1.5/notebooks/auto_examples/svm/plot_svm_margin.ipynb

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        "\n# SVM Margins Example\nThe plots below illustrate the effect the parameter `C` has\non the separation line. A large value of `C` basically tells\nour model that we do not have that much faith in our data's\ndistribution, and will only consider points close to line\nof separation.\n\nA small value of `C` includes more/all the observations, allowing\nthe margins to be calculated using all the data in the area.\n"
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        "# Code source: Ga\u00ebl Varoquaux\n# Modified for documentation by Jaques Grobler\n# License: BSD 3 clause\n\nimport matplotlib.pyplot as plt\nimport numpy as np\n\nfrom sklearn import svm\n\n# we create 40 separable points\nnp.random.seed(0)\nX = np.r_[np.random.randn(20, 2) - [2, 2], np.random.randn(20, 2) + [2, 2]]\nY = [0] * 20 + [1] * 20\n\n# figure number\nfignum = 1\n\n# fit the model\nfor name, penalty in ((\"unreg\", 1), (\"reg\", 0.05)):\n    clf = svm.SVC(kernel=\"linear\", C=penalty)\n    clf.fit(X, Y)\n\n    # get the separating hyperplane\n    w = clf.coef_[0]\n    a = -w[0] / w[1]\n    xx = np.linspace(-5, 5)\n    yy = a * xx - (clf.intercept_[0]) / w[1]\n\n    # plot the parallels to the separating hyperplane that pass through the\n    # support vectors (margin away from hyperplane in direction\n    # perpendicular to hyperplane). This is sqrt(1+a^2) away vertically in\n    # 2-d.\n    margin = 1 / np.sqrt(np.sum(clf.coef_**2))\n    yy_down = yy - np.sqrt(1 + a**2) * margin\n    yy_up = yy + np.sqrt(1 + a**2) * margin\n\n    # plot the line, the points, and the nearest vectors to the plane\n    plt.figure(fignum, figsize=(4, 3))\n    plt.clf()\n    plt.plot(xx, yy, \"k-\")\n    plt.plot(xx, yy_down, \"k--\")\n    plt.plot(xx, yy_up, \"k--\")\n\n    plt.scatter(\n        clf.support_vectors_[:, 0],\n        clf.support_vectors_[:, 1],\n        s=80,\n        facecolors=\"none\",\n        zorder=10,\n        edgecolors=\"k\",\n        cmap=plt.get_cmap(\"RdBu\"),\n    )\n    plt.scatter(\n        X[:, 0], X[:, 1], c=Y, zorder=10, cmap=plt.get_cmap(\"RdBu\"), edgecolors=\"k\"\n    )\n\n    plt.axis(\"tight\")\n    x_min = -4.8\n    x_max = 4.2\n    y_min = -6\n    y_max = 6\n\n    YY, XX = np.meshgrid(yy, xx)\n    xy = np.vstack([XX.ravel(), YY.ravel()]).T\n    Z = clf.decision_function(xy).reshape(XX.shape)\n\n    # Put the result into a contour plot\n    plt.contourf(XX, YY, Z, cmap=plt.get_cmap(\"RdBu\"), alpha=0.5, linestyles=[\"-\"])\n\n    plt.xlim(x_min, x_max)\n    plt.ylim(y_min, y_max)\n\n    plt.xticks(())\n    plt.yticks(())\n    fignum = fignum + 1\n\nplt.show()"
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