diff --git a/sklearn/base.py b/sklearn/base.py
index e438ef534..ff0d2818b 100644
--- a/sklearn/base.py
+++ b/sklearn/base.py
@@ -45,10 +45,10 @@ def clone(estimator, safe=True):
 
     Parameters
     ----------
-    estimator : estimator object, or list, tuple or set of objects
-        The estimator or group of estimators to be cloned
+    estimator : {list, tuple, set} of estimator object or estimator object
+        The estimator or group of estimators to be cloned.
 
-    safe : boolean, default=True
+    safe : bool, default=True
         If safe is false, clone will fall back to a deep copy on objects
         that are not estimators.
 
@@ -429,7 +429,8 @@ class ClusterMixin:
 
         Parameters
         ----------
-        X : ndarray, shape (n_samples, n_features)
+        X : {array-like, sparse matrix, dataframe} of shape \
+                (n_samples, n_features)
             Input data.
 
         y : Ignored
@@ -437,7 +438,7 @@ class ClusterMixin:
 
         Returns
         -------
-        labels : ndarray, shape (n_samples,)
+        labels : ndarray of shape (n_samples,)
             Cluster labels.
         """
         # non-optimized default implementation; override when a better
@@ -469,9 +470,9 @@ class BiclusterMixin:
 
         Returns
         -------
-        row_ind : np.array, dtype=np.intp
+        row_ind : ndarray, dtype=np.intp
             Indices of rows in the dataset that belong to the bicluster.
-        col_ind : np.array, dtype=np.intp
+        col_ind : ndarray, dtype=np.intp
             Indices of columns in the dataset that belong to the bicluster.
 
         """
@@ -489,7 +490,7 @@ class BiclusterMixin:
 
         Returns
         -------
-        shape : (int, int)
+        shape : tuple (int, int)
             Number of rows and columns (resp.) in the bicluster.
         """
         indices = self.get_indices(i)
@@ -533,10 +534,11 @@ class TransformerMixin:
 
         Parameters
         ----------
-        X : numpy array of shape [n_samples, n_features]
+        X : {array-like, sparse matrix, dataframe} of shape \
+                (n_samples, n_features)
             Training set.
 
-        y : numpy array of shape [n_samples], default=None
+        y : array-like of shape (n_samples,), default=None
             Target values.
 
         **fit_params : dict
@@ -544,7 +546,7 @@ class TransformerMixin:
 
         Returns
         -------
-        X_new : numpy array of shape [n_samples, n_features_new]
+        X_new : ndarray of shape (n_samples, n_features_new)
             Transformed array.
         """
         # non-optimized default implementation; override when a better
@@ -586,7 +588,8 @@ class OutlierMixin:
 
         Parameters
         ----------
-        X : ndarray, shape (n_samples, n_features)
+        X : {array-like, sparse matrix, dataframe} of shape \
+                (n_samples, n_features)
             Input data.
 
         y : Ignored
@@ -594,7 +597,7 @@ class OutlierMixin:
 
         Returns
         -------
-        y : ndarray, shape (n_samples,)
+        y : ndarray of shape (n_samples,)
             1 for inliers, -1 for outliers.
         """
         # override for transductive outlier detectors like LocalOulierFactor
diff --git a/sklearn/cluster/_birch.py b/sklearn/cluster/_birch.py
index d160d581e..48266a70c 100644
--- a/sklearn/cluster/_birch.py
+++ b/sklearn/cluster/_birch.py
@@ -108,28 +108,28 @@ class _CFNode:
 
     Attributes
     ----------
-    subclusters_ : array-like
-        list of subclusters for a particular CFNode.
+    subclusters_ : list
+        List of subclusters for a particular CFNode.
 
     prev_leaf_ : _CFNode
-        prev_leaf. Useful only if is_leaf is True.
+        Useful only if is_leaf is True.
 
     next_leaf_ : _CFNode
-        next_leaf. Useful only if is_leaf is True.
+        Useful only if is_leaf is True.
         the final subclusters.
 
-    init_centroids_ : ndarray, shape (branching_factor + 1, n_features)
-        manipulate ``init_centroids_`` throughout rather than centroids_ since
+    init_centroids_ : ndarray of shape (branching_factor + 1, n_features)
+        Manipulate ``init_centroids_`` throughout rather than centroids_ since
         the centroids are just a view of the ``init_centroids_`` .
 
-    init_sq_norm_ : ndarray, shape (branching_factor + 1,)
+    init_sq_norm_ : ndarray of shape (branching_factor + 1,)
         manipulate init_sq_norm_ throughout. similar to ``init_centroids_``.
 
-    centroids_ : ndarray
-        view of ``init_centroids_``.
+    centroids_ : ndarray of shape (branching_factor + 1, n_features)
+        View of ``init_centroids_``.
 
-    squared_norm_ : ndarray
-        view of ``init_sq_norm_``.
+    squared_norm_ : ndarray of shape (branching_factor + 1,)
+        View of ``init_sq_norm_``.
 
     """
     def __init__(self, threshold, branching_factor, is_leaf, n_features):
@@ -245,7 +245,7 @@ class _CFSubcluster:
 
     Parameters
     ----------
-    linear_sum : ndarray, shape (n_features,), default=None
+    linear_sum : ndarray of shape (n_features,), default=None
         Sample. This is kept optional to allow initialization of empty
         subclusters.
 
@@ -261,7 +261,7 @@ class _CFSubcluster:
     squared_sum_ : float
         Sum of the squared l2 norms of all samples belonging to a subcluster.
 
-    centroid_ : ndarray
+    centroid_ : ndarray of shape (branching_factor + 1, n_features)
         Centroid of the subcluster. Prevent recomputing of centroids when
         ``CFNode.centroids_`` is called.
 
@@ -269,7 +269,7 @@ class _CFSubcluster:
         Child Node of the subcluster. Once a given _CFNode is set as the child
         of the _CFNode, it is set to ``self.child_``.
 
-    sq_norm_ : ndarray
+    sq_norm_ : ndarray of shape (branching_factor + 1,)
         Squared norm of the subcluster. Used to prevent recomputing when
         pairwise minimum distances are computed.
     """
@@ -376,14 +376,14 @@ class Birch(ClusterMixin, TransformerMixin, BaseEstimator):
     dummy_leaf_ : _CFNode
         Start pointer to all the leaves.
 
-    subcluster_centers_ : ndarray,
+    subcluster_centers_ : ndarray
         Centroids of all subclusters read directly from the leaves.
 
-    subcluster_labels_ : ndarray,
+    subcluster_labels_ : ndarray
         Labels assigned to the centroids of the subclusters after
         they are clustered globally.
 
-    labels_ : ndarray, shape (n_samples,)
+    labels_ : ndarray of shape (n_samples,)
         Array of labels assigned to the input data.
         if partial_fit is used instead of fit, they are assigned to the
         last batch of data.
@@ -444,7 +444,7 @@ class Birch(ClusterMixin, TransformerMixin, BaseEstimator):
 
         Parameters
         ----------
-        X : {array-like, sparse matrix}, shape (n_samples, n_features)
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
             Input data.
 
         y : Ignored
@@ -515,7 +515,7 @@ class Birch(ClusterMixin, TransformerMixin, BaseEstimator):
 
         Returns
         -------
-        leaves : array-like
+        leaves : list of shape (n_leaves,)
             List of the leaf nodes.
         """
         leaf_ptr = self.dummy_leaf_.next_leaf_
@@ -531,7 +531,8 @@ class Birch(ClusterMixin, TransformerMixin, BaseEstimator):
 
         Parameters
         ----------
-        X : {array-like, sparse matrix}, shape (n_samples, n_features), None
+        X : {array-like, sparse matrix} of shape (n_samples, n_features), \
+                default=None
             Input data. If X is not provided, only the global clustering
             step is done.
 
@@ -569,12 +570,12 @@ class Birch(ClusterMixin, TransformerMixin, BaseEstimator):
 
         Parameters
         ----------
-        X : {array-like, sparse matrix}, shape (n_samples, n_features)
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
             Input data.
 
         Returns
         -------
-        labels : ndarray, shape(n_samples)
+        labels : ndarray of shape (n_samples,)
             Labelled data.
         """
         X = check_array(X, accept_sparse='csr')
@@ -593,12 +594,12 @@ class Birch(ClusterMixin, TransformerMixin, BaseEstimator):
 
         Parameters
         ----------
-        X : {array-like, sparse matrix}, shape (n_samples, n_features)
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
             Input data.
 
         Returns
         -------
-        X_trans : {array-like, sparse matrix}, shape (n_samples, n_clusters)
+        X_trans : {array-like, sparse matrix} of shape (n_samples, n_clusters)
             Transformed data.
         """
         check_is_fitted(self)