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        "value": "import numpy as np\nfrom scipy.cluster.vq import vq, kmeans, whiten\nimport matplotlib.pyplot as plt\nfeatures  = np.array([[ 1.9,2.3],\n                      [ 1.5,2.5],\n                      [ 0.8,0.6],\n                      [ 0.4,1.8],\n                      [ 0.1,0.1],\n                      [ 0.2,1.8],\n                      [ 2.0,0.5],\n                      [ 0.3,1.5],\n                      [ 1.0,1.0]])\nwhitened = whiten(features)\nbook = np.array((whitened[0],whitened[2]))\n",
        "execution_status": "success"
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        "value": "kmeans(whitened,book)\n",
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        "value": "codes = 3\n",
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        "value": "kmeans(whitened,codes)\n",
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        "value": "\n"
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        "value": "pts = 50\nrng = np.random.default_rng()\na = rng.multivariate_normal([0, 0], [[4, 1], [1, 4]], size=pts)\nb = rng.multivariate_normal([30, 10],\n                            [[10, 2], [2, 1]],\n                            size=pts)\nfeatures = np.concatenate((a, b))\nwhitened = whiten(features)\ncodebook, distortion = kmeans(whitened, 2)\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "plt.scatter(whitened[:, 0], whitened[:, 1])\nplt.scatter(codebook[:, 0], codebook[:, 1], c='r')\n",
        "execution_status": "failure"
      },
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        "value": "plt.show()\n",
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          "module": "scipy",
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          "kind": "assets",
          "path": "fig-1d3b0f5b7f1f1246.png"
        }
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    "title": [],
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    {
      "__type": "SeeAlsoItem",
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      "name": {
        "__type": "CrossRef",
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        "value": "kmeans2",
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          "__type": "Paragraph",
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          "children": [
            {
              "__type": "Text",
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              "value": "a different implementation of k-means clustering with more methods for generating initial centroids but without using a distortion change threshold as a stopping criterion."
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          ]
        }
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    {
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              "value": "must be called prior to passing an observation matrix to kmeans."
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}