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[DOCS] Fixed NDCG formula issues
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When j is 0, log(j+1) will be 0, and this leads to division by 0 issue.

## What changes were proposed in this pull request?

(Please fill in changes proposed in this fix)

## How was this patch tested?

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Please review http://spark.apache.org/contributing.html before opening a pull request.

Closes #22090 from yueguoguo/patch-1.

Authored-by: Zhang Le <[email protected]>
Signed-off-by: Sean Owen <[email protected]>
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yueguoguo authored and srowen committed Aug 20, 2018
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6 changes: 3 additions & 3 deletions docs/mllib-evaluation-metrics.md
Original file line number Diff line number Diff line change
Expand Up @@ -462,13 +462,13 @@ $$rel_D(r) = \begin{cases}1 & \text{if $r \in D$}, \\ 0 & \text{otherwise}.\end{
<td>Normalized Discounted Cumulative Gain</td>
<td>
$NDCG(k)=\frac{1}{M} \sum_{i=0}^{M-1} {\frac{1}{IDCG(D_i, k)}\sum_{j=0}^{n-1}
\frac{rel_{D_i}(R_i(j))}{\text{ln}(j+1)}} \\
\frac{rel_{D_i}(R_i(j))}{\text{ln}(j+2)}} \\
\text{Where} \\
\hspace{5 mm} n = \text{min}\left(\text{max}\left(|R_i|,|D_i|\right),k\right) \\
\hspace{5 mm} IDCG(D, k) = \sum_{j=0}^{\text{min}(\left|D\right|, k) - 1} \frac{1}{\text{ln}(j+1)}$
\hspace{5 mm} IDCG(D, k) = \sum_{j=0}^{\text{min}(\left|D\right|, k) - 1} \frac{1}{\text{ln}(j+2)}$
</td>
<td>
<a href="https://en.wikipedia.org/wiki/Information_retrieval#Discounted_cumulative_gain">NDCG at k</a> is a
<a href="https://en.wikipedia.org/wiki/Discounted_cumulative_gain#Normalized_DCG">NDCG at k</a> is a
measure of how many of the first k recommended documents are in the set of true relevant documents averaged
across all users. In contrast to precision at k, this metric takes into account the order of the recommendations
(documents are assumed to be in order of decreasing relevance).
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