diff --git a/sklearn/manifold/_locally_linear.py b/sklearn/manifold/_locally_linear.py
index a1c70950a9fd0..1c4d79feefdec 100644
--- a/sklearn/manifold/_locally_linear.py
+++ b/sklearn/manifold/_locally_linear.py
@@ -42,7 +42,7 @@ def barycenter_weights(X, Y, indices, reg=1e-3):
             Indices of the points in Y used to compute the barycenter
 
     reg : float, default=1e-3
-        amount of regularization to add for the problem to be
+        Amount of regularization to add for the problem to be
         well-posed in the case of n_neighbors > n_dim
 
     Returns
@@ -224,13 +224,13 @@ def locally_linear_embedding(
         numpy array or a NearestNeighbors object.
 
     n_neighbors : int
-        number of neighbors to consider for each point.
+        Number of neighbors to consider for each point.
 
     n_components : int
-        number of coordinates for the manifold.
+        Number of coordinates for the manifold.
 
     reg : float, default=1e-3
-        regularization constant, multiplies the trace of the local covariance
+        Regularization constant, multiplies the trace of the local covariance
         matrix of the distances.
 
     eigen_solver : {'auto', 'arpack', 'dense'}, default='auto'
@@ -252,7 +252,7 @@ def locally_linear_embedding(
         Not used if eigen_solver=='dense'.
 
     max_iter : int, default=100
-        maximum number of iterations for the arpack solver.
+        Maximum number of iterations for the arpack solver.
 
     method : {'standard', 'hessian', 'modified', 'ltsa'}, default='standard'
         standard : use the standard locally linear embedding algorithm.
@@ -267,11 +267,11 @@ def locally_linear_embedding(
 
     hessian_tol : float, default=1e-4
         Tolerance for Hessian eigenmapping method.
-        Only used if method == 'hessian'
+        Only used if method == 'hessian'.
 
     modified_tol : float, default=1e-12
         Tolerance for modified LLE method.
-        Only used if method == 'modified'
+        Only used if method == 'modified'.
 
     random_state : int, RandomState instance, default=None
         Determines the random number generator when ``solver`` == 'arpack'.
diff --git a/sklearn/tests/test_docstrings.py b/sklearn/tests/test_docstrings.py
index e522e6b904b3b..b106ab30bceff 100644
--- a/sklearn/tests/test_docstrings.py
+++ b/sklearn/tests/test_docstrings.py
@@ -15,7 +15,6 @@
     "sklearn.decomposition._dict_learning.dict_learning",
     "sklearn.externals._packaging.version.parse",
     "sklearn.inspection._plot.partial_dependence.plot_partial_dependence",
-    "sklearn.manifold._locally_linear.locally_linear_embedding",
     "sklearn.manifold._t_sne.trustworthiness",
     "sklearn.metrics._plot.det_curve.plot_det_curve",
     "sklearn.metrics._plot.precision_recall_curve.plot_precision_recall_curve",