}(R_i(j))}{\text{ln}(j+1)}} \\
\text{Where} \\
\hspace{5 mm} n = \text{min}\left(\text{max}\left(|R_i|,|D_i|\right),k\right) \\
\hspace{5 mm} IDCG(D, k) = \sum_{j=0}^{\text{min}(\left|D\right|, k) - 1} \frac{1}{\text{ln}(j+1)}$
\hspace{5 mm} IDCG(D, k) = \sum_{j=1}^{\text{min}(\left|D\right|, k)} \frac{1}{\text{ln}(j+1)}$
</td>
<td>
<a href="https://en.wikipedia.org/wiki/Information_retrieval#Discounted_cumulative_gain">NDCG at k</a> is a
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@srowen srowen Aug 16, 2018

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We can update the link here to https://en.wikipedia.org/wiki/Discounted_cumulative_gain#Normalized_DCG

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