[Doc] Fix cosinesimil OpenSearch Score and Distance Function formula (#…

…4138) (#4139) (#4176) (cherry picked from commit 8d394f5) Signed-off-by: Alireza Fatemi <[email protected]> Signed-off-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com> Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>
opensearch-project · May 25, 2023 · 7a84065 · 7a84065
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diff --git a/_search-plugins/knn/approximate-knn.md b/_search-plugins/knn/approximate-knn.md
@@ -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>

diff --git a/_search-plugins/knn/knn-score-script.md b/_search-plugins/knn/knn-score-script.md
@@ -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>