From 8a697f741c3690858216e4f8f588b22978e77071 Mon Sep 17 00:00:00 2001
From: Ash Vardanian <1983160+ashvardanian@users.noreply.github.com>
Date: Sun, 31 Mar 2024 20:18:13 +0000
Subject: [PATCH] Improve: Normalize Pearson as distance

---
 include/usearch/index_plugins.hpp | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/include/usearch/index_plugins.hpp b/include/usearch/index_plugins.hpp
index 25ab8ce4..b3ad5edf 100644
--- a/include/usearch/index_plugins.hpp
+++ b/include/usearch/index_plugins.hpp
@@ -1204,7 +1204,9 @@ template <typename scalar_at = float, typename result_at = float> struct metric_
             return 0;
         result_t corr = dim * ab_sum - a_sum * b_sum;
         denom = std::sqrt(denom);
-        return -corr / denom;
+        // The normal Pearson correlation value is between -1 and 1, but we are looking for a distance.
+        // So instead of returning `corr / denom`, we return `1 - corr / denom`.
+        return 1 - corr / denom;
     }
 };