Pushing the docs to dev/ for branch: main, commit 18c1972eb9637034b8e9fbd0df966c10058770f5

Author: sklearn-ci

dev/.buildinfo

@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: 8e49001559d8412c6c31e2e5ae0dd686
+config: 1f0325ead478dd709d7d2aa77cd5a9b0
 tags: 645f666f9bcd5a90fca523b33c5a78b7

dev/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip

@@ -51,7 +51,7 @@
       },
       "outputs": [],
       "source": [
-        "from sklearn import svm\nfrom sklearn.inspection import DecisionBoundaryDisplay\n\n\ndef plot_training_data_with_decision_boundary(kernel):\n    # Train the SVC\n    clf = svm.SVC(kernel=kernel, gamma=2).fit(X, y)\n\n    # Settings for plotting\n    _, ax = plt.subplots(figsize=(4, 3))\n    x_min, x_max, y_min, y_max = -3, 3, -3, 3\n    ax.set(xlim=(x_min, x_max), ylim=(y_min, y_max))\n\n    # Plot decision boundary and margins\n    common_params = {\"estimator\": clf, \"X\": X, \"ax\": ax}\n    DecisionBoundaryDisplay.from_estimator(\n        **common_params,\n        response_method=\"predict\",\n        plot_method=\"pcolormesh\",\n        alpha=0.3,\n    )\n    DecisionBoundaryDisplay.from_estimator(\n        **common_params,\n        response_method=\"decision_function\",\n        plot_method=\"contour\",\n        levels=[-1, 0, 1],\n        colors=[\"k\", \"k\", \"k\"],\n        linestyles=[\"--\", \"-\", \"--\"],\n    )\n\n    # Plot bigger circles around samples that serve as support vectors\n    ax.scatter(\n        clf.support_vectors_[:, 0],\n        clf.support_vectors_[:, 1],\n        s=250,\n        facecolors=\"none\",\n        edgecolors=\"k\",\n    )\n    # Plot samples by color and add legend\n    ax.scatter(X[:, 0], X[:, 1], c=y, s=150, edgecolors=\"k\")\n    ax.legend(*scatter.legend_elements(), loc=\"upper right\", title=\"Classes\")\n    ax.set_title(f\" Decision boundaries of {kernel} kernel in SVC\")\n\n    _ = plt.show()"
+        "from sklearn import svm\nfrom sklearn.inspection import DecisionBoundaryDisplay\n\n\ndef plot_training_data_with_decision_boundary(\n    kernel, ax=None, long_title=True, support_vectors=True\n):\n    # Train the SVC\n    clf = svm.SVC(kernel=kernel, gamma=2).fit(X, y)\n\n    # Settings for plotting\n    if ax is None:\n        _, ax = plt.subplots(figsize=(4, 3))\n    x_min, x_max, y_min, y_max = -3, 3, -3, 3\n    ax.set(xlim=(x_min, x_max), ylim=(y_min, y_max))\n\n    # Plot decision boundary and margins\n    common_params = {\"estimator\": clf, \"X\": X, \"ax\": ax}\n    DecisionBoundaryDisplay.from_estimator(\n        **common_params,\n        response_method=\"predict\",\n        plot_method=\"pcolormesh\",\n        alpha=0.3,\n    )\n    DecisionBoundaryDisplay.from_estimator(\n        **common_params,\n        response_method=\"decision_function\",\n        plot_method=\"contour\",\n        levels=[-1, 0, 1],\n        colors=[\"k\", \"k\", \"k\"],\n        linestyles=[\"--\", \"-\", \"--\"],\n    )\n\n    if support_vectors:\n        # Plot bigger circles around samples that serve as support vectors\n        ax.scatter(\n            clf.support_vectors_[:, 0],\n            clf.support_vectors_[:, 1],\n            s=150,\n            facecolors=\"none\",\n            edgecolors=\"k\",\n        )\n\n    # Plot samples by color and add legend\n    ax.scatter(X[:, 0], X[:, 1], c=y, s=30, edgecolors=\"k\")\n    ax.legend(*scatter.legend_elements(), loc=\"upper right\", title=\"Classes\")\n    if long_title:\n        ax.set_title(f\" Decision boundaries of {kernel} kernel in SVC\")\n    else:\n        ax.set_title(kernel)\n\n    if ax is None:\n        plt.show()"
       ]
     },
     {
@@ -132,6 +132,31 @@
       "source": [
         "We can see that the decision boundaries obtained with the sigmoid kernel\nappear curved and irregular. The decision boundary tries to separate the\nclasses by fitting a sigmoid-shaped curve, resulting in a complex boundary\nthat may not generalize well to unseen data. From this example it becomes\nobvious, that the sigmoid kernel has very specific use cases, when dealing\nwith data that exhibits a sigmoidal shape. In this example, careful fine\ntuning might find more generalizable decision boundaries. Because of it's\nspecificity, the sigmoid kernel is less commonly used in practice compared to\nother kernels.\n\n## Conclusion\nIn this example, we have visualized the decision boundaries trained with the\nprovided dataset. The plots serve as an intuitive demonstration of how\ndifferent kernels utilize the training data to determine the classification\nboundaries.\n\nThe hyperplanes and margins, although computed indirectly, can be imagined as\nplanes in the transformed feature space. However, in the plots, they are\nrepresented relative to the original feature space, resulting in curved\ndecision boundaries for the polynomial, RBF, and sigmoid kernels.\n\nPlease note that the plots do not evaluate the individual kernel's accuracy or\nquality. They are intended to provide a visual understanding of how the\ndifferent kernels use the training data.\n\nFor a comprehensive evaluation, fine-tuning of :class:`~sklearn.svm.SVC`\nparameters using techniques such as\n:class:`~sklearn.model_selection.GridSearchCV` is recommended to capture the\nunderlying structures within the data.\n\n"
       ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## XOR dataset\nA classical example of a dataset which is not linearly separable is the XOR\npattern. HEre we demonstrate how different kernels work on such a dataset.\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "xx, yy = np.meshgrid(np.linspace(-3, 3, 500), np.linspace(-3, 3, 500))\nnp.random.seed(0)\nX = np.random.randn(300, 2)\ny = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)\n\n_, ax = plt.subplots(2, 2, figsize=(8, 8))\nargs = dict(long_title=False, support_vectors=False)\nplot_training_data_with_decision_boundary(\"linear\", ax[0, 0], **args)\nplot_training_data_with_decision_boundary(\"poly\", ax[0, 1], **args)\nplot_training_data_with_decision_boundary(\"rbf\", ax[1, 0], **args)\nplot_training_data_with_decision_boundary(\"sigmoid\", ax[1, 1], **args)\nplt.show()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "As you can see from the plots above, only the `rbf` kernel can find a\nreasonable decision boundary for the above dataset.\n\n"
+      ]
     }
   ],
   "metadata": {

dev/_downloads/264f6891fa2130246a013d5f089e7b2e/plot_svm_kernels.ipynb

@@ -110,12 +110,15 @@
 from sklearn.inspection import DecisionBoundaryDisplay
 
 
-def plot_training_data_with_decision_boundary(kernel):
+def plot_training_data_with_decision_boundary(
+    kernel, ax=None, long_title=True, support_vectors=True
+):
     # Train the SVC
     clf = svm.SVC(kernel=kernel, gamma=2).fit(X, y)
 
     # Settings for plotting
-    _, ax = plt.subplots(figsize=(4, 3))
+    if ax is None:
+        _, ax = plt.subplots(figsize=(4, 3))
     x_min, x_max, y_min, y_max = -3, 3, -3, 3
     ax.set(xlim=(x_min, x_max), ylim=(y_min, y_max))
 
@@ -136,20 +139,26 @@ def plot_training_data_with_decision_boundary(kernel):
         linestyles=["--", "-", "--"],
     )
 
-    # Plot bigger circles around samples that serve as support vectors
-    ax.scatter(
-        clf.support_vectors_[:, 0],
-        clf.support_vectors_[:, 1],
-        s=250,
-        facecolors="none",
-        edgecolors="k",
-    )
+    if support_vectors:
+        # Plot bigger circles around samples that serve as support vectors
+        ax.scatter(
+            clf.support_vectors_[:, 0],
+            clf.support_vectors_[:, 1],
+            s=150,
+            facecolors="none",
+            edgecolors="k",
+        )
+
     # Plot samples by color and add legend
-    ax.scatter(X[:, 0], X[:, 1], c=y, s=150, edgecolors="k")
+    ax.scatter(X[:, 0], X[:, 1], c=y, s=30, edgecolors="k")
     ax.legend(*scatter.legend_elements(), loc="upper right", title="Classes")
-    ax.set_title(f" Decision boundaries of {kernel} kernel in SVC")
+    if long_title:
+        ax.set_title(f" Decision boundaries of {kernel} kernel in SVC")
+    else:
+        ax.set_title(kernel)
 
-    _ = plt.show()
+    if ax is None:
+        plt.show()
 
 
 # %%
@@ -237,7 +246,6 @@ def plot_training_data_with_decision_boundary(kernel):
 # using the hyperbolic tangent function (:math:`\tanh`). The kernel function
 # scales and possibly shifts the dot product of the two points
 # (:math:`\mathbf{x}_1` and :math:`\mathbf{x}_2`).
-
 plot_training_data_with_decision_boundary("sigmoid")
 
 # %%
@@ -271,3 +279,26 @@ def plot_training_data_with_decision_boundary(kernel):
 # parameters using techniques such as
 # :class:`~sklearn.model_selection.GridSearchCV` is recommended to capture the
 # underlying structures within the data.
+
+# %%
+# XOR dataset
+# -----------
+# A classical example of a dataset which is not linearly separable is the XOR
+# pattern. HEre we demonstrate how different kernels work on such a dataset.
+
+xx, yy = np.meshgrid(np.linspace(-3, 3, 500), np.linspace(-3, 3, 500))
+np.random.seed(0)
+X = np.random.randn(300, 2)
+y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)
+
+_, ax = plt.subplots(2, 2, figsize=(8, 8))
+args = dict(long_title=False, support_vectors=False)
+plot_training_data_with_decision_boundary("linear", ax[0, 0], **args)
+plot_training_data_with_decision_boundary("poly", ax[0, 1], **args)
+plot_training_data_with_decision_boundary("rbf", ax[1, 0], **args)
+plot_training_data_with_decision_boundary("sigmoid", ax[1, 1], **args)
+plt.show()
+
+# %%
+# As you can see from the plots above, only the `rbf` kernel can find a
+# reasonable decision boundary for the above dataset.