12 - Tiny-ImageNet and YOLO v2 Anchor Boxes/EVA4S12_YOLOv2_Anchor_Boxes.ipynb

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      "name": "python3",
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      "pygments_lexer": "ipython3",
      "version": "3.6.6"
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    "colab": {
      "name": "EVA4S12 - YOLOv2 Anchor Boxes.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aO-7t1Y7-hV4",
        "colab_type": "text"
      },
      "source": [
        "# Imports\n",
        "Importing necessary packages and modules"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-yVpodAMpoCi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "%matplotlib inline\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.collections import PatchCollection\n",
        "from matplotlib.patches import Rectangle"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W5VeEGdPqjZ5",
        "colab_type": "text"
      },
      "source": [
        "# Data Preparation\n",
        "\n",
        "Parse the JSON file to obtain annotations.\n",
        "\n",
        "<br/>\n",
        "\n",
        "### JSON File Structure\n",
        "\n",
        "The annotation file will be of COCO format and have the following structure\n",
        "- **images**\n",
        "  - **id**: Image id\n",
        "  - **width**: Width of the image\n",
        "  - **height**: Height of the image\n",
        "  - **filename**: Image file name\n",
        "  - **license**: License id for the image\n",
        "  - **date_captured**: Date of capture of the image\n",
        "- **annotations**\n",
        "  - **id**: Annotation id\n",
        "  - **image_id**: Id of the image the annotation is associated with\n",
        "  - **category_id**: Id of the class the annotation belongs to\n",
        "  - **segmentation**: (x, y) coordinates of the four corners of the bounding box\n",
        "  - **area**: Area of the bounding box\n",
        "  - **bbox**: (x, y) coordinate of the top-left corner and width and height of the bounding box\n",
        "  - **iscrowd**: If the image has a crowd of objects denoted by this annotation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YFH7EYOYiTPw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def load_json(path):\n",
        "    \"\"\"Read the input JSON file.\n",
        "\n",
        "    Args:\n",
        "        path (str): Path to the JSON file.\n",
        "    \n",
        "    Returns:\n",
        "        Image annotations.\n",
        "    \"\"\"\n",
        "    with open(path) as f:\n",
        "        img_annotations = eval(f.read())\n",
        "    return img_annotations"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JHrJgNyXqxgP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def fetch_data_points(img_annotations):\n",
        "    \"\"\"Fetch data points from the image\n",
        "    annotations.\n",
        "\n",
        "    Args:\n",
        "        img_annotations (dict): Image annotations.\n",
        "    \n",
        "    Returns:\n",
        "        Array containing data points.\n",
        "    \"\"\"\n",
        "    data_points = []\n",
        "    for annotation in img_annotations['annotations']:\n",
        "        bbox = annotation['bbox']\n",
        "        img = img_annotations['images'][int(annotation['image_id'])]\n",
        "\n",
        "        # Normalize the height and width of the bounding box\n",
        "        data_points.append((\n",
        "            bbox[2] / img['width'],\n",
        "            bbox[3] / img['height']\n",
        "        ))\n",
        "    return np.array(data_points)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2pfOA6_e0KWz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "img_annotations = load_json('dogs.json')\n",
        "data_points = fetch_data_points(img_annotations)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sQfts7wxrX6x",
        "colab_type": "text"
      },
      "source": [
        "## Visualize Data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "89BayfGMXIuY",
        "colab_type": "text"
      },
      "source": [
        "Display a scatter plot of the height and width of the normalized bounding boxes"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ISCNvp4-0XrE",
        "colab_type": "code",
        "outputId": "ad94ac7d-5b6b-474e-e45c-5771742f03b1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        }
      },
      "source": [
        "plt.scatter(data_points[:, 0], data_points[:, 1])\n",
        "plt.xlabel('width')\n",
        "plt.ylabel('height')"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'height')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Iny2CdF_XXJi",
        "colab_type": "text"
      },
      "source": [
        "Display a scatter plot of the log of height and width of the normalized bounding boxes"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pVuwf10JWowk",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "37943e3c-0d65-4ea2-dd5f-fe0520b961d8"
      },
      "source": [
        "plt.scatter(np.log(data_points[:, 0]), np.log(data_points[:, 1]))\n",
        "plt.xlabel('log(width)')\n",
        "plt.ylabel('log(height)')"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'log(height)')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TX3Ld3Lfrmv_",
        "colab_type": "text"
      },
      "source": [
        "# K-Means Clustering"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AIKzfJYFXqF1",
        "colab_type": "text"
      },
      "source": [
        "Define the K-Means algorithm"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9CzBxKst0cED",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class KMeans:\n",
        "    \"\"\"K-Means clustering algorithm.\"\"\"\n",
        "\n",
        "    def __init__(self, num_clusters, points, iterations):\n",
        "        \"\"\"Initialize parameters of the algorithm.\n",
        "\n",
        "        Args:\n",
        "            num_clusters (int): Number of clusters to\n",
        "                segment the data into.\n",
        "            points (numpy.ndarray): Points in the dataset.\n",
        "            iterations (int): Number of iterations for\n",
        "                running the algorithm.\n",
        "        \"\"\"\n",
        "        self.num_clusters = num_clusters\n",
        "        self.points = points\n",
        "        self.iterations = iterations\n",
        "\n",
        "        self.centroids = self.initialize_centroids()\n",
        "        self.closest = None\n",
        "        self.mean_iou = None\n",
        "\n",
        "        self.find_clusters()\n",
        "        self.iou()\n",
        "\n",
        "    def initialize_centroids(self):\n",
        "        \"\"\"Select random inital centroids from the points.\n",
        "        \n",
        "        Returns:\n",
        "            Array containing initial centroids.\n",
        "        \"\"\"\n",
        "        centroids = self.points.copy()\n",
        "        np.random.shuffle(centroids)\n",
        "        return centroids[:self.num_clusters]\n",
        "\n",
        "    def closest_centroid(self):\n",
        "        \"\"\"Find the closest centroid for each point in the dataset.\"\"\"\n",
        "        distances = np.sqrt(\n",
        "            ((self.points - self.centroids[:, np.newaxis]) ** 2).sum(axis=2)\n",
        "        )\n",
        "        self.closest = np.argmin(distances, axis=0)\n",
        "\n",
        "    def move_centroids(self):\n",
        "        \"\"\"Find new centroids based on the points in the cluser.\"\"\"\n",
        "        self.centroids =  np.array([\n",
        "            self.points[self.closest == k].mean(axis=0)\n",
        "            for k in range(self.centroids.shape[0])\n",
        "        ])\n",
        "    \n",
        "    def find_clusters(self):\n",
        "        \"\"\"Run the K-Means algorithm.\"\"\"\n",
        "        for _ in range(self.iterations):\n",
        "            self.closest_centroid()\n",
        "            self.move_centroids()\n",
        "    \n",
        "    def iou(self):\n",
        "        \"\"\"Calculate Intersection over Union (IoU) for each point\n",
        "        with its closest centroid.\"\"\"\n",
        "        closest_centroids = self.centroids[self.closest]\n",
        "        width = np.minimum(\n",
        "            closest_centroids[:, 0], self.points[:, 0]\n",
        "        )\n",
        "        height = np.minimum(\n",
        "            closest_centroids[:, 1], self.points[:, 1]\n",
        "        )\n",
        "\n",
        "        intersection = width * height\n",
        "        points_area = self.points[:, 0] * self.points[:, 1]\n",
        "        cluster_area = closest_centroids[:, 0] * closest_centroids[:, 1]\n",
        "\n",
        "        self.mean_iou = np.mean(\n",
        "            intersection / (points_area + cluster_area - intersection)\n",
        "        )"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lvUxzJLKXvSi",
        "colab_type": "text"
      },
      "source": [
        "Run the algorithm for a number of clusters ranging from 1 to 18. Store the mean IoU for each cluster in a list."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tRd6P4Cz9NgF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# List containing the mean IoU for each set of\n",
        "# number of clusters\n",
        "iou_list = []\n",
        "kmeans_model = {}\n",
        "\n",
        "# Range of number of clusters to try out\n",
        "num_clusters_start = 1\n",
        "num_clusters_end = 16\n",
        "\n",
        "# Number of iterations to run each pass\n",
        "iterations = 300\n",
        "\n",
        "# Run K-Means for each range of number of clusters\n",
        "for k in range(num_clusters_start, num_clusters_end + 1):\n",
        "    kmeans_model[k + 1] = KMeans(k + 1, data_points, iterations)\n",
        "    iou_list.append(kmeans_model[k + 1].mean_iou)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oN3CBY9gfp7D",
        "colab_type": "text"
      },
      "source": [
        "## Visualize Results"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RlhOAhUWfuE7",
        "colab_type": "text"
      },
      "source": [
        "Display the Number of clusters vs Mean IoU graph"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hDvgXwy4DSfs",
        "colab_type": "code",
        "outputId": "4a3048c9-834d-4a20-8120-2e7255d2ee06",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        }
      },
      "source": [
        "fig = plt.figure(figsize=(9, 5))\n",
        "\n",
        "_ = plt.plot(iou_list, '-s', markeredgecolor='green', markeredgewidth=3)\n",
        "\n",
        "plt.xlabel('Number of Clusters (k)')\n",
        "plt.ylabel('Mean IoU')\n",
        "\n",
        "plt.xticks(np.arange(len(iou_list)), np.arange(1, len(iou_list)+1))\n",
        "plt.title('Number of Clusters vs Mean IoU')\n",
        "\n",
        "fig.savefig('kmeans_iou.png')"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HaknTPoPf08j",
        "colab_type": "text"
      },
      "source": [
        "For the above plot, k = 3 or k = 4 seems to be the best choice because for after 4, the curve becomes almost linear."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tjdA3Fi70fpZ",
        "colab_type": "text"
      },
      "source": [
        "## Plot clusters\n",
        "\n",
        "Let's display plots for points with k = 3 and k = 4"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YTK--Qs2f3tN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def display_clusters(kmeans):\n",
        "    num_clusters = kmeans.num_clusters\n",
        "\n",
        "    # Plot points for each cluster\n",
        "    for cluster_id in range(num_clusters):\n",
        "        points = kmeans.points[kmeans.closest == cluster_id]\n",
        "        plt.scatter(points[:, 0], points[:, 1])\n",
        "    \n",
        "    # Plot centroids\n",
        "    plt.scatter(kmeans.centroids[:, 0], kmeans.centroids[:, 1], c='black', s=90, marker='x')\n",
        "    plt.xlabel('width')\n",
        "    plt.ylabel('height')\n",
        "    plt.title(f'Cluster Plot for k = {num_clusters}')\n",
        "\n",
        "    # Save figure\n",
        "    plt.savefig(f'cluster_plot_k{num_clusters}.png')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sLeNZIxDBTzg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "outputId": "78a36d41-d8fd-420a-f10d-92769894c6dc"
      },
      "source": [
        "# Plot for k = 3\n",
        "display_clusters(kmeans_model[3])"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AE0/u2fv4d3/a3fa7mfPSJePqpFYGWSaCNcBxkmaQJIDZwLuG7fOfwKnAdZJeAhwMZN/304Qyl1LIw2D5WBaMyYqrk1q3y6zNHxFPAhcCq4EHSGYH3S9psaQz090+BnxQ0k+BG4Dzw6t+d1weBsvdJWPWPpneWRwRt5IMAldvu7Tq8XrglCxjsNFrx93Mje5edpeMWfu4xIQ9zfzTj9+v4im0drC82Yqq7pIxa49OzxqyHMr6bmbfvWyWL24R2F7tKjaXhzEIM9vHLQID2ltfqcw37JnlkROBAe3trsnbDXtZl7LIQ6kMs3rcNWRAe7tr8nTDXqWUReUu5kopC6AlA9VZH9+sFZwIDGj/Ajh5uWEv6+qirl5qReCuIQPy113TLlmXsshLqQyzepwIDGj/Ajh5kXV1UVcvtSJw15DtlZfumna6+KSL9+vDh9aWsmh0/FWbVvnuaes4JwIrtaxLWdQ7vgeSLS9UtBpvvb29MTg42OkwzA7YaTedVrPC6uRDJvOdd36nAxFZN5N0T0T01nrNYwTW9fI6j98DyZYXTgTW1fKy5GUtHki2vHAisK6WlyUva/GaC5YXHiy2rpbn7hevuWB54URQIJs3b2b58uUsXLgQSU97PSJYunQpc+bMYdq0aR2IsLVaUQ01T0te1uI1FywP3DVUIMuXL6e/v5958+YxfLZXRDBv3jz6+/tZvnx5hyJsnVZVQy1K90teB7StHNwiKJCFCxeyfft2BgYGAFi2bBmS9iaBgYEB5s6dy8KFCzsc6YGrVw11NK2CInS/+H4C6zQnggKRxLJlywD2SwbVSaCSHIquldVQ89794sJ01mlOBAUzPBlUEkI3JQFofzXUTsrzgLaVg8cICqg6GVR0UxKAclVD9f0E1mmZJgJJsyRtkLRR0oIar18p6Sfp14OSdmQZTxHcsnaIUy6/nRkLVnHK5bfXHBytjAlUqzWAXGRlqoZalAFt616ZdQ1JGgdcDbwJ2AKskbQyItZX9omIj1bt/xHgxKziKYLKTJnKIGllpgzsW9Vr+MBw9RgBdFfLoCzVUIswoG3dralEIOmrEfGeRtuGORnYGBGb0v1vBM4C1o+w/3nAPzYTT5HVmxvfaKZMrSQw0gBytySDssj7gLZ1t2ZbBC+tfpJe7b+ywXumAA9XPd8CvKrWjpKmATOA20d4/QLgAoBjjjmmuYhzqNEVf6OZMkuXLq05O2h4Mujp6aGvry/rX8fMukTdRCDpEmAhMEHS7yubgT8D17QwjtnATRHxVK0XI+Kays/r7e0tbEd4oyv+RjNl5syZA1DzzuJKMujp6dm7n5lZM+oOFkfEZRFxGHBFRByefh0WEc+LiEsaHHsIOLrq+dR0Wy2zgRuajrqgGl3xN5opM23aNPr6+kbs9pFEX19fV5SXMLP2aaprKCIukTQFmFb9noi4s87b1gDHSZpBkgBmA+8avpOkFwPPAe4aRdyF1OiKv3qs4EDq65iZjUazg8WXk5zI1wOVvo0ARkwEEfGkpAuB1cA44NqIuF/SYmAwIlamu84Gboxumvs4gvmnH7/fGAE8fW58WWbKmFl+NLVUpaQNwMyIeCL7kOor+lKVraioaWY2WvWWqmx21tAmYDzQ8URQdL7iN7O8aTRr6J9JuoD+BPxE0m1UJYOIuCjb8MzMLGuNWgSVPph7gJX1djQzs2Kqmwgi4vp2BWJmZp3R7Kyh+0i6iKrtJGkxfDIiftPqwMzMrD2aHSz+Nsm00a+nz2cDzwYeBa4D3tbyyKwtPIvJzJpNBG+MiJOqnt8n6d6IOEmS6xkUVDPVTs2s+zW7HsE4SSdXnkj6K5KbxACebHlUBjS3NsGBqFf7yMzKo9kWwQeAayUdSlJ07vfAByQdAlyWVXBl1o6r9VauC2xmxdVsraE1wMslHZE+31n18oosAus2o+2Lb1SptBXKtC6wmY2s0Q1lcyJiuaR5w7YDEBHLar7R9jOWq/t2XK03U/vIzLpfozGCQ9Lvh43wZU0YS1/8SFflrbxaL9O6wGY2skY3lP1r+v0T7QmnO43l6r5dV+uufWRmTc0akvQiSbdJ+ln6fKak/mxD6x5jubr31bqZtUuzs4a+CMwHKi2EdZK+Dnwyq8C6yViv7n21bmbt0GwieHZE/MewJRJ9/0CTvPKYmeVZs4lgu6QXkNYbkvRO4JHMoupCvro3s7xqNhF8GLgGeLGkIeCXwLszi8rMWmPdCrhtMezcAkdMhVMvhZnndjoqy5lmE8EQ8GXgDuC5JHcWvxdYnFFcZnag1q2Ab10Eu9PZaTsfTp6Dk4Htp9laQ/+HpMLobmAr8EfgsayCMrMWuG3xviRQsXtXst2sSrMtgqkRMSvTSMystXZuGd12K61mE8GPJb08Iu7LNJqcc+1+K5QjpibdQbW2m1Wp2zUk6T5J64C/Ae6VtEHSuqrtdUmalb5no6QFI+xzrqT1ku5P703IpUq9oKEduwj21QtqdWlos5Y59VIYP+ymxfETku1mVRq1CN461gNLGgdcDbwJ2AKskbQyItZX7XMccAlwSkT8TtLzx/rzstaOaqCj5RaK1VUZEPasIWugUa2hzQdw7JOBjRGxCUDSjcBZwPqqfT4IXB0Rv0t/3q8P4OdlKm+1+726mDVl5rk+8VtDzc4aGospQHUH5ZZ0W7UXAS+S9CNJd0uqOSAt6QJJg5IGt23bllG49TVTLyjrFcWqeXUxM2uVLBNBM54BHAe8HjgP+KKkicN3iohrIqI3InonTZrU5hAT808/ngnjx+23rbpeULvHEPLWQjGz4soyEQwBR1c9n5puq7YFWBkRuyPil8CDJIkhdxpVA233FXo71ivIQjtbTWbWnGanj47FGuA4STNIEsBs4F3D9rmFpCXwZUk9JF1FmzKM6YDUqxfU7iv0Iq4u5nENs3zKrEUQEU8CFwKrgQeAFRFxv6TFks5Md1sN/EbSepLyFfMj4jdZxZSldl+h12uh5PWqu6vHNdatgCtfBosmJt/XdWgp77zEYYWiiOh0DKPS29sbg4ODnQ7jaYZf7UJyhd7uxWTyEkctMxasotZfm4BfXn5Gu8NpneE1fSCZr/+2z7Z3xk5e4rBcknRPRPTWeq3Tg8VdIy8riuX5qruo4xoN5aWmT17isMLJcoygdPKw5kCeZxMVcVyjKXmp6ZOXOKxw3CLoMnm+6s5Lq6nlRqrd0+6aPnmJwwrHLYIuk/er7jy0mlru1Etr9823u6ZPXuKwwnEi6DJeH7kD8lLTJy9xWOF41pCZWQl41pCZmY3IicDMrOScCMzMSs6JwMys5JwIzMxKzonAzKzknAjMSmDz5s0sWbKEkaaLRwRLlixh8+YDWZ3WisqJwKwEli9fTn9/P/PmzXtaMogI5s2bR39/P8uXL+9QhNZJvrPYrJPWrWjLncALFy5k+/btDAwMALBs2TIk7U0CAwMDzJ07l4ULF7b8Z1v+ORGYdcrw9QN2Ppw8h5YnA0ksW7YMYL9kUJ0EKsnBysclJsw65cqXJSf/4Y44Gj76s+Rxi1sM1S2ACieBcqhXYsKJwKxTFk2EkdZsW7QjsxXHIoKDDto3PLhnzx4ngRJwrSGzPGq0fkAGK45VWgTVag0gW7k4EZh1yqmXJlf41arXD2jximPDB4b37NnD3LlzGRgYcDIoOQ8Wm3VKo/UDjpg6whjC6FccG54EKmMCtQaQ3U1UPk4EZp0089yR+/tbuOLY0qVLa84OGp4Menp66OvrG/XxrdgyTQSSZgFXAeOAL0XE5cNePx+4AhhKN30uIr6UZUxmhdHCFcfmzJkDJPcTDL/irySDnp6evftZuWQ2a0jSOOBB4E3AFmANcF5ErK/a53ygNyIubPa4njVkZjZ6nZo1dDKwMSI2RcSfgRuBszL8eWZmNgZZJoIpQPVI15Z023DvkLRO0k2Sjs4wHjMzq6HT00e/BUyPiJnAd4Hra+0k6QJJg5IGt23b1tYAzcy6XZaJYAiovsKfyr5BYQAi4jcR8UT69EvAK2sdKCKuiYjeiOidNGlSJsGamZVVlolgDXCcpBmSngnMBlZW7yBpctXTM4EHMozHzMxqyGz6aEQ8KelCYDXJ9NFrI+J+SYuBwYhYCVwk6UzgSeC3wPlZxWNmZrW56JyZWQm46JyZmY3IicDMrOScCMzMSs6JwMys5JwIzMxKzonAzKzknAjMzErOicDMrOScCMzMSs6JwMys5JwIzMxKzonAzKzknAjMzEouszLUeXLL2iGuWL2BrTt2cdTECcw//XjOPrHWqplmZuXT9YnglrVDXHLzfeza/RQAQzt2ccnN9wE4GZiZUYKuoStWb9ibBCp27X6KK1Zv6FBEZmb50vWJYOuOXaPabmZWNl2fCI6aOGFU283MyqbrE8H8049nwvhx+22bMH4c808/vkMRmZnlS9cPFlcGhD1ryMystq5PBJAkA5/4zcxq6/quITMzq8+JwMys5DJNBJJmSdogaaOkBXX2e4ekkNSbZTxmZvZ0mSUCSeOAq4E3AycA50k6ocZ+hwEXA/+eVSxmZjayLFsEJwMbI2JTRPwZuBE4q8Z+/wR8Cng8w1jMzGwEWSaCKcDDVc+3pNv2knQScHRErKp3IEkXSBqUNLht27bWR5qhW9YOccrltzNjwSpOufx2blk71OmQzMz207HBYkkHAcuAjzXaNyKuiYjeiOidNGlS9sG1SKXg3dCOXQT7Ct45GZhZnmSZCIaAo6ueT023VRwGvAz4vqSHgFcDK7tpwNgF78ysCLJMBGuA4yTNkPRMYDawsvJiROyMiJ6ImB4R04G7gTMjYjDDmNrKBe/MrAgySwQR8SRwIbAaeABYERH3S1os6cysfm6euOCdmRVBpiUmIuJW4NZh2y4dYd/XZxlLJ8w//fj9FsUBF7wzs/wpRa2hTnHBOzMrAieCjLngnZnlnWsNmZmVnBOBmVnJORGYmZWcE4GZWck5EZiZlZwTgZlZyTkRmJnl3boVcOXLYNHE5Pu6FS09vO8jMDPLs3Ur4FsXwe60RtnOh5PnADPPbcmPcIvAzCzPblu8LwlU7N6VbG8RJwIzszzbuWV028fAicDMLM+OmDq67WPgRGBmlmenXgrjh5WuHz8h2d4iTgRmZnk281x422fhiKMBJd/f9tmWDRSDZw2ZmeXfzHNbeuIfzi0CM7OScyIwMys5JwIzs5JzIjAzKzknAjOzklNEdDqGUZG0Ddjc4sP2ANtbfMxWcFyjl9fYHNfo5TW2osY1LSIm1XqhcIkgC5IGI6K303EM57hGL6+xOa7Ry2ts3RiXu4bMzErOicDMrOScCBLXdDqAETiu0ctrbI5r9PIaW9fF5TECM7OSc4vAzKzknAjMzEquVIlA0ixJGyRtlLSgxuvzJK2XtE7SbZKm5SSuD0m6T9JPJP1Q0gl5iKtqv3dICkltm1LXxGd2vqRt6Wf2E0kfyENc6T7npn9n90v6eh7iknRl1Wf1oKQd7YirydiOkXSHpLXp/8235CSuael5Yp2k70tq3Uox9eO6VtKvJf1shNcl6bNp3OskndTwoBFRii9gHPAL4FjgmcBPgROG7fNfgGenj/8e+LecxHV41eMzgf+bh7jS/Q4D7gTuBnpz9G95PvC5HP6NHQesBZ6TPn9+HuIatv9HgGtz9JldA/x9+vgE4KGcxPUN4L3p4zcAX23TZ/a3wEnAz0Z4/S3AtwEBrwb+vdExy9QiOBnYGBGbIuLPwI3AWdU7RMQdEfGn9OndQDsyfDNx/b7q6SFAO0b4G8aV+ifgU8DjbYhptLG1WzNxfRC4OiJ+BxARv85JXNXOA25oQ1zQXGwBHJ4+PgLYmpO4TgBuTx/fUeP1TETEncBv6+xyFvCVSNwNTJQ0ud4xy5QIpgAPVz3fkm4byftJsmrWmopL0ocl/QL4NHBRHuJKm5xHR8SqNsRTrdl/y3ekTeObJB2dk7heBLxI0o8k3S1pVk7iApLuDmAG+05wWWsmtkXAHElbgFtJWix5iOunwDnp47cDh0l6Xhtia2S057pSJYKmSZoD9AJXdDqWioi4OiJeAPwD0N/peCQdBCwDPtbpWEbwLWB6RMwEvgtc3+F4Kp5B0j30epIr7y9KmtjRiPY3G7gpItCrkw4AAAM7SURBVJ7qdCBVzgOui4ipJN0eX03//jrt48DrJK0FXgcMAXn63JqWhw+zXYaA6qvCqem2/Uh6I9AHnBkRT+Qlrio3AmdnGlGiUVyHAS8Dvi/pIZK+yJVtGjBu+JlFxG+q/v2+BLwyD3GRXJ2tjIjdEfFL4EGSxNDpuCpm075uIWgutvcDKwAi4i7gYJICax2NKyK2RsQ5EXEiyTmDiGjbIHsdoz2nlGqw+BnAJpJmb2Xw56XD9jmRZIDouJzFdVzV47cBg3mIa9j+36d9g8XNfGaTqx6/Hbg7J3HNAq5PH/eQNOGf1+m40v1eDDxEeqNpjv4tvw2cnz5+CckYQaYxNhlXD3BQ+ngJsLiNn9t0Rh4sPoP9B4v/o+Hx2hV4Hr5ImpUPpif7vnTbYpKrf4DvAb8CfpJ+rcxJXFcB96cx3VHvhNzOuIbt27ZE0ORndln6mf00/cxenJO4RNKlth64D5idh7jS54uAy9v1bziKz+wE4Efpv+VPgNNyEtc7gZ+n+3wJeFab4roBeATYTdLCfD/wIeBDVX9jV6dx39fM/0uXmDAzK7kyjRGYmVkNTgRmZiXnRGBmVnJOBGZmJedEYGZWck4EZmMg6dZadwRLWiTp4+nj8yUdVfXaQ5KyvhHKbNScCMzGICLeEo3vIj0fOKrBPmYd50RgVoOk+ZIuSh9fKen29PEbJH2t+upeUl9aw/+HwPHptneS1Kv6Wlrjf0J66I9IujddX+LF7f/NzJ7OicCsth8Ar00f9wKHShqfbruzspOkV5LU53kFyZ2ofwUQETcBg8C7I+IVEbErfcv2iDgJ+DxJ0TKzjnMiMKvtHuCVkg4HngDuIkkIryVJEhWvBb4ZEX+KZN2IlQ2Oe3PV8ae3NGKzMXpGpwMwy6OI2C3plyT9/D8G1pGsYPdC4IEDOHSlIupT+P+f5YRbBGYj+wFJ982d6eMPAWtj/wJddwJnS5og6TCS6rAVfyAp122Wa04EZiP7ATAZuCsifkWyHGd1txARcS/wbySVMb8NrKl6+TrgC8MGi81yx9VHzcxKzi0CM7OScyIwMys5JwIzs5JzIjAzKzknAjOzknMiMDMrOScCM7OS+/99ydUXJbLLfgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JHL0MKpTbmQx",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "outputId": "0515dcda-a609-4e25-e8e7-86d487a6cd22"
      },
      "source": [
        "# Plot for k = 4\n",
        "display_clusters(kmeans_model[4])"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8qWKYAAMsGmq",
        "colab_type": "text"
      },
      "source": [
        "# Plot Anchor Boxes\n",
        "Plot the anchor boxes obtained for k = 3 and k = 4"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6WIg_lhTp8bo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def make_anchor_boxes(ax, clusters, edgecolor='b', alpha=1):\n",
        "    \"\"\"Make anchor boxes given cluster centroids.\"\"\"\n",
        "\n",
        "    xdata = np.array([0.5]*len(clusters))\n",
        "    ydata = np.array([0.5]*len(clusters))\n",
        "\n",
        "    xerror = np.array([list(np.exp(clusters[:, 0])/2)]*2)\n",
        "    yerror = np.array([list(np.exp(clusters[:, 1])/2)]*2)\n",
        "\n",
        "    # Create list for all the error patches\n",
        "    errorboxes = []\n",
        "\n",
        "    # Loop over data points; create box from errors at each point\n",
        "    for x, y, xe, ye in zip(xdata, ydata, xerror.T, yerror.T):\n",
        "        rect = Rectangle((x - xe[0], y - ye[0]), xe.sum(), ye.sum())\n",
        "        errorboxes.append(rect)\n",
        "\n",
        "    # Create patch collection with specified colour/alpha\n",
        "    pc = PatchCollection(\n",
        "        errorboxes, facecolor='None', alpha=alpha, edgecolor=edgecolor\n",
        "    )\n",
        "\n",
        "    # Add collection to axes\n",
        "    ax.add_collection(pc)\n",
        "\n",
        "    # Plot errorbars\n",
        "    artists = ax.errorbar(\n",
        "        xdata, ydata, xerr=xerror, yerr=yerror, fmt='None', ecolor='None'\n",
        "    )\n",
        "\n",
        "    return artists"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7KVIuZUjwJim",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "84ffc2a9-1738-47de-f93f-aef2b0b6e7cf"
      },
      "source": [
        "# Create figure and axes\n",
        "fig, ax = plt.subplots(1)\n",
        "\n",
        "# Create error boxes\n",
        "_ = make_anchor_boxes(ax, kmeans_model[3].centroids)\n",
        "\n",
        "# Show plot\n",
        "plt.title('Anchor boxes for k = 3')\n",
        "plt.show()\n",
        "fig.savefig('anchor_bbox_k3.png')"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j5R1OCpBwR3n",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "55d7e4b6-e989-4d0b-c66b-fa1232443bc1"
      },
      "source": [
        "# Create figure and axes\n",
        "fig, ax = plt.subplots(1)\n",
        "\n",
        "# Create error boxes\n",
        "_ = make_anchor_boxes(ax, kmeans_model[4].centroids)\n",
        "\n",
        "# Show plot\n",
        "plt.title('Anchor boxes for k = 4')\n",
        "plt.show()\n",
        "fig.savefig('anchor_bbox_k4.png')"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_8nn-1VO1K6j",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}