diff --git a/sklearn/utils/estimator_checks.py b/sklearn/utils/estimator_checks.py
index c2c01caf68e2e..337bbc20b3928 100644
--- a/sklearn/utils/estimator_checks.py
+++ b/sklearn/utils/estimator_checks.py
@@ -103,7 +103,7 @@ def _yield_non_meta_checks(name, Estimator):
         yield check_sparsify_coefficients
 
     yield check_estimator_sparse_data
-
+    yield check_estimator_sparse_dense
     # Test that estimators can be pickled, and once pickled
     # give the same answer as before.
     yield check_estimators_pickle
@@ -312,6 +312,11 @@ def set_testing_parameters(estimator):
         if not isinstance(estimator, ProjectedGradientNMF):
             estimator.set_params(solver='cd')
 
+    if "KNeighbors" in estimator.__class__.__name__ :
+        # Override the default 'auto' for sparse dense equivalence
+        # since only 'brute' algo is used for sparse see #1572
+        estimator.set_params(algorithm='brute')
+
 
 class NotAnArray(object):
     " An object that is convertable to an array"
@@ -344,6 +349,7 @@ def check_estimator_sparse_data(name, Estimator):
                 estimator = Estimator()
         set_testing_parameters(estimator)
         # fit and predict
+
         try:
             with ignore_warnings(category=DeprecationWarning):
                 estimator.fit(X, y)
@@ -1554,3 +1560,52 @@ def check_classifiers_regression_target(name, Estimator):
     e = Estimator()
     msg = 'Unknown label type: '
     assert_raises_regex(ValueError, msg, e.fit, X, y)
+
+
+def check_estimator_sparse_dense(name, Estimator):
+    rng = np.random.RandomState(0)
+    X = rng.rand(40, 10)
+    X[X < .8] = 0
+    X_csr = sparse.csr_matrix(X)
+    y = (4 * rng.rand(40)).astype(np.int)
+    for sparse_format in ['csr', 'csc', 'dok', 'lil', 'coo', 'dia', 'bsr']:
+        X_sp = X_csr.asformat(sparse_format)
+        # catch deprecation warnings
+        with ignore_warnings(category=DeprecationWarning):
+            if name in ['Scaler', 'StandardScaler']:
+                estimator = Estimator(with_mean=False)
+                estimator_sp = Estimator(with_mean=False)
+            else:
+                estimator = Estimator()
+                estimator_sp = Estimator()
+        set_testing_parameters(estimator)
+        set_testing_parameters(estimator_sp)
+        set_random_state(estimator)
+        set_random_state(estimator_sp)
+        #print(np.where(X!=X_sp.toarray()))
+        # fit and predict
+        try:
+            with ignore_warnings(category=DeprecationWarning):
+                estimator_sp.fit(X_sp, y)
+                estimator.fit(X, y)
+            if hasattr(estimator, "predict"):
+                pred = estimator.predict(X)
+                pred_sp = estimator_sp.predict(X_sp)
+                assert_array_almost_equal(pred, pred_sp, 2)
+                assert_equal(pred.shape, pred_sp.shape)
+            if hasattr(estimator, 'predict_proba'):
+                probs = estimator.predict_proba(X)
+                assert_equal(probs.shape, (X.shape[0], 4))
+        except TypeError as e:
+            if 'sparse' not in repr(e):
+                print("Estimator %s doesn't seem to fail gracefully on "
+                      "sparse data: error message state explicitly that "
+                      "sparse input is not supported if this is not the case."
+                      % name)
+                raise
+        except Exception:
+            print("Estimator %s doesn't seem to fail gracefully on "
+                  "sparse data: it should raise a TypeError if sparse input "
+                  "is explicitly not supported." % name)
+            raise
+