Pushing the docs to dev/ for branch: main, commit a3893d3bdc7b63f236536b0c0f4d47b5ab575c07

Author: sklearn-ci

dev/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip

@@ -18,6 +18,67 @@
         "\n# Linear and Quadratic Discriminant Analysis with covariance ellipsoid\n\nThis example plots the covariance ellipsoids of each class and\ndecision boundary learned by LDA and QDA. The ellipsoids display\nthe double standard deviation for each class. With LDA, the\nstandard deviation is the same for all the classes, while each\nclass has its own standard deviation with QDA.\n"
       ]
     },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Colormap\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import matplotlib.pyplot as plt\nimport matplotlib as mpl\nfrom matplotlib import colors\n\ncmap = colors.LinearSegmentedColormap(\n    \"red_blue_classes\",\n    {\n        \"red\": [(0, 1, 1), (1, 0.7, 0.7)],\n        \"green\": [(0, 0.7, 0.7), (1, 0.7, 0.7)],\n        \"blue\": [(0, 0.7, 0.7), (1, 1, 1)],\n    },\n)\nplt.cm.register_cmap(cmap=cmap)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Datasets generation functions\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n\n\ndef dataset_fixed_cov():\n    \"\"\"Generate 2 Gaussians samples with the same covariance matrix\"\"\"\n    n, dim = 300, 2\n    np.random.seed(0)\n    C = np.array([[0.0, -0.23], [0.83, 0.23]])\n    X = np.r_[\n        np.dot(np.random.randn(n, dim), C),\n        np.dot(np.random.randn(n, dim), C) + np.array([1, 1]),\n    ]\n    y = np.hstack((np.zeros(n), np.ones(n)))\n    return X, y\n\n\ndef dataset_cov():\n    \"\"\"Generate 2 Gaussians samples with different covariance matrices\"\"\"\n    n, dim = 300, 2\n    np.random.seed(0)\n    C = np.array([[0.0, -1.0], [2.5, 0.7]]) * 2.0\n    X = np.r_[\n        np.dot(np.random.randn(n, dim), C),\n        np.dot(np.random.randn(n, dim), C.T) + np.array([1, 4]),\n    ]\n    y = np.hstack((np.zeros(n), np.ones(n)))\n    return X, y"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Plot functions\n\n"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "from scipy import linalg\n\n\ndef plot_data(lda, X, y, y_pred, fig_index):\n    splot = plt.subplot(2, 2, fig_index)\n    if fig_index == 1:\n        plt.title(\"Linear Discriminant Analysis\")\n        plt.ylabel(\"Data with\\n fixed covariance\")\n    elif fig_index == 2:\n        plt.title(\"Quadratic Discriminant Analysis\")\n    elif fig_index == 3:\n        plt.ylabel(\"Data with\\n varying covariances\")\n\n    tp = y == y_pred  # True Positive\n    tp0, tp1 = tp[y == 0], tp[y == 1]\n    X0, X1 = X[y == 0], X[y == 1]\n    X0_tp, X0_fp = X0[tp0], X0[~tp0]\n    X1_tp, X1_fp = X1[tp1], X1[~tp1]\n\n    # class 0: dots\n    plt.scatter(X0_tp[:, 0], X0_tp[:, 1], marker=\".\", color=\"red\")\n    plt.scatter(X0_fp[:, 0], X0_fp[:, 1], marker=\"x\", s=20, color=\"#990000\")  # dark red\n\n    # class 1: dots\n    plt.scatter(X1_tp[:, 0], X1_tp[:, 1], marker=\".\", color=\"blue\")\n    plt.scatter(\n        X1_fp[:, 0], X1_fp[:, 1], marker=\"x\", s=20, color=\"#000099\"\n    )  # dark blue\n\n    # class 0 and 1 : areas\n    nx, ny = 200, 100\n    x_min, x_max = plt.xlim()\n    y_min, y_max = plt.ylim()\n    xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx), np.linspace(y_min, y_max, ny))\n    Z = lda.predict_proba(np.c_[xx.ravel(), yy.ravel()])\n    Z = Z[:, 1].reshape(xx.shape)\n    plt.pcolormesh(\n        xx, yy, Z, cmap=\"red_blue_classes\", norm=colors.Normalize(0.0, 1.0), zorder=0\n    )\n    plt.contour(xx, yy, Z, [0.5], linewidths=2.0, colors=\"white\")\n\n    # means\n    plt.plot(\n        lda.means_[0][0],\n        lda.means_[0][1],\n        \"*\",\n        color=\"yellow\",\n        markersize=15,\n        markeredgecolor=\"grey\",\n    )\n    plt.plot(\n        lda.means_[1][0],\n        lda.means_[1][1],\n        \"*\",\n        color=\"yellow\",\n        markersize=15,\n        markeredgecolor=\"grey\",\n    )\n\n    return splot\n\n\ndef plot_ellipse(splot, mean, cov, color):\n    v, w = linalg.eigh(cov)\n    u = w[0] / linalg.norm(w[0])\n    angle = np.arctan(u[1] / u[0])\n    angle = 180 * angle / np.pi  # convert to degrees\n    # filled Gaussian at 2 standard deviation\n    ell = mpl.patches.Ellipse(\n        mean,\n        2 * v[0] ** 0.5,\n        2 * v[1] ** 0.5,\n        180 + angle,\n        facecolor=color,\n        edgecolor=\"black\",\n        linewidth=2,\n    )\n    ell.set_clip_box(splot.bbox)\n    ell.set_alpha(0.2)\n    splot.add_artist(ell)\n    splot.set_xticks(())\n    splot.set_yticks(())\n\n\ndef plot_lda_cov(lda, splot):\n    plot_ellipse(splot, lda.means_[0], lda.covariance_, \"red\")\n    plot_ellipse(splot, lda.means_[1], lda.covariance_, \"blue\")\n\n\ndef plot_qda_cov(qda, splot):\n    plot_ellipse(splot, qda.means_[0], qda.covariance_[0], \"red\")\n    plot_ellipse(splot, qda.means_[1], qda.covariance_[1], \"blue\")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "## Plot\n\n"
+      ]
+    },
     {
       "cell_type": "code",
       "execution_count": null,
@@ -26,7 +87,7 @@
       },
       "outputs": [],
       "source": [
-        "from scipy import linalg\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport matplotlib as mpl\nfrom matplotlib import colors\n\nfrom sklearn.discriminant_analysis import LinearDiscriminantAnalysis\nfrom sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis\n\n# #############################################################################\n# Colormap\ncmap = colors.LinearSegmentedColormap(\n    \"red_blue_classes\",\n    {\n        \"red\": [(0, 1, 1), (1, 0.7, 0.7)],\n        \"green\": [(0, 0.7, 0.7), (1, 0.7, 0.7)],\n        \"blue\": [(0, 0.7, 0.7), (1, 1, 1)],\n    },\n)\nplt.cm.register_cmap(cmap=cmap)\n\n\n# #############################################################################\n# Generate datasets\ndef dataset_fixed_cov():\n    \"\"\"Generate 2 Gaussians samples with the same covariance matrix\"\"\"\n    n, dim = 300, 2\n    np.random.seed(0)\n    C = np.array([[0.0, -0.23], [0.83, 0.23]])\n    X = np.r_[\n        np.dot(np.random.randn(n, dim), C),\n        np.dot(np.random.randn(n, dim), C) + np.array([1, 1]),\n    ]\n    y = np.hstack((np.zeros(n), np.ones(n)))\n    return X, y\n\n\ndef dataset_cov():\n    \"\"\"Generate 2 Gaussians samples with different covariance matrices\"\"\"\n    n, dim = 300, 2\n    np.random.seed(0)\n    C = np.array([[0.0, -1.0], [2.5, 0.7]]) * 2.0\n    X = np.r_[\n        np.dot(np.random.randn(n, dim), C),\n        np.dot(np.random.randn(n, dim), C.T) + np.array([1, 4]),\n    ]\n    y = np.hstack((np.zeros(n), np.ones(n)))\n    return X, y\n\n\n# #############################################################################\n# Plot functions\ndef plot_data(lda, X, y, y_pred, fig_index):\n    splot = plt.subplot(2, 2, fig_index)\n    if fig_index == 1:\n        plt.title(\"Linear Discriminant Analysis\")\n        plt.ylabel(\"Data with\\n fixed covariance\")\n    elif fig_index == 2:\n        plt.title(\"Quadratic Discriminant Analysis\")\n    elif fig_index == 3:\n        plt.ylabel(\"Data with\\n varying covariances\")\n\n    tp = y == y_pred  # True Positive\n    tp0, tp1 = tp[y == 0], tp[y == 1]\n    X0, X1 = X[y == 0], X[y == 1]\n    X0_tp, X0_fp = X0[tp0], X0[~tp0]\n    X1_tp, X1_fp = X1[tp1], X1[~tp1]\n\n    # class 0: dots\n    plt.scatter(X0_tp[:, 0], X0_tp[:, 1], marker=\".\", color=\"red\")\n    plt.scatter(X0_fp[:, 0], X0_fp[:, 1], marker=\"x\", s=20, color=\"#990000\")  # dark red\n\n    # class 1: dots\n    plt.scatter(X1_tp[:, 0], X1_tp[:, 1], marker=\".\", color=\"blue\")\n    plt.scatter(\n        X1_fp[:, 0], X1_fp[:, 1], marker=\"x\", s=20, color=\"#000099\"\n    )  # dark blue\n\n    # class 0 and 1 : areas\n    nx, ny = 200, 100\n    x_min, x_max = plt.xlim()\n    y_min, y_max = plt.ylim()\n    xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx), np.linspace(y_min, y_max, ny))\n    Z = lda.predict_proba(np.c_[xx.ravel(), yy.ravel()])\n    Z = Z[:, 1].reshape(xx.shape)\n    plt.pcolormesh(\n        xx, yy, Z, cmap=\"red_blue_classes\", norm=colors.Normalize(0.0, 1.0), zorder=0\n    )\n    plt.contour(xx, yy, Z, [0.5], linewidths=2.0, colors=\"white\")\n\n    # means\n    plt.plot(\n        lda.means_[0][0],\n        lda.means_[0][1],\n        \"*\",\n        color=\"yellow\",\n        markersize=15,\n        markeredgecolor=\"grey\",\n    )\n    plt.plot(\n        lda.means_[1][0],\n        lda.means_[1][1],\n        \"*\",\n        color=\"yellow\",\n        markersize=15,\n        markeredgecolor=\"grey\",\n    )\n\n    return splot\n\n\ndef plot_ellipse(splot, mean, cov, color):\n    v, w = linalg.eigh(cov)\n    u = w[0] / linalg.norm(w[0])\n    angle = np.arctan(u[1] / u[0])\n    angle = 180 * angle / np.pi  # convert to degrees\n    # filled Gaussian at 2 standard deviation\n    ell = mpl.patches.Ellipse(\n        mean,\n        2 * v[0] ** 0.5,\n        2 * v[1] ** 0.5,\n        180 + angle,\n        facecolor=color,\n        edgecolor=\"black\",\n        linewidth=2,\n    )\n    ell.set_clip_box(splot.bbox)\n    ell.set_alpha(0.2)\n    splot.add_artist(ell)\n    splot.set_xticks(())\n    splot.set_yticks(())\n\n\ndef plot_lda_cov(lda, splot):\n    plot_ellipse(splot, lda.means_[0], lda.covariance_, \"red\")\n    plot_ellipse(splot, lda.means_[1], lda.covariance_, \"blue\")\n\n\ndef plot_qda_cov(qda, splot):\n    plot_ellipse(splot, qda.means_[0], qda.covariance_[0], \"red\")\n    plot_ellipse(splot, qda.means_[1], qda.covariance_[1], \"blue\")\n\n\nplt.figure(figsize=(10, 8), facecolor=\"white\")\nplt.suptitle(\n    \"Linear Discriminant Analysis vs Quadratic Discriminant Analysis\",\n    y=0.98,\n    fontsize=15,\n)\nfor i, (X, y) in enumerate([dataset_fixed_cov(), dataset_cov()]):\n    # Linear Discriminant Analysis\n    lda = LinearDiscriminantAnalysis(solver=\"svd\", store_covariance=True)\n    y_pred = lda.fit(X, y).predict(X)\n    splot = plot_data(lda, X, y, y_pred, fig_index=2 * i + 1)\n    plot_lda_cov(lda, splot)\n    plt.axis(\"tight\")\n\n    # Quadratic Discriminant Analysis\n    qda = QuadraticDiscriminantAnalysis(store_covariance=True)\n    y_pred = qda.fit(X, y).predict(X)\n    splot = plot_data(qda, X, y, y_pred, fig_index=2 * i + 2)\n    plot_qda_cov(qda, splot)\n    plt.axis(\"tight\")\nplt.tight_layout()\nplt.subplots_adjust(top=0.92)\nplt.show()"
+        "plt.figure(figsize=(10, 8), facecolor=\"white\")\nplt.suptitle(\n    \"Linear Discriminant Analysis vs Quadratic Discriminant Analysis\",\n    y=0.98,\n    fontsize=15,\n)\n\nfrom sklearn.discriminant_analysis import LinearDiscriminantAnalysis\nfrom sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis\n\nfor i, (X, y) in enumerate([dataset_fixed_cov(), dataset_cov()]):\n    # Linear Discriminant Analysis\n    lda = LinearDiscriminantAnalysis(solver=\"svd\", store_covariance=True)\n    y_pred = lda.fit(X, y).predict(X)\n    splot = plot_data(lda, X, y, y_pred, fig_index=2 * i + 1)\n    plot_lda_cov(lda, splot)\n    plt.axis(\"tight\")\n\n    # Quadratic Discriminant Analysis\n    qda = QuadraticDiscriminantAnalysis(store_covariance=True)\n    y_pred = qda.fit(X, y).predict(X)\n    splot = plot_data(qda, X, y, y_pred, fig_index=2 * i + 2)\n    plot_qda_cov(qda, splot)\n    plt.axis(\"tight\")\n\nplt.tight_layout()\nplt.subplots_adjust(top=0.92)\nplt.show()"
       ]
     }
   ],

dev/_downloads/1a2ab00bbfd4eb80e0afca13d83e2a14/plot_lda_qda.ipynb

@@ -11,17 +11,14 @@ class has its own standard deviation with QDA.
 
 """
 
-from scipy import linalg
-import numpy as np
+# %%
+# Colormap
+# --------
+
 import matplotlib.pyplot as plt
 import matplotlib as mpl
 from matplotlib import colors
 
-from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
-from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
-
-# #############################################################################
-# Colormap
 cmap = colors.LinearSegmentedColormap(
     "red_blue_classes",
     {
@@ -33,8 +30,13 @@ class has its own standard deviation with QDA.
 plt.cm.register_cmap(cmap=cmap)
 
 
-# #############################################################################
-# Generate datasets
+# %%
+# Datasets generation functions
+# -----------------------------
+
+import numpy as np
+
+
 def dataset_fixed_cov():
     """Generate 2 Gaussians samples with the same covariance matrix"""
     n, dim = 300, 2
@@ -61,8 +63,13 @@ def dataset_cov():
     return X, y
 
 
-# #############################################################################
+# %%
 # Plot functions
+# --------------
+
+from scipy import linalg
+
+
 def plot_data(lda, X, y, y_pred, fig_index):
     splot = plt.subplot(2, 2, fig_index)
     if fig_index == 1:
@@ -154,12 +161,20 @@ def plot_qda_cov(qda, splot):
     plot_ellipse(splot, qda.means_[1], qda.covariance_[1], "blue")
 
 
+# %%
+# Plot
+# ----
+
 plt.figure(figsize=(10, 8), facecolor="white")
 plt.suptitle(
     "Linear Discriminant Analysis vs Quadratic Discriminant Analysis",
     y=0.98,
     fontsize=15,
 )
+
+from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
+from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
+
 for i, (X, y) in enumerate([dataset_fixed_cov(), dataset_cov()]):
     # Linear Discriminant Analysis
     lda = LinearDiscriminantAnalysis(solver="svd", store_covariance=True)
@@ -174,6 +189,7 @@ def plot_qda_cov(qda, splot):
     splot = plot_data(qda, X, y, y_pred, fig_index=2 * i + 2)
     plot_qda_cov(qda, splot)
     plt.axis("tight")
+
 plt.tight_layout()
 plt.subplots_adjust(top=0.92)
 plt.show()