[MRG] Fix LocalOutlierFactor's output for data with duplicated samples

sklearn/neighbors/_lof.py

@@ -317,6 +317,16 @@ def fit(self, X, y=None):
                 self.negative_outlier_factor_, 100.0 * self.contamination
             )
 
+        """
+        Verify if negative_outlier_factor_ values are within acceptable range
+        Novelty must also be false to detect outliers
+        """
+        if np.min(self.negative_outlier_factor_) < -1e7 and not self.novelty:
+            warnings.warn(
+                "Duplicate values are leading to incorrect results. "
+                "Increase the number of neighbors for more accurate results."
+            )
+
         return self
 
     def _check_novelty_predict(self):

sklearn/neighbors/tests/test_lof.py

@@ -359,3 +359,37 @@ def test_lof_dtype_equivalence(algorithm, novelty, contamination):
             y_pred_32 = getattr(lof_32, method)(X_32)
             y_pred_64 = getattr(lof_64, method)(X_64)
             assert_allclose(y_pred_32, y_pred_64, atol=0.0002)
+
+
+def test_lof_duplicate_samples():
+    """
+    Check that LocalOutlierFactor raises a warning when duplicate values
+    in the training data are causing innacurate results.
+
+    Test for: https://github.com/scikit-learn/scikit-learn/issues/27839
+    """
+
+    rng = np.random.default_rng(0)
+
+    # 100 times the number of elements of the example shown in the issue
+    x = rng.permutation(
+        np.hstack(
+            [
+                [0.1] * 1000,  # constant values
+                np.linspace(0.1, 0.3, num=3000),
+                rng.random(500) * 100,  # the clear outliers
+            ]
+        )
+    )
+    X = x.reshape(-1, 1)
+
+    error_msg = (
+        "Duplicate values are leading to incorrect results. "
+        "Increase the number of neighbors for more accurate results."
+    )
+
+    lof = neighbors.LocalOutlierFactor(n_neighbors=5, contamination=0.1)
+
+    # Catch the warning
+    with pytest.warns(UserWarning, match=re.escape(error_msg)):
+        lof.fit_predict(X)