jeremiedbb
diff --git a/‎doc/whats_new/v1.5.rst
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diff --git a/‎sklearn/cluster/_mean_shift.py
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diff --git a/‎sklearn/cluster/tests/test_mean_shift.py
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@@ -183,6 +183,9 @@ Changelog
 :mod:`sklearn.cluster`
 ......................
 
+- |Fix| The :class:`cluster.MeanShift` class now properly converges for constant data.
+  :pr:`28951` by :user:`Akihiro Kuno <akikuno>`.
+
 - |FIX| Create copy of precomputed sparse matrix within the `fit` method of
   :class:`~cluster.OPTICS` to avoid in-place modification of the sparse matrix.
   :pr:`28491` by :user:`Thanh Lam Dang <lamdang2k>`.
 
@@ -122,7 +122,7 @@ def _mean_shift_single_seed(my_mean, X, nbrs, max_iter):
         my_mean = np.mean(points_within, axis=0)
         # If converged or at max_iter, adds the cluster
         if (
-            np.linalg.norm(my_mean - my_old_mean) < stop_thresh
+            np.linalg.norm(my_mean - my_old_mean) <= stop_thresh
             or completed_iterations == max_iter
         ):
             break
 
@@ -25,6 +25,15 @@
 )
 
 
+def test_convergence_of_1d_constant_data():
+    # Test convergence using 1D constant data
+    # Non-regression test for:
+    # https://github.com/scikit-learn/scikit-learn/issues/28926
+    model = MeanShift()
+    n_iter = model.fit(np.ones(10).reshape(-1, 1)).n_iter_
+    assert n_iter < model.max_iter
+
+
 def test_estimate_bandwidth():
     # Test estimate_bandwidth
     bandwidth = estimate_bandwidth(X, n_samples=200)