Fixing pcovc scaling

examples/pcovc/KPCovC_Comparison.py

@@ -33,6 +33,7 @@
 
 random_state = 0
 n_components = 2
+scale_z = True
 
 # %%
 #
@@ -85,7 +86,7 @@
 # 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
 
@@ -95,6 +96,7 @@
         n_components=n_components,
         random_state=random_state,
         mixing=mixing,
+        scale_z=scale_z,
         classifier=LinearSVC(),
     ): "PCovC",
 }
@@ -138,6 +140,7 @@
         random_state=random_state,
         mixing=mixing,
         center=center,
+        scale_z=scale_z,
         **kernel_params,
     ): {"title": "Kernel PCovC", "eps": 2},
 }
@@ -220,6 +223,7 @@
         mixing=mixing,
         classifier=model,
         center=center,
+        scale_z=scale_z,
         **models[model]["kernel_params"],
     )
     t_kpcovc_train = kpcovc.fit_transform(X_train_scaled, y_train)

examples/pcovc/KPCovC_Hyperparameters.py

@@ -65,7 +65,8 @@
 fig, axs = plt.subplots(2, len(kernels), figsize=(len(kernels) * 4, 8))
 
 center = True
-mixing = 0.10
+mixing = 0.5
+scale_z = True
 
 for i, kernel in enumerate(kernels):
     kpca = KernelPCA(
@@ -83,6 +84,7 @@
         random_state=random_state,
         **kernel_params.get(kernel, {}),
         center=center,
+        scale_z=scale_z,
     )
     t_kpcovc = kpcovc.fit_transform(X_scaled, y)
 
@@ -118,7 +120,7 @@
     kpcovc = KernelPCovC(
         n_components=n_components,
         random_state=random_state,
-        mixing=mixing,
+        mixing=0.1,
         center=center,
         kernel="rbf",
         gamma=gamma,

examples/pcovc/PCovC_Hyperparameters.py

@@ -77,6 +77,7 @@
         n_components=n_components,
         random_state=random_state,
         classifier=LogisticRegressionCV(),
+        scale_z=True,
     )
 
     pcovc.fit(X_scaled, y)
@@ -120,6 +121,7 @@
         n_components=n_components,
         random_state=random_state,
         classifier=model,
+        scale_z=True,
     )
 
     pcovc.fit(X_scaled, y)

src/skmatter/decomposition/_kernel_pcovc.py

@@ -1,3 +1,4 @@
+import warnings
 import numpy as np
 
 from sklearn import clone
@@ -16,7 +17,7 @@
 from sklearn.linear_model._base import LinearClassifierMixin
 from sklearn.utils.multiclass import check_classification_targets, type_of_target
 
-from skmatter.preprocessing import KernelNormalizer
+from skmatter.preprocessing import KernelNormalizer, StandardFlexibleScaler
 from skmatter.utils import check_cl_fit
 from skmatter.decomposition import _BaseKPCov
 
@@ -86,6 +87,9 @@ class KernelPCovC(LinearClassifierMixin, _BaseKPCov):
         If None, ``sklearn.linear_model.LogisticRegression()``
         is used as the classifier.
 
+    scale_z: bool, default=False
+        Whether to scale Z prior to eigendecomposition.
+
     kernel : {"linear", "poly", "rbf", "sigmoid", "precomputed"} or callable, default="linear"
         Kernel.
 
@@ -116,6 +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.
@@ -167,14 +179,17 @@ class KernelPCovC(LinearClassifierMixin, _BaseKPCov):
         The data used to fit the model. This attribute is used to build kernels
         from new data.
 
+    scale_z: bool
+        Whether Z is being scaled prior to eigendecomposition.
+
     Examples
     --------
     >>> import numpy as np
     >>> from skmatter.decomposition import KernelPCovC
     >>> 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,
@@ -200,6 +215,7 @@ def __init__(
         n_components=None,
         svd_solver="auto",
         classifier=None,
+        scale_z=False,
         kernel="linear",
         gamma=None,
         degree=3,
@@ -208,6 +224,8 @@ 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,
@@ -229,6 +247,9 @@ def __init__(
             fit_inverse_transform=fit_inverse_transform,
         )
         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.
@@ -323,6 +344,25 @@ def fit(self, X, Y, W=None):
                 W = LogisticRegression().fit(K, Y).coef_.T
 
         Z = K @ W
+        if self.scale_z:
+            Z = StandardFlexibleScaler().fit_transform(Z)
+
+        z_means_ = np.mean(Z, axis=0)
+        z_vars_ = np.var(Z, axis=0)
+
+        if np.max(np.abs(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(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)
 

src/skmatter/decomposition/_pcovc.py

@@ -16,6 +16,8 @@
 from sklearn.utils.validation import check_is_fitted, validate_data
 from skmatter.decomposition import _BasePCov
 from skmatter.utils import check_cl_fit
+from skmatter.preprocessing import StandardFlexibleScaler
+import warnings
 
 
 class PCovC(LinearClassifierMixin, _BasePCov):
@@ -96,6 +98,14 @@ 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}}`
@@ -123,6 +133,9 @@ class PCovC(LinearClassifierMixin, _BasePCov):
         If None, ``sklearn.linear_model.LogisticRegression()``
         is used as the classifier.
 
+    scale_z: bool, default=False
+        Whether to scale Z prior to eigendecomposition.
+
     iterated_power : int or 'auto', default='auto'
         Number of iterations for the power method computed by
         svd_solver == 'randomized'.
@@ -143,6 +156,14 @@ class PCovC(LinearClassifierMixin, _BasePCov):
         Tolerance for singular values computed by svd_solver == 'arpack'.
         Must be of range [0.0, infinity).
 
+    z_mean_tol: float
+        Tolerance for the column means of Z.
+        Must be of range [0.0, infinity).
+
+    z_var_tol: float
+        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}}`
@@ -174,6 +195,9 @@ class PCovC(LinearClassifierMixin, _BasePCov):
         the projector, or weights, from the latent-space projection
         :math:`\mathbf{T}` to the class confidence scores :math:`\mathbf{Z}`
 
+    scale_z: bool
+        Whether Z is being scaled prior to eigendecomposition
+
     explained_variance_ : numpy.ndarray of shape (n_components,)
         The amount of variance explained by each of the selected components.
         Equal to n_components largest eigenvalues
@@ -208,8 +232,11 @@ 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=False,
         iterated_power="auto",
         random_state=None,
         whiten=False,
@@ -225,6 +252,9 @@ def __init__(
             whiten=whiten,
         )
         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.
@@ -291,7 +321,7 @@ 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
@@ -301,6 +331,28 @@ def fit(self, X, Y, W=None):
 
         Z = X @ W
 
+        if self.scale_z:
+            z_scaler = StandardFlexibleScaler().fit(Z)
+            Z = z_scaler.transform(Z)
+            W /= z_scaler.scale_.reshape(1, -1)
+
+        z_means_ = np.mean(Z, axis=0)
+        z_vars_ = np.var(Z, axis=0)
+
+        if np.max(np.abs(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(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:

tests/test_kernel_pcovc.py

@@ -1,4 +1,5 @@
 import unittest
+import warnings
 
 import numpy as np
 from sklearn import exceptions
@@ -34,10 +35,12 @@ def __init__(self, *args, **kwargs):
             lambda mixing=0.5,
             classifier=LogisticRegression(),
             n_components=4,
+            scale_z=True,
             **kwargs: KernelPCovC(
                 mixing=mixing,
                 classifier=classifier,
                 n_components=n_components,
+                scale_z=scale_z,
                 svd_solver=kwargs.pop("svd_solver", "full"),
                 **kwargs,
             )
@@ -327,6 +330,44 @@ 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_)
+
+    def test_z_scaling(self):
+        """
+        Check that KPCovC raises a warning if Z is not of scale, and does not
+        if it is.
+        """
+        kpcovc = self.model(n_components=2, scale_z=True)
+
+        with warnings.catch_warnings():
+            kpcovc.fit(self.X, self.Y)
+            warnings.simplefilter("error")
+            self.assertEqual(1 + 1, 2)
+
+        kpcovc = self.model(n_components=2, scale_z=False, z_mean_tol=0, z_var_tol=0)
+
+        with warnings.catch_warnings(record=True) as w:
+            kpcovc.fit(self.X, self.Y)
+            self.assertEqual(
+                str(w[0].message),
+                "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`.",
+            )
+            self.assertEqual(
+                str(w[1].message),
+                "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`.",
+            )
+
 
 class KernelTests(KernelPCovCBaseTest):
     def test_kernel_types(self):