diff --git a/river/anomaly/lof.py b/river/anomaly/lof.py
index 12b4eea44b..ecb54c5f00 100644
--- a/river/anomaly/lof.py
+++ b/river/anomaly/lof.py
@@ -221,7 +221,25 @@ class LocalOutlierFactor(anomaly.base.AnomalyDetector):
     ...     scores.append(lof.score_one(x))
 
     >>> [round(score, 3) for score in scores]
-    [1.802, 1.937, 1.567, 1.181, 1.28]
+    [1.802, 1.936, 1.566, 1.181, 1.272]
+
+    >>> X = [0.5, 0.45, 0.43, 0.44, 0.445, 0.45, 0.0]
+    >>> lof = anomaly.LocalOutlierFactor()
+
+    >>> for x in X[:3]:
+    ...     lof.learn_one({'x': x})  # Warming up
+
+    >>> for x in X:
+    ...     features = {'x': x}
+    ...     print(f'Anomaly score for x={x:.3f}: {lof.score_one(features):.3f}')
+    ...     lof.learn_one(features)
+    Anomaly score for x=0.500: 0.000
+    Anomaly score for x=0.450: 0.000
+    Anomaly score for x=0.430: 0.000
+    Anomaly score for x=0.440: 1.020
+    Anomaly score for x=0.445: 1.032
+    Anomaly score for x=0.450: 0.000
+    Anomaly score for x=0.000: 0.980
 
     References
     ----------
diff --git a/river/anomaly/test_lof.py b/river/anomaly/test_lof.py
index 9703b8cdc9..c4933b0091 100644
--- a/river/anomaly/test_lof.py
+++ b/river/anomaly/test_lof.py
@@ -80,3 +80,33 @@ def test_issue_1328():
     X = [{"a": 1, "b": 1}, {"a": 1, "b": 1}]
     for x in X:
         lof.learn_one(x)
+
+
+def test_issue_1331():
+    import copy
+
+    from river import anomaly
+
+    lof = anomaly.LocalOutlierFactor()
+
+    X = [{"a": 1, "b": 1}, {"a": 1, "b": 1}]
+    for x in X:
+        lof.learn_one(x)
+
+    neighborhoods_ = lof.neighborhoods.copy()
+    rev_neighborhoods = lof.rev_neighborhoods.copy()
+    k_dist_ = lof.k_dist.copy()
+    reach_dist_ = copy.deepcopy(lof.reach_dist)
+    dist_dict_ = copy.deepcopy(lof.dist_dict)
+    local_reach_ = lof.local_reach.copy()
+    lof_ = lof.lof.copy()
+
+    lof.score_one({"a": 0.5, "b": 1})
+
+    assert neighborhoods_ == lof.neighborhoods
+    assert rev_neighborhoods == lof.rev_neighborhoods
+    assert k_dist_ == lof.k_dist
+    assert reach_dist_ == lof.reach_dist
+    assert dist_dict_ == lof.dist_dict
+    assert local_reach_ == lof.local_reach
+    assert lof_ == lof.lof