diff --git a/alibi/explainers/tests/test_shap_wrappers.py b/alibi/explainers/tests/test_shap_wrappers.py
index 7a517be7a..95f2b484b 100644
--- a/alibi/explainers/tests/test_shap_wrappers.py
+++ b/alibi/explainers/tests/test_shap_wrappers.py
@@ -742,10 +742,10 @@ def test__summarise_background_kernel(caplog,
         msg = "Received option to summarise the data but the background_data object was an " \
               "instance of shap_utils.Data"
         assert_message_in_logs(msg, caplog.records)
-        assert type(background_data) == type(summary_data)
+        assert type(background_data) == type(summary_data)  # noqa: E721
     else:
         if use_groups or categorical_names:
-            assert type(background_data) == type(summary_data)
+            assert type(background_data) == type(summary_data)  # noqa: E721
             if data_type == 'series':
                 assert summary_data.shape == background_data.shape
             else:
@@ -1181,14 +1181,14 @@ def test__summarise_background_tree(mock_tree_shap_explainer, data_dimension, da
     assert explainer.summarise_background
     if n_background_samples > n_instances:
         if categorical_names:
-            assert type(background_data) == type(summary_data)
+            assert type(background_data) == type(summary_data)  # noqa: E721
         else:
             assert isinstance(summary_data, shap_utils.Data)
             assert summary_data.data.shape == background_data.shape
     else:
         if categorical_names:
             assert summary_data.shape[0] == n_background_samples
-            assert type(background_data) == type(summary_data)
+            assert type(background_data) == type(summary_data)  # noqa: E721
         else:
             assert summary_data.data.shape[0] == n_background_samples
             assert isinstance(summary_data, shap_utils.Data)
diff --git a/alibi/utils/distance.py b/alibi/utils/distance.py
index 21f7d73dc..d050915c6 100644
--- a/alibi/utils/distance.py
+++ b/alibi/utils/distance.py
@@ -299,7 +299,7 @@ def batch_compute_kernel_matrix(x: Union[list, np.ndarray],
     -------
     Kernel matrix in the form of a `numpy` array.
     """
-    if type(x) != type(y):
+    if type(x) != type(y):  # noqa: E721
         raise ValueError("x and y should be of the same type")
 
     n_x, n_y = len(x), len(y)
diff --git a/alibi/utils/mapping.py b/alibi/utils/mapping.py
index 047a27024..d689b029b 100644
--- a/alibi/utils/mapping.py
+++ b/alibi/utils/mapping.py
@@ -52,7 +52,7 @@ def ord_to_num(data: np.ndarray, dist: dict) -> np.ndarray:
     for k, v in dist.items():
         cat_col = X[:, k].copy()
         cat_col = np.array([v[int(cat_col[i])] for i in range(rng)])
-        if type(X) == np.matrix:
+        if isinstance(X, np.matrix):
             X[:, k] = cat_col.reshape(-1, 1)
         else:
             X[:, k] = cat_col