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        "\n# Segmenting the picture of greek coins in regions\n\nThis example uses `spectral_clustering` on a graph created from\nvoxel-to-voxel difference on an image to break this image into multiple\npartly-homogeneous regions.\n\nThis procedure (spectral clustering on an image) is an efficient\napproximate solution for finding normalized graph cuts.\n\nThere are three options to assign labels:\n\n* 'kmeans' spectral clustering clusters samples in the embedding space\n  using a kmeans algorithm\n* 'discrete' iteratively searches for the closest partition\n  space to the embedding space of spectral clustering.\n* 'cluster_qr' assigns labels using the QR factorization with pivoting\n  that directly determines the partition in the embedding space.\n"
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        "# Authors: The scikit-learn developers\n# SPDX-License-Identifier: BSD-3-Clause\n\nimport time\n\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom scipy.ndimage import gaussian_filter\nfrom skimage.data import coins\nfrom skimage.transform import rescale\n\nfrom sklearn.cluster import spectral_clustering\nfrom sklearn.feature_extraction import image\n\n# load the coins as a numpy array\norig_coins = coins()\n\n# Resize it to 20% of the original size to speed up the processing\n# Applying a Gaussian filter for smoothing prior to down-scaling\n# reduces aliasing artifacts.\nsmoothened_coins = gaussian_filter(orig_coins, sigma=2)\nrescaled_coins = rescale(smoothened_coins, 0.2, mode=\"reflect\", anti_aliasing=False)\n\n# Convert the image into a graph with the value of the gradient on the\n# edges.\ngraph = image.img_to_graph(rescaled_coins)\n\n# Take a decreasing function of the gradient: an exponential\n# The smaller beta is, the more independent the segmentation is of the\n# actual image. For beta=1, the segmentation is close to a voronoi\nbeta = 10\neps = 1e-6\ngraph.data = np.exp(-beta * graph.data / graph.data.std()) + eps\n\n# The number of segmented regions to display needs to be chosen manually.\n# The current version of 'spectral_clustering' does not support determining\n# the number of good quality clusters automatically.\nn_regions = 26"
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "Compute and visualize the resulting regions\n\n"
      ]
    },
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        "# Computing a few extra eigenvectors may speed up the eigen_solver.\n# The spectral clustering quality may also benefit from requesting\n# extra regions for segmentation.\nn_regions_plus = 3\n\n# Apply spectral clustering using the default eigen_solver='arpack'.\n# Any implemented solver can be used: eigen_solver='arpack', 'lobpcg', or 'amg'.\n# Choosing eigen_solver='amg' requires an extra package called 'pyamg'.\n# The quality of segmentation and the speed of calculations is mostly determined\n# by the choice of the solver and the value of the tolerance 'eigen_tol'.\n# TODO: varying eigen_tol seems to have no effect for 'lobpcg' and 'amg' #21243.\nfor assign_labels in (\"kmeans\", \"discretize\", \"cluster_qr\"):\n    t0 = time.time()\n    labels = spectral_clustering(\n        graph,\n        n_clusters=(n_regions + n_regions_plus),\n        eigen_tol=1e-7,\n        assign_labels=assign_labels,\n        random_state=42,\n    )\n\n    t1 = time.time()\n    labels = labels.reshape(rescaled_coins.shape)\n    plt.figure(figsize=(5, 5))\n    plt.imshow(rescaled_coins, cmap=plt.cm.gray)\n\n    plt.xticks(())\n    plt.yticks(())\n    title = \"Spectral clustering: %s, %.2fs\" % (assign_labels, (t1 - t0))\n    print(title)\n    plt.title(title)\n    for l in range(n_regions):\n        colors = [plt.cm.nipy_spectral((l + 4) / float(n_regions + 4))]\n        plt.contour(labels == l, colors=colors)\n        # To view individual segments as appear comment in plt.pause(0.5)\nplt.show()\n\n# TODO: After #21194 is merged and #21243 is fixed, check which eigen_solver\n# is the best and set eigen_solver='arpack', 'lobpcg', or 'amg' and eigen_tol\n# explicitly in this example."
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