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[Doc] Fix cosinesimil OpenSearch Score and Distance Function formula (#4138) (#4139) 

Signed-off-by: Alireza Fatemi <seyedalirezafatemijahromi@gmail.com>
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Seyed Alireza Fatemi Jahromi 2023-05-25 19:45:55 +03:00 committed by GitHub
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2 changed files with 4 additions and 4 deletions
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2
_search-plugins/knn/approximate-knn.md
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@ -299,7 +299,7 @@ A space corresponds to the function used to measure the distance between two poi
<td>\[ d(\mathbf{x}, \mathbf{y}) = 1 - cos { \theta } = 1 - {\mathbf{x} &middot; \mathbf{y} \over \|\mathbf{x}\| &middot; \|\mathbf{y}\|}\]\[ = 1 -
{\sum_{i=1}^n x_i y_i \over \sqrt{\sum_{i=1}^n x_i^2} &middot; \sqrt{\sum_{i=1}^n y_i^2}}\]
where \(\|\mathbf{x}\|\) and \(\|\mathbf{y}\|\) represent the norms of vectors x and y respectively.</td>
<td><b>nmslib</b> and <b>faiss:</b>\[ score = {1 \over 1 + d } \]<br><b>Lucene:</b>\[ score = {1 + d \over 2}\]</td>
<td><b>nmslib</b> and <b>faiss:</b>\[ score = {1 \over 1 + d } \]<br><b>Lucene:</b>\[ score = {2 - d \over 2}\]</td>
</tr>
<tr>
<td>innerproduct (not supported for Lucene)</td>

6
_search-plugins/knn/knn-score-script.md
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@ -306,10 +306,10 @@ A space corresponds to the function used to measure the distance between two poi
</tr>
<tr>
<td>cosinesimil</td>
<td>\[ d(\mathbf{x}, \mathbf{y}) = cos \theta = {\mathbf{x} &middot; \mathbf{y} \over \|\mathbf{x}\| &middot; \|\mathbf{y}\|}\]\[ =
<td>\[ d(\mathbf{x}, \mathbf{y}) = 1 - cos { \theta } = 1 - {\mathbf{x} &middot; \mathbf{y} \over \|\mathbf{x}\| &middot; \|\mathbf{y}\|}\]\[ = 1 -
{\sum_{i=1}^n x_i y_i \over \sqrt{\sum_{i=1}^n x_i^2} &middot; \sqrt{\sum_{i=1}^n y_i^2}}\]
where \(\|\mathbf{x}\|\) and \(\|\mathbf{y}\|\) represent normalized vectors.</td>
<td>\[ score = 1 + d \]</td>
where \(\|\mathbf{x}\|\) and \(\|\mathbf{y}\|\) represent the norms of vectors x and y respectively.</td>
<td>\[ score = 2 - d \]</td>
</tr>
<tr>
<td>innerproduct (not supported for Lucene)</td>