FIX Using custom init for KMeans does a single init (#26657)

doc/whats_new/v1.3.rst

@@ -231,6 +231,11 @@ Changelog
   :user:`Jérémie du Boisberranger <jeremiedbb>`,
   :user:`Guillaume Lemaitre <glemaitre>`.
 
+- |Fix| :class:`cluster.KMeans`, :class:`cluster.MiniBatchKMeans` and
+  :func:`cluster.k_means` now correctly handle the combination of `n_init="auto"`
+  and `init` being an array-like, running one initialization in that case.
+  :pr:`26657` by :user:`Binesh Bannerjee <bnsh>`.
+
 - |API| The `sample_weight` parameter in `predict` for
   :meth:`cluster.KMeans.predict` and :meth:`cluster.MiniBatchKMeans.predict`
   is now deprecated and will be removed in v1.5.

sklearn/cluster/_kmeans.py

@@ -354,7 +354,8 @@ def k_means(
         n_init consecutive runs in terms of inertia.
 
         When `n_init='auto'`, the number of runs depends on the value of init:
-        10 if using `init='random'`, 1 if using `init='k-means++'`.
+        10 if using `init='random'` or `init` is a callable;
+        1 if using `init='k-means++'` or `init` is an array-like.
 
         .. versionadded:: 1.2
            Added 'auto' option for `n_init`.
@@ -884,10 +885,14 @@ def _check_params_vs_input(self, X, default_n_init=None):
             )
             self._n_init = default_n_init
         if self._n_init == "auto":
-            if self.init == "k-means++":
+            if isinstance(self.init, str) and self.init == "k-means++":
                 self._n_init = 1
-            else:
+            elif isinstance(self.init, str) and self.init == "random":
+                self._n_init = default_n_init
+            elif callable(self.init):
                 self._n_init = default_n_init
+            else:  # array-like
+                self._n_init = 1
 
         if _is_arraylike_not_scalar(self.init) and self._n_init != 1:
             warnings.warn(
@@ -1241,7 +1246,8 @@ class KMeans(_BaseKMeans):
         high-dimensional problems (see :ref:`kmeans_sparse_high_dim`).
 
         When `n_init='auto'`, the number of runs depends on the value of init:
-        10 if using `init='random'`, 1 if using `init='k-means++'`.
+        10 if using `init='random'` or `init` is a callable;
+        1 if using `init='k-means++'` or `init` is an array-like.
 
         .. versionadded:: 1.2
            Added 'auto' option for `n_init`.
@@ -1777,7 +1783,8 @@ class MiniBatchKMeans(_BaseKMeans):
         :ref:`kmeans_sparse_high_dim`).
 
         When `n_init='auto'`, the number of runs depends on the value of init:
-        3 if using `init='random'`, 1 if using `init='k-means++'`.
+        3 if using `init='random'` or `init` is a callable;
+        1 if using `init='k-means++'` or `init` is an array-like.
 
         .. versionadded:: 1.2
            Added 'auto' option for `n_init`.

sklearn/cluster/tests/test_k_means.py

@@ -348,6 +348,37 @@ def test_minibatch_kmeans_partial_fit_init(init):
     _check_fitted_model(km)
 
 
+@pytest.mark.parametrize(
+    "init, expected_n_init",
+    [
+        ("k-means++", 1),
+        ("random", "default"),
+        (
+            lambda X, n_clusters, random_state: random_state.uniform(
+                size=(n_clusters, X.shape[1])
+            ),
+            "default",
+        ),
+        ("array-like", 1),
+    ],
+)
+@pytest.mark.parametrize("Estimator", [KMeans, MiniBatchKMeans])
+def test_kmeans_init_auto_with_initial_centroids(Estimator, init, expected_n_init):
+    """Check that `n_init="auto"` chooses the right number of initializations.
+    Non-regression test for #26657:
+    https://github.com/scikit-learn/scikit-learn/pull/26657
+    """
+    n_sample, n_features, n_clusters = 100, 10, 5
+    X = np.random.randn(n_sample, n_features)
+    if init == "array-like":
+        init = np.random.randn(n_clusters, n_features)
+    if expected_n_init == "default":
+        expected_n_init = 3 if Estimator is MiniBatchKMeans else 10
+
+    kmeans = Estimator(n_clusters=n_clusters, init=init, n_init="auto").fit(X)
+    assert kmeans._n_init == expected_n_init
+
+
 @pytest.mark.parametrize("Estimator", [KMeans, MiniBatchKMeans])
 def test_fortran_aligned_data(Estimator, global_random_seed):
     # Check that KMeans works with fortran-aligned data.