diff --git a/umap/sparse.py b/umap/sparse.py
index dac4e0bb..2c4025f8 100644
--- a/umap/sparse.py
+++ b/umap/sparse.py
@@ -696,8 +696,8 @@ def sparse_correlation(ind1, data1, ind2, data2, n_features):
     for i in range(data2.shape[0]):
         shifted_data2[i] = data2[i] - mu_y
 
-    norm1 = norm(shifted_data1)
-    norm2 = norm(shifted_data2)
+    norm1 = np.sqrt(norm(shifted_data1) ** 2 + (n_features - ind1.shape[0]) * mu_x ** 2)
+    norm2 = np.sqrt(norm(shifted_data2) ** 2 + (n_features - ind2.shape[0]) * mu_y ** 2)
 
     dot_prod_inds, dot_prod_data = sparse_mul(ind1, shifted_data1,
                                               ind2, shifted_data2)
@@ -705,9 +705,22 @@ def sparse_correlation(ind1, data1, ind2, data2, n_features):
     if dot_prod_data.shape[0] == 0:
         return 1.0
 
+    common_indices = set(dot_prod_inds)
+
     for i in range(dot_prod_data.shape[0]):
         dot_product += dot_prod_data[i]
 
+    for i in range(ind1.shape[0]):
+        if ind1[i] not in common_indices:
+            dot_product -= data1[i] * (mu_y)
+
+    for i in range(ind2.shape[0]):
+        if ind2[i] not in common_indices:
+            dot_product -= data2[i] * (mu_x)
+
+    all_indices = arr_union(ind1, ind2)
+    dot_product += mu_x * mu_y * all_indices.shape[0]
+
     if dot_product == 0.0:
         return 1.0
     else: