From e5cd4f0c520f4558855668134ed1d656280e03f6 Mon Sep 17 00:00:00 2001
From: Christian Jorgensen <cajorgensen@wisc.edu>
Date: Tue, 16 Sep 2025 12:50:02 -0500
Subject: [PATCH 01/11] Adding standardscaler calls

---
 src/skmatter/decomposition/_kernel_pcovc.py |  9 +++++++++
 src/skmatter/decomposition/_pcovc.py        | 10 ++++++++++
 2 files changed, 19 insertions(+)

diff --git a/src/skmatter/decomposition/_kernel_pcovc.py b/src/skmatter/decomposition/_kernel_pcovc.py
index e8965a223..bc46e9326 100644
--- a/src/skmatter/decomposition/_kernel_pcovc.py
+++ b/src/skmatter/decomposition/_kernel_pcovc.py
@@ -15,6 +15,7 @@
 from sklearn.utils.validation import check_is_fitted, validate_data
 from sklearn.linear_model._base import LinearClassifierMixin
 from sklearn.utils.multiclass import check_classification_targets, type_of_target
+from sklearn.preprocessing import StandardScaler
 
 from skmatter.preprocessing import KernelNormalizer
 from skmatter.utils import check_cl_fit
@@ -85,6 +86,10 @@ class KernelPCovC(LinearClassifierMixin, _BaseKPCov):
         If a pre-fitted classifier is provided, it is used to compute :math:`{\mathbf{Z}}`.
         If None, ``sklearn.linear_model.LogisticRegression()``
         is used as the classifier.
+    
+    scale_z: boolean, default=True
+        whether to scale Z to zero mean and unit variance prior to
+        eigendecomposition.
 
     kernel : {"linear", "poly", "rbf", "sigmoid", "precomputed"} or callable, default="linear"
         Kernel.
@@ -200,6 +205,7 @@ def __init__(
         n_components=None,
         svd_solver="auto",
         classifier=None,
+        scale_z=True,
         kernel="linear",
         gamma=None,
         degree=3,
@@ -229,6 +235,7 @@ def __init__(
             fit_inverse_transform=fit_inverse_transform,
         )
         self.classifier = classifier
+        self.scale_z = scale_z
 
     def fit(self, X, Y, W=None):
         r"""Fit the model with X and Y.
@@ -323,6 +330,8 @@ def fit(self, X, Y, W=None):
                 W = LogisticRegression().fit(K, Y).coef_.T
 
         Z = K @ W
+        if self.scale_z:
+            Z = StandardScaler().fit_transform(Z)
 
         self._fit(K, Z, W)
 
diff --git a/src/skmatter/decomposition/_pcovc.py b/src/skmatter/decomposition/_pcovc.py
index e0cee034e..7473b12b7 100644
--- a/src/skmatter/decomposition/_pcovc.py
+++ b/src/skmatter/decomposition/_pcovc.py
@@ -16,6 +16,7 @@
 from sklearn.utils.validation import check_is_fitted, validate_data
 from skmatter.decomposition import _BasePCov
 from skmatter.utils import check_cl_fit
+from sklearn.preprocessing import StandardScaler
 
 
 class PCovC(LinearClassifierMixin, _BasePCov):
@@ -122,6 +123,10 @@ class PCovC(LinearClassifierMixin, _BasePCov):
         training data as the composite estimator.
         If None, ``sklearn.linear_model.LogisticRegression()``
         is used as the classifier.
+    
+    scale_z: boolean, default=True
+        whether to scale Z to zero mean and unit variance prior to
+        eigendecomposition.
 
     iterated_power : int or 'auto', default='auto'
         Number of iterations for the power method computed by
@@ -210,9 +215,11 @@ def __init__(
         tol=1e-12,
         space="auto",
         classifier=None,
+        scale_z=True,
         iterated_power="auto",
         random_state=None,
         whiten=False,
+        
     ):
         super().__init__(
             mixing=mixing,
@@ -225,6 +232,7 @@ def __init__(
             whiten=whiten,
         )
         self.classifier = classifier
+        self.scale_z = scale_z
 
     def fit(self, X, Y, W=None):
         r"""Fit the model with X and Y.
@@ -300,6 +308,8 @@ def fit(self, X, Y, W=None):
                 W = LogisticRegression().fit(X, Y).coef_.T
 
         Z = X @ W
+        if self.scale_z:
+            Z = StandardScaler().fit_transform(Z)
 
         if self.space_ == "feature":
             self._fit_feature_space(X, Y, Z)

From 6272caee6d1a32bc15c2abd6a6ded55a0be7122e Mon Sep 17 00:00:00 2001
From: Christian Jorgensen <cajorgensen@wisc.edu>
Date: Thu, 18 Sep 2025 10:35:46 -0500
Subject: [PATCH 02/11] Fixing sample space pcovc scaling

---
 src/skmatter/decomposition/_pcovc.py | 7 +++++--
 tests/test_pcovc.py                  | 2 ++
 2 files changed, 7 insertions(+), 2 deletions(-)

diff --git a/src/skmatter/decomposition/_pcovc.py b/src/skmatter/decomposition/_pcovc.py
index 7473b12b7..551589f5d 100644
--- a/src/skmatter/decomposition/_pcovc.py
+++ b/src/skmatter/decomposition/_pcovc.py
@@ -299,7 +299,7 @@ def fit(self, X, Y, W=None):
                 classifier = self.classifier
 
             self.z_classifier_ = check_cl_fit(classifier, X, Y)
-            W = self.z_classifier_.coef_.T
+            W = self.z_classifier_.coef_.T.copy()
 
         else:
             # If precomputed, use default classifier to predict Y from T
@@ -308,8 +308,11 @@ def fit(self, X, Y, W=None):
                 W = LogisticRegression().fit(X, Y).coef_.T
 
         Z = X @ W
+
         if self.scale_z:
-            Z = StandardScaler().fit_transform(Z)
+            z_scaler = StandardScaler().fit(Z)
+            Z = z_scaler.transform(Z)
+            W /= np.sqrt(z_scaler.var_).reshape(1, -1)
 
         if self.space_ == "feature":
             self._fit_feature_space(X, Y, Z)
diff --git a/tests/test_pcovc.py b/tests/test_pcovc.py
index 8607a2e2a..b476e80e8 100644
--- a/tests/test_pcovc.py
+++ b/tests/test_pcovc.py
@@ -464,6 +464,8 @@ def test_default_ncomponents(self):
         self.assertEqual(pcovc.n_components_, min(self.X.shape))
 
     def test_prefit_classifier(self):
+        """Check that a passed prefit classifier is not modified in
+        PCovC's `fit` call."""
         classifier = LinearSVC()
         classifier.fit(self.X, self.Y)
         pcovc = self.model(mixing=0.5, classifier=classifier)

From d0dace417676aebc183694e94ee6f66900a18925 Mon Sep 17 00:00:00 2001
From: Christian Jorgensen <cajorgensen@wisc.edu>
Date: Thu, 18 Sep 2025 10:42:54 -0500
Subject: [PATCH 03/11] Adjusting some params in the examples

---
 examples/pcovc/KPCovC_Comparison.py      | 2 +-
 examples/pcovc/KPCovC_Hyperparameters.py | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/examples/pcovc/KPCovC_Comparison.py b/examples/pcovc/KPCovC_Comparison.py
index 5028a9b5c..0811224a2 100644
--- a/examples/pcovc/KPCovC_Comparison.py
+++ b/examples/pcovc/KPCovC_Comparison.py
@@ -85,7 +85,7 @@
 # Both PCA and PCovC fail to produce linearly separable latent space
 # maps. We will need a kernel method to effectively separate the moon classes.
 
-mixing = 0.10
+mixing = 0.5
 alpha_d = 0.5
 alpha_p = 0.4
 
diff --git a/examples/pcovc/KPCovC_Hyperparameters.py b/examples/pcovc/KPCovC_Hyperparameters.py
index ce3948e25..3b02cab62 100644
--- a/examples/pcovc/KPCovC_Hyperparameters.py
+++ b/examples/pcovc/KPCovC_Hyperparameters.py
@@ -65,7 +65,7 @@
 fig, axs = plt.subplots(2, len(kernels), figsize=(len(kernels) * 4, 8))
 
 center = True
-mixing = 0.10
+mixing = 0.5
 
 for i, kernel in enumerate(kernels):
     kpca = KernelPCA(

From 858f6a2feb5ce00736a860c32bf415eba3ac4f66 Mon Sep 17 00:00:00 2001
From: Christian Jorgensen <cajorgensen@wisc.edu>
Date: Thu, 18 Sep 2025 13:01:55 -0500
Subject: [PATCH 04/11] oops wrong scaler

---
 src/skmatter/decomposition/_kernel_pcovc.py | 5 ++---
 src/skmatter/decomposition/_pcovc.py        | 6 +++---
 2 files changed, 5 insertions(+), 6 deletions(-)

diff --git a/src/skmatter/decomposition/_kernel_pcovc.py b/src/skmatter/decomposition/_kernel_pcovc.py
index bc46e9326..46f789057 100644
--- a/src/skmatter/decomposition/_kernel_pcovc.py
+++ b/src/skmatter/decomposition/_kernel_pcovc.py
@@ -15,9 +15,8 @@
 from sklearn.utils.validation import check_is_fitted, validate_data
 from sklearn.linear_model._base import LinearClassifierMixin
 from sklearn.utils.multiclass import check_classification_targets, type_of_target
-from sklearn.preprocessing import StandardScaler
 
-from skmatter.preprocessing import KernelNormalizer
+from skmatter.preprocessing import KernelNormalizer, StandardFlexibleScaler
 from skmatter.utils import check_cl_fit
 from skmatter.decomposition import _BaseKPCov
 
@@ -331,7 +330,7 @@ def fit(self, X, Y, W=None):
 
         Z = K @ W
         if self.scale_z:
-            Z = StandardScaler().fit_transform(Z)
+            Z = StandardFlexibleScaler().fit_transform(Z)
 
         self._fit(K, Z, W)
 
diff --git a/src/skmatter/decomposition/_pcovc.py b/src/skmatter/decomposition/_pcovc.py
index 551589f5d..74197bd37 100644
--- a/src/skmatter/decomposition/_pcovc.py
+++ b/src/skmatter/decomposition/_pcovc.py
@@ -16,7 +16,7 @@
 from sklearn.utils.validation import check_is_fitted, validate_data
 from skmatter.decomposition import _BasePCov
 from skmatter.utils import check_cl_fit
-from sklearn.preprocessing import StandardScaler
+from skmatter.preprocessing import StandardFlexibleScaler
 
 
 class PCovC(LinearClassifierMixin, _BasePCov):
@@ -310,9 +310,9 @@ def fit(self, X, Y, W=None):
         Z = X @ W
 
         if self.scale_z:
-            z_scaler = StandardScaler().fit(Z)
+            z_scaler = StandardFlexibleScaler().fit(Z)
             Z = z_scaler.transform(Z)
-            W /= np.sqrt(z_scaler.var_).reshape(1, -1)
+            W /= z_scaler.scale_.reshape(1, -1)
 
         if self.space_ == "feature":
             self._fit_feature_space(X, Y, Z)

From 03618738e3e1770cb32bdc4767a9e20ec11f1762 Mon Sep 17 00:00:00 2001
From: Christian Jorgensen <cajorgensen@wisc.edu>
Date: Thu, 18 Sep 2025 13:19:36 -0500
Subject: [PATCH 05/11] Touch up docs

---
 src/skmatter/decomposition/_kernel_pcovc.py | 2 +-
 src/skmatter/decomposition/_pcovc.py        | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/skmatter/decomposition/_kernel_pcovc.py b/src/skmatter/decomposition/_kernel_pcovc.py
index 46f789057..4e364677a 100644
--- a/src/skmatter/decomposition/_kernel_pcovc.py
+++ b/src/skmatter/decomposition/_kernel_pcovc.py
@@ -86,7 +86,7 @@ class KernelPCovC(LinearClassifierMixin, _BaseKPCov):
         If None, ``sklearn.linear_model.LogisticRegression()``
         is used as the classifier.
     
-    scale_z: boolean, default=True
+    scale_z: bool, default=True
         whether to scale Z to zero mean and unit variance prior to
         eigendecomposition.
 
diff --git a/src/skmatter/decomposition/_pcovc.py b/src/skmatter/decomposition/_pcovc.py
index 74197bd37..37ab98e09 100644
--- a/src/skmatter/decomposition/_pcovc.py
+++ b/src/skmatter/decomposition/_pcovc.py
@@ -124,7 +124,7 @@ class PCovC(LinearClassifierMixin, _BasePCov):
         If None, ``sklearn.linear_model.LogisticRegression()``
         is used as the classifier.
     
-    scale_z: boolean, default=True
+    scale_z: bool, default=True
         whether to scale Z to zero mean and unit variance prior to
         eigendecomposition.
 

From 3f00c562bdf208bb80c0a9831ceba675299f481d Mon Sep 17 00:00:00 2001
From: Christian Jorgensen <cajorgensen@wisc.edu>
Date: Thu, 18 Sep 2025 13:21:34 -0500
Subject: [PATCH 06/11] Fix docs again

---
 src/skmatter/decomposition/_kernel_pcovc.py | 5 ++---
 src/skmatter/decomposition/_pcovc.py        | 6 ++----
 tests/test_pcovc.py                         | 3 ++-
 3 files changed, 6 insertions(+), 8 deletions(-)

diff --git a/src/skmatter/decomposition/_kernel_pcovc.py b/src/skmatter/decomposition/_kernel_pcovc.py
index 4e364677a..c7a95fa26 100644
--- a/src/skmatter/decomposition/_kernel_pcovc.py
+++ b/src/skmatter/decomposition/_kernel_pcovc.py
@@ -85,10 +85,9 @@ class KernelPCovC(LinearClassifierMixin, _BaseKPCov):
         If a pre-fitted classifier is provided, it is used to compute :math:`{\mathbf{Z}}`.
         If None, ``sklearn.linear_model.LogisticRegression()``
         is used as the classifier.
-    
+
     scale_z: bool, default=True
-        whether to scale Z to zero mean and unit variance prior to
-        eigendecomposition.
+        whether to scale Z prior to eigendecomposition.
 
     kernel : {"linear", "poly", "rbf", "sigmoid", "precomputed"} or callable, default="linear"
         Kernel.
diff --git a/src/skmatter/decomposition/_pcovc.py b/src/skmatter/decomposition/_pcovc.py
index 37ab98e09..9b1660894 100644
--- a/src/skmatter/decomposition/_pcovc.py
+++ b/src/skmatter/decomposition/_pcovc.py
@@ -123,10 +123,9 @@ class PCovC(LinearClassifierMixin, _BasePCov):
         training data as the composite estimator.
         If None, ``sklearn.linear_model.LogisticRegression()``
         is used as the classifier.
-    
+
     scale_z: bool, default=True
-        whether to scale Z to zero mean and unit variance prior to
-        eigendecomposition.
+        whether to scale Z to zero prior to eigendecomposition.
 
     iterated_power : int or 'auto', default='auto'
         Number of iterations for the power method computed by
@@ -219,7 +218,6 @@ def __init__(
         iterated_power="auto",
         random_state=None,
         whiten=False,
-        
     ):
         super().__init__(
             mixing=mixing,
diff --git a/tests/test_pcovc.py b/tests/test_pcovc.py
index b476e80e8..283403324 100644
--- a/tests/test_pcovc.py
+++ b/tests/test_pcovc.py
@@ -465,7 +465,8 @@ def test_default_ncomponents(self):
 
     def test_prefit_classifier(self):
         """Check that a passed prefit classifier is not modified in
-        PCovC's `fit` call."""
+        PCovC's `fit` call.
+        """
         classifier = LinearSVC()
         classifier.fit(self.X, self.Y)
         pcovc = self.model(mixing=0.5, classifier=classifier)

From fb207629ddeb7bcf0d2f0d58fa847d8e6e96e546 Mon Sep 17 00:00:00 2001
From: Christian Jorgensen <cajorgensen@wisc.edu>
Date: Thu, 18 Sep 2025 13:23:40 -0500
Subject: [PATCH 07/11] fix docs

---
 src/skmatter/decomposition/_pcovc.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/skmatter/decomposition/_pcovc.py b/src/skmatter/decomposition/_pcovc.py
index 9b1660894..091df6023 100644
--- a/src/skmatter/decomposition/_pcovc.py
+++ b/src/skmatter/decomposition/_pcovc.py
@@ -125,7 +125,7 @@ class PCovC(LinearClassifierMixin, _BasePCov):
         is used as the classifier.
 
     scale_z: bool, default=True
-        whether to scale Z to zero prior to eigendecomposition.
+        whether to scale Z prior to eigendecomposition.
 
     iterated_power : int or 'auto', default='auto'
         Number of iterations for the power method computed by

From cd2d27ba58f6d11b29294f6b9a2c24852ebcca92 Mon Sep 17 00:00:00 2001
From: Christian Jorgensen <cajorgensen@wisc.edu>
Date: Thu, 18 Sep 2025 13:24:57 -0500
Subject: [PATCH 08/11] One last docs fix

---
 src/skmatter/decomposition/_kernel_pcovc.py | 2 +-
 src/skmatter/decomposition/_pcovc.py        | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/skmatter/decomposition/_kernel_pcovc.py b/src/skmatter/decomposition/_kernel_pcovc.py
index c7a95fa26..7ceff5983 100644
--- a/src/skmatter/decomposition/_kernel_pcovc.py
+++ b/src/skmatter/decomposition/_kernel_pcovc.py
@@ -87,7 +87,7 @@ class KernelPCovC(LinearClassifierMixin, _BaseKPCov):
         is used as the classifier.
 
     scale_z: bool, default=True
-        whether to scale Z prior to eigendecomposition.
+        Whether to scale Z prior to eigendecomposition.
 
     kernel : {"linear", "poly", "rbf", "sigmoid", "precomputed"} or callable, default="linear"
         Kernel.
diff --git a/src/skmatter/decomposition/_pcovc.py b/src/skmatter/decomposition/_pcovc.py
index 091df6023..fd8abe566 100644
--- a/src/skmatter/decomposition/_pcovc.py
+++ b/src/skmatter/decomposition/_pcovc.py
@@ -125,7 +125,7 @@ class PCovC(LinearClassifierMixin, _BasePCov):
         is used as the classifier.
 
     scale_z: bool, default=True
-        whether to scale Z prior to eigendecomposition.
+        Whether to scale Z prior to eigendecomposition.
 
     iterated_power : int or 'auto', default='auto'
         Number of iterations for the power method computed by

From 04cfab0a3642f36ad90aa33930b645109c9e7cba Mon Sep 17 00:00:00 2001
From: Christian Jorgensen <cajorgensen@wisc.edu>
Date: Thu, 18 Sep 2025 13:41:46 -0500
Subject: [PATCH 09/11] Adding tests

---
 tests/test_kernel_pcovc.py |  9 +++++++++
 tests/test_pcovc.py        | 11 +++++++++++
 2 files changed, 20 insertions(+)

diff --git a/tests/test_kernel_pcovc.py b/tests/test_kernel_pcovc.py
index 9b29b8437..bbfe8fbb3 100644
--- a/tests/test_kernel_pcovc.py
+++ b/tests/test_kernel_pcovc.py
@@ -327,6 +327,15 @@ def test_precomputed_classification(self):
         self.assertTrue(np.linalg.norm(t3 - t2) < self.error_tol)
         self.assertTrue(np.linalg.norm(t3 - t1) < self.error_tol)
 
+    def test_scale_z_parameter(self):
+        """Check that changing scale_z changes the eigendecomposition."""
+        kpcovc_scaled = self.model(scale_z=True)
+        kpcovc_scaled.fit(self.X, self.Y)
+
+        kpcovc_unscaled = self.model(scale_z=False)
+        kpcovc_unscaled.fit(self.X, self.Y)
+        assert not np.allclose(kpcovc_scaled.pkt_, kpcovc_unscaled.pkt_)
+
 
 class KernelTests(KernelPCovCBaseTest):
     def test_kernel_types(self):
diff --git a/tests/test_pcovc.py b/tests/test_pcovc.py
index 283403324..883279b59 100644
--- a/tests/test_pcovc.py
+++ b/tests/test_pcovc.py
@@ -578,6 +578,17 @@ def test_incompatible_coef_shape(self):
             % (len(pcovc_multi.classes_), self.X.shape[1], cl_binary.coef_.shape),
         )
 
+    def test_scale_z_parameter(self):
+        """Check that changing scale_z changes the eigendecomposition."""
+        pcovc_scaled = self.model(scale_z=True)
+        pcovc_scaled.fit(self.X, self.Y)
+
+        pcovc_unscaled = self.model(scale_z=False)
+        pcovc_unscaled.fit(self.X, self.Y)
+        assert not np.allclose(
+            pcovc_scaled.singular_values_, pcovc_unscaled.singular_values_
+        )
+
 
 if __name__ == "__main__":
     unittest.main(verbosity=2)

From d77d013a70388c35872d2e2e28416ae0db166b1f Mon Sep 17 00:00:00 2001
From: Christian Jorgensen <cajorgensen@wisc.edu>
Date: Fri, 19 Sep 2025 12:31:19 -0500
Subject: [PATCH 10/11] Fixed doctests

---
 src/skmatter/decomposition/_kernel_pcovc.py | 10 +++++-----
 src/skmatter/decomposition/_pcovc.py        |  8 ++++----
 2 files changed, 9 insertions(+), 9 deletions(-)

diff --git a/src/skmatter/decomposition/_kernel_pcovc.py b/src/skmatter/decomposition/_kernel_pcovc.py
index 7ceff5983..976946dd7 100644
--- a/src/skmatter/decomposition/_kernel_pcovc.py
+++ b/src/skmatter/decomposition/_kernel_pcovc.py
@@ -177,7 +177,7 @@ class KernelPCovC(LinearClassifierMixin, _BaseKPCov):
     >>> from sklearn.preprocessing import StandardScaler
     >>> X = np.array([[-2, 3, -1, 0], [2, 0, -3, 1], [3, 0, -1, 3], [2, -2, 1, 0]])
     >>> X = StandardScaler().fit_transform(X)
-    >>> Y = np.array([[2], [0], [1], [2]])
+    >>> Y = np.array([2, 0, 1, 2])
     >>> kpcovc = KernelPCovC(
     ...     mixing=0.1,
     ...     n_components=2,
@@ -187,10 +187,10 @@ class KernelPCovC(LinearClassifierMixin, _BaseKPCov):
     >>> kpcovc.fit(X, Y)
     KernelPCovC(gamma=1, kernel='rbf', mixing=0.1, n_components=2)
     >>> kpcovc.transform(X)
-    array([[-4.45970689e-01,  8.95327566e-06],
-           [ 4.52745933e-01,  5.54810948e-01],
-           [ 4.52881359e-01, -5.54708315e-01],
-           [-4.45921092e-01, -7.32157649e-05]])
+    array([[-4.41692911e-01,  6.87831803e-06],
+           [ 4.47719340e-01,  5.47456981e-01],
+           [ 4.47850288e-01, -5.47360522e-01],
+           [-4.41645711e-01, -7.05197801e-05]])
     >>> kpcovc.predict(X)
     array([2, 0, 1, 2])
     >>> kpcovc.score(X, Y)
diff --git a/src/skmatter/decomposition/_pcovc.py b/src/skmatter/decomposition/_pcovc.py
index fd8abe566..e4f6698be 100644
--- a/src/skmatter/decomposition/_pcovc.py
+++ b/src/skmatter/decomposition/_pcovc.py
@@ -198,10 +198,10 @@ class PCovC(LinearClassifierMixin, _BasePCov):
     >>> pcovc.fit(X, Y)
     PCovC(mixing=0.1, n_components=2)
     >>> pcovc.transform(X)
-    array([[-0.4794854 , -0.46228114],
-           [ 1.9416966 ,  0.2532831 ],
-           [-1.08744947,  0.89117784],
-           [-0.37476173, -0.6821798 ]])
+    array([[-0.38989065, -0.21368409],
+           [ 1.55313271,  0.20273297],
+           [-0.87105559,  0.68233882],
+           [-0.29218647, -0.6713877 ]])
     >>> pcovc.predict(X)
     array([0, 1, 2, 0])
     """  # NoQa: E501

From f3a372fc808f368e5de21f4e17a060089d68a7b3 Mon Sep 17 00:00:00 2001
From: Christian Jorgensen <cajorgensen@wisc.edu>
Date: Tue, 23 Sep 2025 15:41:35 -0500
Subject: [PATCH 11/11] Changing default and adding warnings

---
 src/skmatter/decomposition/_kernel_pcovc.py | 32 ++++++++++++++++++-
 src/skmatter/decomposition/_pcovc.py        | 34 +++++++++++++++++++--
 2 files changed, 63 insertions(+), 3 deletions(-)

diff --git a/src/skmatter/decomposition/_kernel_pcovc.py b/src/skmatter/decomposition/_kernel_pcovc.py
index 976946dd7..0b1b6e55a 100644
--- a/src/skmatter/decomposition/_kernel_pcovc.py
+++ b/src/skmatter/decomposition/_kernel_pcovc.py
@@ -1,3 +1,4 @@
+import warnings
 import numpy as np
 
 from sklearn import clone
@@ -119,6 +120,14 @@ class KernelPCovC(LinearClassifierMixin, _BaseKPCov):
         and for matrix inversions.
         Must be of range [0.0, infinity).
 
+    z_mean_tol: float, default=1e-12
+    Tolerance for the column means of Z.
+    Must be of range [0.0, infinity).
+
+    z_var_tol: float, default=1.5
+        Tolerance for the column variances of Z.
+        Must be of range [0.0, infinity).
+
     n_jobs : int, default=None
         The number of parallel jobs to run.
         :obj:`None` means 1 unless in a :obj:`joblib.parallel_backend` context.
@@ -203,7 +212,7 @@ def __init__(
         n_components=None,
         svd_solver="auto",
         classifier=None,
-        scale_z=True,
+        scale_z=False,
         kernel="linear",
         gamma=None,
         degree=3,
@@ -212,6 +221,8 @@ def __init__(
         center=False,
         fit_inverse_transform=False,
         tol=1e-12,
+        z_mean_tol=1e-12,
+        z_var_tol=1.5,
         n_jobs=None,
         iterated_power="auto",
         random_state=None,
@@ -234,6 +245,8 @@ def __init__(
         )
         self.classifier = classifier
         self.scale_z = scale_z
+        self.z_mean_tol = z_mean_tol
+        self.z_var_tol = z_var_tol
 
     def fit(self, X, Y, W=None):
         r"""Fit the model with X and Y.
@@ -331,6 +344,23 @@ def fit(self, X, Y, W=None):
         if self.scale_z:
             Z = StandardFlexibleScaler().fit_transform(Z)
 
+        self.z_means_ = np.mean(Z, axis=0)
+        self.z_vars_ = np.var(Z, axis=0)
+
+        if np.max(np.abs(self.z_means_)) > self.z_mean_tol:
+            warnings.warn(
+                "This class does not automatically center Z, and the column means "
+                "of Z are greater than the supplied tolerance. We recommend scaling "
+                "Z (and the weights) by setting `scale_z=True`."
+            )
+
+        if np.max(self.z_vars_) > self.z_var_tol:
+            warnings.warn(
+                "This class does not automatically scale Z, and the column variances "
+                "of Z are greater than the supplied tolerance. We recommend scaling "
+                "Z (and the weights) by setting `scale_z=True`. "
+            )
+
         self._fit(K, Z, W)
 
         self.ptk_ = self.pt__ @ K
diff --git a/src/skmatter/decomposition/_pcovc.py b/src/skmatter/decomposition/_pcovc.py
index e4f6698be..8f2b93555 100644
--- a/src/skmatter/decomposition/_pcovc.py
+++ b/src/skmatter/decomposition/_pcovc.py
@@ -17,6 +17,7 @@
 from skmatter.decomposition import _BasePCov
 from skmatter.utils import check_cl_fit
 from skmatter.preprocessing import StandardFlexibleScaler
+import warnings
 
 
 class PCovC(LinearClassifierMixin, _BasePCov):
@@ -124,7 +125,7 @@ class PCovC(LinearClassifierMixin, _BasePCov):
         If None, ``sklearn.linear_model.LogisticRegression()``
         is used as the classifier.
 
-    scale_z: bool, default=True
+    scale_z: bool, default=False
         Whether to scale Z prior to eigendecomposition.
 
     iterated_power : int or 'auto', default='auto'
@@ -147,6 +148,14 @@ class PCovC(LinearClassifierMixin, _BasePCov):
         Tolerance for singular values computed by svd_solver == 'arpack'.
         Must be of range [0.0, infinity).
 
+    z_mean_tol: float, default=1e-12
+        Tolerance for the column means of Z.
+        Must be of range [0.0, infinity).
+
+    z_var_tol: float, default=1.5
+        Tolerance for the column variances of Z.
+        Must be of range [0.0, infinity).
+
     space: {'feature', 'sample', 'auto'}, default='auto'
         whether to compute the PCovC in ``sample`` or ``feature`` space.
         The default is equal to ``sample`` when :math:`{n_{samples} < n_{features}}`
@@ -212,9 +221,11 @@ def __init__(
         n_components=None,
         svd_solver="auto",
         tol=1e-12,
+        z_mean_tol=1e-12,
+        z_var_tol=1.5,
         space="auto",
         classifier=None,
-        scale_z=True,
+        scale_z=False,
         iterated_power="auto",
         random_state=None,
         whiten=False,
@@ -231,6 +242,8 @@ def __init__(
         )
         self.classifier = classifier
         self.scale_z = scale_z
+        self.z_mean_tol = z_mean_tol
+        self.z_var_tol = z_var_tol
 
     def fit(self, X, Y, W=None):
         r"""Fit the model with X and Y.
@@ -312,6 +325,23 @@ def fit(self, X, Y, W=None):
             Z = z_scaler.transform(Z)
             W /= z_scaler.scale_.reshape(1, -1)
 
+        self.z_means_ = np.mean(Z, axis=0)
+        self.z_vars_ = np.var(Z, axis=0)
+
+        if np.max(np.abs(self.z_means_)) > self.z_mean_tol:
+            warnings.warn(
+                "This class does not automatically center Z, and the column means "
+                "of Z are greater than the supplied tolerance. We recommend scaling "
+                "Z (and the weights) by setting `scale_z=True`."
+            )
+
+        if np.max(self.z_vars_) > self.z_var_tol:
+            warnings.warn(
+                "This class does not automatically scale Z, and the column variances "
+                "of Z are greater than the supplied tolerance. We recommend scaling "
+                "Z (and the weights) by setting `scale_z=True`."
+            )
+
         if self.space_ == "feature":
             self._fit_feature_space(X, Y, Z)
         else: