diff --git a/metric_learn/constraints.py b/metric_learn/constraints.py
index 17523a46..c4ddcae8 100644
--- a/metric_learn/constraints.py
+++ b/metric_learn/constraints.py
@@ -89,17 +89,6 @@ def chunks(self, num_chunks=100, chunk_size=2, random_state=np.random):
                        (num_chunks, chunk_size))
     return chunks
 
-  @staticmethod
-  def random_subset(all_labels, num_preserved=np.inf, random_state=np.random):
-    """
-    the random state object to be passed must be a numpy random seed
-    """
-    n = len(all_labels)
-    num_ignored = max(0, n - num_preserved)
-    idx = random_state.randint(n, size=num_ignored)
-    partial_labels = np.array(all_labels, copy=True)
-    partial_labels[idx] = -1
-    return Constraints(partial_labels)
 
 def wrap_pairs(X, constraints):
   a = np.array(constraints[0])
@@ -109,4 +98,4 @@ def wrap_pairs(X, constraints):
   constraints = np.vstack((np.column_stack((a, b)), np.column_stack((c, d))))
   y = np.vstack([np.ones((len(a), 1)), - np.ones((len(c), 1))])
   pairs = X[constraints]
-  return pairs, y
\ No newline at end of file
+  return pairs, y
diff --git a/metric_learn/itml.py b/metric_learn/itml.py
index 48e71f56..8a251fe0 100644
--- a/metric_learn/itml.py
+++ b/metric_learn/itml.py
@@ -14,6 +14,7 @@
 """
 
 from __future__ import print_function, absolute_import
+import warnings
 import numpy as np
 from six.moves import xrange
 from sklearn.metrics import pairwise_distances
@@ -172,8 +173,8 @@ class ITML_Supervised(_BaseITML, TransformerMixin):
   """
 
   def __init__(self, gamma=1., max_iter=1000, convergence_threshold=1e-3,
-               num_labeled=np.inf, num_constraints=None, bounds=None, A0=None,
-               verbose=False, preprocessor=None):
+               num_labeled='deprecated', num_constraints=None, bounds=None,
+               A0=None, verbose=False, preprocessor=None):
     """Initialize the supervised version of `ITML`.
 
     `ITML_Supervised` creates pairs of similar sample by taking same class
@@ -186,10 +187,10 @@ def __init__(self, gamma=1., max_iter=1000, convergence_threshold=1e-3,
         value for slack variables
     max_iter : int, optional
     convergence_threshold : float, optional
-    num_labeled : int, optional (default=np.inf)
-        number of labeled points to keep for building pairs. Extra
-        labeled points will be considered unlabeled, and ignored as such.
-        Use np.inf (default) to use all labeled points.
+    num_labeled : Not used
+          .. deprecated:: 0.5.0
+             `num_labeled` was deprecated in version 0.5.0 and will
+             be removed in 0.6.0.
     num_constraints: int, optional
         number of constraints to generate
     bounds : list (pos,neg) pairs, optional
@@ -224,14 +225,17 @@ def fit(self, X, y, random_state=np.random):
     random_state : numpy.random.RandomState, optional
         If provided, controls random number generation.
     """
+    if self.num_labeled != 'deprecated':
+      warnings.warn('"num_labeled" parameter is not used.'
+                    ' It has been deprecated in version 0.5.0 and will be'
+                    'removed in 0.6.0', DeprecationWarning)
     X, y = self._prepare_inputs(X, y, ensure_min_samples=2)
     num_constraints = self.num_constraints
     if num_constraints is None:
       num_classes = len(np.unique(y))
       num_constraints = 20 * num_classes**2
 
-    c = Constraints.random_subset(y, self.num_labeled,
-                                  random_state=random_state)
+    c = Constraints(y)
     pos_neg = c.positive_negative_pairs(num_constraints,
                                         random_state=random_state)
     pairs, y = wrap_pairs(X, pos_neg)
diff --git a/metric_learn/lsml.py b/metric_learn/lsml.py
index 73296b46..9090a431 100644
--- a/metric_learn/lsml.py
+++ b/metric_learn/lsml.py
@@ -8,6 +8,7 @@
 """
 
 from __future__ import print_function, absolute_import, division
+import warnings
 import numpy as np
 import scipy.linalg
 from six.moves import xrange
@@ -172,8 +173,9 @@ class LSML_Supervised(_BaseLSML, TransformerMixin):
       metric (See :meth:`transformer_from_metric`.)
   """
 
-  def __init__(self, tol=1e-3, max_iter=1000, prior=None, num_labeled=np.inf,
-               num_constraints=None, weights=None, verbose=False,
+  def __init__(self, tol=1e-3, max_iter=1000, prior=None,
+               num_labeled='deprecated', num_constraints=None, weights=None,
+               verbose=False,
                preprocessor=None):
     """Initialize the supervised version of `LSML`.
 
@@ -188,10 +190,10 @@ def __init__(self, tol=1e-3, max_iter=1000, prior=None, num_labeled=np.inf,
     max_iter : int, optional
     prior : (d x d) matrix, optional
         guess at a metric [default: covariance(X)]
-    num_labeled : int, optional (default=np.inf)
-        number of labeled points to keep for building quadruplets. Extra
-        labeled points will be considered unlabeled, and ignored as such.
-        Use np.inf (default) to use all labeled points.
+    num_labeled : Not used
+      .. deprecated:: 0.5.0
+         `num_labeled` was deprecated in version 0.5.0 and will
+         be removed in 0.6.0.
     num_constraints: int, optional
         number of constraints to generate
     weights : (m,) array of floats, optional
@@ -222,14 +224,17 @@ def fit(self, X, y, random_state=np.random):
     random_state : numpy.random.RandomState, optional
         If provided, controls random number generation.
     """
+    if self.num_labeled != 'deprecated':
+      warnings.warn('"num_labeled" parameter is not used.'
+                    ' It has been deprecated in version 0.5.0 and will be'
+                    'removed in 0.6.0', DeprecationWarning)
     X, y = self._prepare_inputs(X, y, ensure_min_samples=2)
     num_constraints = self.num_constraints
     if num_constraints is None:
       num_classes = len(np.unique(y))
       num_constraints = 20 * num_classes**2
 
-    c = Constraints.random_subset(y, self.num_labeled,
-                                  random_state=random_state)
+    c = Constraints(y)
     pos_neg = c.positive_negative_pairs(num_constraints, same_length=True,
                                         random_state=random_state)
     return _BaseLSML._fit(self, X[np.column_stack(pos_neg)],
diff --git a/metric_learn/mmc.py b/metric_learn/mmc.py
index 596f085f..6d929d6e 100644
--- a/metric_learn/mmc.py
+++ b/metric_learn/mmc.py
@@ -17,6 +17,7 @@
 """
 
 from __future__ import print_function, absolute_import, division
+import warnings
 import numpy as np
 from six.moves import xrange
 from sklearn.base import TransformerMixin
@@ -389,8 +390,8 @@ class MMC_Supervised(_BaseMMC, TransformerMixin):
   """
 
   def __init__(self, max_iter=100, max_proj=10000, convergence_threshold=1e-6,
-               num_labeled=np.inf, num_constraints=None,
-               A0=None, diagonal=False, diagonal_c=1.0, verbose=False,
+               num_labeled='deprecated', num_constraints=None, A0=None,
+               diagonal=False, diagonal_c=1.0, verbose=False,
                preprocessor=None):
     """Initialize the supervised version of `MMC`.
 
@@ -403,10 +404,10 @@ def __init__(self, max_iter=100, max_proj=10000, convergence_threshold=1e-6,
     max_iter : int, optional
     max_proj : int, optional
     convergence_threshold : float, optional
-    num_labeled : int, optional (default=np.inf)
-        number of labeled points to keep for building pairs. Extra
-        labeled points will be considered unlabeled, and ignored as such.
-        Use np.inf (default) to use all labeled points.
+    num_labeled : Not used
+      .. deprecated:: 0.5.0
+         `num_labeled` was deprecated in version 0.5.0 and will
+         be removed in 0.6.0.
     num_constraints: int, optional
         number of constraints to generate
     A0 : (d x d) matrix, optional
@@ -443,14 +444,17 @@ def fit(self, X, y, random_state=np.random):
     random_state : numpy.random.RandomState, optional
         If provided, controls random number generation.
     """
+    if self.num_labeled != 'deprecated':
+      warnings.warn('"num_labeled" parameter is not used.'
+                    ' It has been deprecated in version 0.5.0 and will be'
+                    'removed in 0.6.0', DeprecationWarning)
     X, y = self._prepare_inputs(X, y, ensure_min_samples=2)
     num_constraints = self.num_constraints
     if num_constraints is None:
       num_classes = len(np.unique(y))
       num_constraints = 20 * num_classes**2
 
-    c = Constraints.random_subset(y, self.num_labeled,
-                                  random_state=random_state)
+    c = Constraints(y)
     pos_neg = c.positive_negative_pairs(num_constraints,
                                         random_state=random_state)
     pairs, y = wrap_pairs(X, pos_neg)
diff --git a/metric_learn/sdml.py b/metric_learn/sdml.py
index 1892d176..b1421736 100644
--- a/metric_learn/sdml.py
+++ b/metric_learn/sdml.py
@@ -9,6 +9,7 @@
 """
 
 from __future__ import absolute_import
+import warnings
 import numpy as np
 from sklearn.base import TransformerMixin
 from sklearn.covariance import graph_lasso
@@ -113,7 +114,7 @@ class SDML_Supervised(_BaseSDML, TransformerMixin):
   """
 
   def __init__(self, balance_param=0.5, sparsity_param=0.01, use_cov=True,
-               num_labeled=np.inf, num_constraints=None, verbose=False,
+               num_labeled='deprecated', num_constraints=None, verbose=False,
                preprocessor=None):
     """Initialize the supervised version of `SDML`.
 
@@ -128,10 +129,10 @@ def __init__(self, balance_param=0.5, sparsity_param=0.01, use_cov=True,
         trade off between optimizer and sparseness (see graph_lasso)
     use_cov : bool, optional
         controls prior matrix, will use the identity if use_cov=False
-    num_labeled : int, optional (default=np.inf)
-        number of labeled points to keep for building pairs. Extra
-        labeled points will be considered unlabeled, and ignored as such.
-        Use np.inf (default) to use all labeled points.
+    num_labeled : Not used
+      .. deprecated:: 0.5.0
+         `num_labeled` was deprecated in version 0.5.0 and will
+         be removed in 0.6.0.
     num_constraints : int, optional
         number of constraints to generate
     verbose : bool, optional
@@ -164,14 +165,17 @@ def fit(self, X, y, random_state=np.random):
     self : object
         Returns the instance.
     """
+    if self.num_labeled != 'deprecated':
+      warnings.warn('"num_labeled" parameter is not used.'
+                    ' It has been deprecated in version 0.5.0 and will be'
+                    'removed in 0.6.0', DeprecationWarning)
     X, y = self._prepare_inputs(X, y, ensure_min_samples=2)
     num_constraints = self.num_constraints
     if num_constraints is None:
       num_classes = len(np.unique(y))
       num_constraints = 20 * num_classes**2
 
-    c = Constraints.random_subset(y, self.num_labeled,
-                                  random_state=random_state)
+    c = Constraints(y)
     pos_neg = c.positive_negative_pairs(num_constraints,
                                         random_state=random_state)
     pairs, y = wrap_pairs(X, pos_neg)
diff --git a/test/metric_learn_test.py b/test/metric_learn_test.py
index 74bc25de..85cfcf77 100644
--- a/test/metric_learn_test.py
+++ b/test/metric_learn_test.py
@@ -57,6 +57,17 @@ def test_iris(self):
     csep = class_separation(lsml.transform(self.iris_points), self.iris_labels)
     self.assertLess(csep, 0.8)  # it's pretty terrible
 
+  def test_deprecation(self):
+    # test that the right deprecation message is thrown.
+    # TODO: remove in v.0.5
+    X = np.array([[0, 0], [0, 1], [2, 0], [2, 1]])
+    y = np.array([1, 0, 1, 0])
+    lsml_supervised = LSML_Supervised(num_labeled=np.inf)
+    msg = ('"num_labeled" parameter is not used.'
+           ' It has been deprecated in version 0.5.0 and will be'
+           'removed in 0.6.0')
+    assert_warns_message(DeprecationWarning, msg, lsml_supervised.fit, X, y)
+
 
 class TestITML(MetricTestCase):
   def test_iris(self):
@@ -66,6 +77,17 @@ def test_iris(self):
     csep = class_separation(itml.transform(self.iris_points), self.iris_labels)
     self.assertLess(csep, 0.2)
 
+  def test_deprecation(self):
+    # test that the right deprecation message is thrown.
+    # TODO: remove in v.0.5
+    X = np.array([[0, 0], [0, 1], [2, 0], [2, 1]])
+    y = np.array([1, 0, 1, 0])
+    itml_supervised = ITML_Supervised(num_labeled=np.inf)
+    msg = ('"num_labeled" parameter is not used.'
+           ' It has been deprecated in version 0.5.0 and will be'
+           'removed in 0.6.0')
+    assert_warns_message(DeprecationWarning, msg, itml_supervised.fit, X, y)
+
 
 class TestLMNN(MetricTestCase):
   def test_iris(self):
@@ -121,6 +143,17 @@ def test_iris(self):
     csep = class_separation(sdml.transform(self.iris_points), self.iris_labels)
     self.assertLess(csep, 0.25)
 
+  def test_deprecation(self):
+    # test that the right deprecation message is thrown.
+    # TODO: remove in v.0.5
+    X = np.array([[0, 0], [0, 1], [2, 0], [2, 1]])
+    y = np.array([1, 0, 1, 0])
+    sdml_supervised = SDML_Supervised(num_labeled=np.inf)
+    msg = ('"num_labeled" parameter is not used.'
+           ' It has been deprecated in version 0.5.0 and will be'
+           'removed in 0.6.0')
+    assert_warns_message(DeprecationWarning, msg, sdml_supervised.fit, X, y)
+
 
 class TestNCA(MetricTestCase):
   def test_iris(self):
@@ -242,6 +275,17 @@ def test_iris(self):
     csep = class_separation(mmc.transform(self.iris_points), self.iris_labels)
     self.assertLess(csep, 0.2)
 
+  def test_deprecation(self):
+    # test that the right deprecation message is thrown.
+    # TODO: remove in v.0.5
+    X = np.array([[0, 0], [0, 1], [2, 0], [2, 1]])
+    y = np.array([1, 0, 1, 0])
+    mmc_supervised = MMC_Supervised(num_labeled=np.inf)
+    msg = ('"num_labeled" parameter is not used.'
+           ' It has been deprecated in version 0.5.0 and will be'
+           'removed in 0.6.0')
+    assert_warns_message(DeprecationWarning, msg, mmc_supervised.fit, X, y)
+
 
 @pytest.mark.parametrize(('algo_class', 'dataset'),
                          [(NCA, make_classification()),
diff --git a/test/test_base_metric.py b/test/test_base_metric.py
index c9c8fb57..fdea2949 100644
--- a/test/test_base_metric.py
+++ b/test/test_base_metric.py
@@ -32,7 +32,7 @@ def test_itml(self):
 """.strip('\n'))
     self.assertEqual(str(metric_learn.ITML_Supervised()), """
 ITML_Supervised(A0=None, bounds=None, convergence_threshold=0.001, gamma=1.0,
-        max_iter=1000, num_constraints=None, num_labeled=inf,
+        max_iter=1000, num_constraints=None, num_labeled='deprecated',
         preprocessor=None, verbose=False)
 """.strip('\n'))
 
@@ -42,7 +42,7 @@ def test_lsml(self):
         "LSML(max_iter=1000, preprocessor=None, prior=None, tol=0.001, "
         "verbose=False)")
     self.assertEqual(str(metric_learn.LSML_Supervised()), """
-LSML_Supervised(max_iter=1000, num_constraints=None, num_labeled=inf,
+LSML_Supervised(max_iter=1000, num_constraints=None, num_labeled='deprecated',
         preprocessor=None, prior=None, tol=0.001, verbose=False,
         weights=None)
 """.strip('\n'))
@@ -52,9 +52,9 @@ def test_sdml(self):
                      "SDML(balance_param=0.5, preprocessor=None, "
                      "sparsity_param=0.01, use_cov=True,\n   verbose=False)")
     self.assertEqual(str(metric_learn.SDML_Supervised()), """
-SDML_Supervised(balance_param=0.5, num_constraints=None, num_labeled=inf,
-        preprocessor=None, sparsity_param=0.01, use_cov=True,
-        verbose=False)
+SDML_Supervised(balance_param=0.5, num_constraints=None,
+        num_labeled='deprecated', preprocessor=None, sparsity_param=0.01,
+        use_cov=True, verbose=False)
 """.strip('\n'))
 
   def test_rca(self):
@@ -78,7 +78,7 @@ def test_mmc(self):
     self.assertEqual(str(metric_learn.MMC_Supervised()), """
 MMC_Supervised(A0=None, convergence_threshold=1e-06, diagonal=False,
         diagonal_c=1.0, max_iter=100, max_proj=10000, num_constraints=None,
-        num_labeled=inf, preprocessor=None, verbose=False)
+        num_labeled='deprecated', preprocessor=None, verbose=False)
 """.strip('\n'))
 
 if __name__ == '__main__':
diff --git a/test/test_utils.py b/test/test_utils.py
index de59e9ff..39c718ac 100644
--- a/test/test_utils.py
+++ b/test/test_utils.py
@@ -58,8 +58,7 @@ def build_data():
   input_data, labels = load_iris(return_X_y=True)
   X, y = shuffle(input_data, labels, random_state=SEED)
   num_constraints = 50
-  constraints = (
-      Constraints.random_subset(y, random_state=check_random_state(SEED)))
+  constraints = Constraints(y)
   pairs = (
       constraints
       .positive_negative_pairs(num_constraints, same_length=True,