[BUG] Fix zero-distance instability in Hidalgo (#3068)

aeon/segmentation/_hidalgo.py

@@ -170,7 +170,9 @@ def _get_neighbourhood_params(self, X):
             n_neighbors=q + 1, algorithm="ball_tree", metric=metric
         ).fit(X)
         distances, Iin = nbrs.kneighbors(X)
-        mu = np.divide(distances[:, 2], distances[:, 1])
+        eps = 1e-12
+        # stabilise r2/r1 ratio; protect against zero or near-zero r1
+        mu = np.divide(distances[:, 2], distances[:, 1] + eps)
 
         nbrmat = np.zeros((m, m))
         for n in range(q):

aeon/segmentation/tests/test_hidalgo.py

@@ -1,6 +1,8 @@
 """Test Hidalgo segmenter."""
 
-from aeon.segmentation._hidalgo import _binom, _partition_function
+import numpy as np
+
+from aeon.segmentation._hidalgo import HidalgoSegmenter, _binom, _partition_function
 
 
 def test_partition_function():
@@ -9,3 +11,27 @@ def test_partition_function():
     assert p == 8.0
     b = _binom(10, 2)
     assert b == 45.0
+
+
+def test_hidalgo_zero_distance_duplicate_rows():
+    """Test that Hidalgo handles duplicate rows without numerical errors."""
+    X = np.array(
+        [
+            [1.0, 2.0, 3.0],
+            [1.0, 2.0, 3.0],
+            [4.0, 5.0, 6.0],
+            [7.0, 8.0, 9.0],
+        ]
+    )
+    seg = HidalgoSegmenter(
+        K=2,
+        q=2,
+        n_iter=50,
+        burn_in=0.2,
+        sampling_rate=5,
+        seed=1,
+    )
+    out = seg.fit_predict(X, axis=0)
+    assert out is not None
+    assert isinstance(out, np.ndarray)
+    assert len(out) == len(X)