Roko_Ch_9.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "02afaeb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "from sklearn.cluster import KMeans\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "\n",
    "blob_centers = np.array([[ 0.2,  2.3], [-1.5 ,  2.3], [-2.8,  1.8],\n",
    "                         [-2.8,  2.8], [-2.8,  1.3]])\n",
    "\n",
    "blob_std = np.array([0.4, 0.3, 0.1, 0.1, 0.1])\n",
    "\n",
    "X, y = make_blobs(n_samples=20000, centers=blob_centers,\n",
    "                  cluster_std = blob_std, random_state=42)\n",
    "k = 5\n",
    "kmeans = KMeans(n_clusters=k, random_state=42)\n",
    "y_pred = kmeans.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ba7e0185",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20000, 2)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "04f12242",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_clusters(X, y=None):\n",
    "    plt.scatter(X[:, 0], X[:, 1], c=y, s=1)\n",
    "    plt.xlabel(\"$x_1$\")\n",
    "    plt.ylabel(\"$x_2$\", rotation=0)\n",
    "\n",
    "plt.figure(figsize=(8, 4))\n",
    "plot_clusters(X)\n",
    "plt.gca().set_axisbelow(True)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f7e4f3a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KMeans(n_clusters=5, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">KMeans</label><div class=\"sk-toggleable__content\"><pre>KMeans(n_clusters=5, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "KMeans(n_clusters=5, random_state=42)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "95f5eabf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 1, 4, ..., 3, 3, 1], dtype=int32)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a26b527a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.21932512,  2.29450604],\n",
       "       [-2.7935198 ,  2.79787767],\n",
       "       [-2.80040642,  1.29828066],\n",
       "       [-1.46832891,  2.30446828],\n",
       "       [-2.79308043,  1.80260618]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans.cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "53485e2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, 1], dtype=int32)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#You can easily assign new instances to the cluster whose centroid\n",
    "#is closest:\n",
    "\n",
    "X_new = np.array([[0, 2], [3, 2], [-3, 3], [-3, 2.5]])\n",
    "kmeans.predict(X_new)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e5d0721e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.37, 2.91, 2.89, 1.5 , 2.8 ],\n",
       "       [2.8 , 5.85, 5.84, 4.48, 5.8 ],\n",
       "       [3.3 , 0.29, 1.71, 1.68, 1.22],\n",
       "       [3.23, 0.36, 1.22, 1.54, 0.73]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The vast majority of the instances were clearly assigned to\n",
    "#the appropriate cluster, but a few instances were probably mislabeled,\n",
    "#especially near the boundary between the top-left cluster and the \n",
    "#central cluster. Indeed, the k- means algorithm does not behave very\n",
    "#well when the blobs have very different diameters because all it \n",
    "#cares about when assigning an instance to a cluster is the distance\n",
    "#to the centroid.\n",
    "\n",
    "#Instead of assigning each instance to a single cluster, which is\n",
    "#called hard clustering, it can be useful to give each instance a\n",
    "#score per cluster, which is called soft clustering. The score can\n",
    "#be the distance between the instance and the centroid or a similarity\n",
    "#score (or affinity), such as the Gaussian radial basis function we\n",
    "#used in Chapter 2. In the KMeans class, the transform() method \n",
    "#measures the distance from each instance to every centroid:\n",
    "    \n",
    "    \n",
    "kmeans.transform(X_new).round(2)\n",
    "\n",
    "\n",
    "#In this example, the first instance in X_new is located at a \n",
    "#distance of about 0.37, from the first centroid, 2.91 from the \n",
    "#second centroid, 2.89 from the third centroid, 1.5 from the fourth\n",
    "#centroid, and 2.8 from the fifth centroid. If you have a \n",
    "#high-dimensional dataset and you transform it this way, you end\n",
    "#up with a k-dimensional dataset: this transformation can be a very\n",
    "#efficient nonlinear dimensionality reduction technique. \n",
    "#Alternatively, you can use these distances as extra features \n",
    "#to train another model, as in Chapter 2.\n",
    "\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4877df35",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Although the algorithm is guaranteed to converge, it may not \n",
    "#converge to the right solution (i.e., it may converge to a local \n",
    "#optimum): whether it does or not depends on the centroid initialization\n",
    "#. Figure 9-5 shows two suboptimal solutions that the algorithm can\n",
    "#converge to if you are not lucky with the random initialization step.\n",
    "\n",
    "\n",
    "#Let’s take a look at a few ways you can mitigate this risk by \n",
    "#improving the centroid initialization.\n",
    "#Centroid initialization methods\n",
    "#If you happen to know approximately where the centroids should be\n",
    "#(e.g., if you ran another clustering algorithm earlier), then you\n",
    "#can set the init hyperparameter to a NumPy array containing the list\n",
    "#of centroids, and set n_init to 1:\n",
    "\n",
    "good_init = np.array([[-3, 3], [-3, 2], [-3, 1], [-1, 2], [0, 2]])\n",
    "kmeans = KMeans(n_clusters=5, init=good_init, n_init=1, random_state=42)\n",
    "kmeans.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "370c6e80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2188.833977942637"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Another solution is to run the algorithm multiple times with \n",
    "#different random initializations and keep the best solution. \n",
    "#The number of random initializations is controlled by the n_init \n",
    "#hyperparameter: by default it is equal to 10, which means that the\n",
    "#whole algorithm described earlier runs 10 times when you call fit(),\n",
    "#and Scikit-Learn keeps the best solution. But how exactly does it \n",
    "#know which solution is the best? It uses a performance metric! \n",
    "#That metric is called the model’s inertia, which is the sum of the\n",
    "#squared distances between the instances and their closest centroids.\n",
    "#It is roughly equal to 219.4 for the model on the left in Figure 9-5,\n",
    "#258.6 for the model on the right in Figure 9-5, and only 211.6 for \n",
    "#the model in Figure 9- 3. The KMeans class runs the algorithm n_init \n",
    "#times and keeps the model with the lowest inertia. In this example,\n",
    "#the model in Figure 9-3 will be selected (unless we are very unlucky\n",
    "#with n_init consecutive random initializations). If you are curious, \n",
    "#a model’s inertia is accessible via the\n",
    "#inertia_ instance variable:\n",
    "\n",
    "\n",
    "kmeans.inertia_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d447c32e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2188.833977942637"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The score() method returns the negative inertia (it’s negative \n",
    "#because a predictor’s score() method must always respect Scikit-Learn’s\n",
    "#“greater is better” rule: if a predictor is better than another, its\n",
    "#score() method should return a greater score):\n",
    "\n",
    "kmeans.score(X)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "80679d2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>MiniBatchKMeans(n_clusters=5, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">MiniBatchKMeans</label><div class=\"sk-toggleable__content\"><pre>MiniBatchKMeans(n_clusters=5, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "MiniBatchKMeans(n_clusters=5, random_state=42)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Yet another important variant of the k-means algorithm was proposed\n",
    "#in a 2010 paper by David Sculley.5 Instead of using the full dataset\n",
    "#at each iteration, the algorithm is capable of using mini-batches, \n",
    "#moving the centroids just slightly at each iteration. This speeds up\n",
    "#the algorithm (typically by a factor of three to four) and makes it\n",
    "#possible to cluster huge datasets that do not fit in memory. \n",
    "#Scikit-Learn implements this algorithm in the MiniBatchKMeans class,\n",
    "#which you can use just like the KMeans class:\n",
    "\n",
    "\n",
    "from sklearn.cluster import MiniBatchKMeans\n",
    "\n",
    "minibatch_kmeans = MiniBatchKMeans(n_clusters=5, random_state=42)\n",
    "minibatch_kmeans.fit(X)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "eaa77307",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Limits of k-means\n",
    "#Despite its many merits, most notably being fast and scalable, \n",
    "#k-means is not perfect. As we saw, it is necessary to run the \n",
    "#algorithm several times to avoid suboptimal solutions, plus you \n",
    "#need to specify the number of clusters, which can be quite a hassle.\n",
    "#Moreover, k-means does not behave very well when the clusters have \n",
    "#varying sizes, different densities, or nonspherical shapes. For example,\n",
    "#Figure 9-11 shows how k-means clusters a dataset containing three \n",
    "#ellipsoidal clusters of different dimensions, densities, and \n",
    "#orientations.\n",
    "#As you can see, neither of these solutions is any good. The solution\n",
    "#on the left is better, but it still chops off 25% of the middle \n",
    "#cluster and assigns it to the cluster on the right. The solution\n",
    "#on the right is just terrible, even though its inertia is lower. \n",
    "#So, depending on the data, different clustering algorithms may \n",
    "#perform better. On these types of elliptical clusters, Gaussian \n",
    "#mixture models work great.\n",
    "\n",
    "\n",
    "#It is important to scale the input features (see Chapter 2) \n",
    "#before you run k-means, or the clusters may be very stretched \n",
    "#and k-means will perform poorly. Scaling the features does not \n",
    "#guarantee that all the clusters will be nice and spherical, but it \n",
    "#generally helps k-means.\n",
    "\n",
    "#Now let’s look at a few ways we can benefit from clustering. \n",
    "#We will use k- means, but feel free to experiment with other \n",
    "#clustering algorithms.\n",
    "\n",
    "#Using Clustering for Image Segmentation\n",
    "#Image segmentation is the task of partitioning an image into \n",
    "#multiple segments. There are several variants:\n",
    "#In color segmentation, pixels with a similar color get assigned \n",
    "#to the same segment. This is sufficient in many applications. \n",
    "#For example, if you want to analyze satellite images to measure \n",
    "#how much total forest area there is in a region, color segmentation\n",
    "#may be just fine.\n",
    "#In semantic segmentation, all pixels that are part of the same o\n",
    "#bject type get assigned to the same segment. For example, in a \n",
    "#self-driving car’s vision system, all pixels that are part of a \n",
    "#pedestrian’s image might be assigned to the “pedestrian” segment \n",
    "#(there would be one segment containing all the pedestrians).\n",
    "\n",
    "#In instance segmentation, all pixels that are part of the same \n",
    "#individual object are assigned to the same segment. In this case\n",
    "#there would be a different segment for each pedestrian.\n",
    "\n",
    "\n",
    "\n",
    "#The state of the art in semantic or instance segmentation today is\n",
    "#achieved using complex architectures based on convolutional neural \n",
    "#networks (see Chapter 14). In this chapter we are going to focus on\n",
    "#the (much simpler) color segmentation task, using k-means.\n",
    "\n",
    "#We’ll start by importing the Pillow package (successor to the Python\n",
    "#Imaging Library, PIL), which we’ll then use to load the ladybug.png \n",
    "#image (see the upper-left image in Figure 9-12), assuming it’s\n",
    "#located at filepath:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "9ee50547",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using Clustering for Semi-Supervised Learning\n",
    "\n",
    "\n",
    "#Another use case for clustering is in semi-supervised learning, when\n",
    "#we have plenty of unlabeled instances and very few labeled instances.\n",
    "#In this section, we’ll use the digits dataset, which is a simple\n",
    "#MNIST-like dataset containing 1,797 grayscale 8 × 8 images representing\n",
    "#the digits 0 to 9. First, let’s load and split the dataset (it’s already\n",
    "#shuffled):\n",
    "\n",
    "from sklearn.datasets import load_digits\n",
    "\n",
    "X_digits, y_digits = load_digits(return_X_y=True)\n",
    "X_train, y_train = X_digits[:1400], y_digits[:1400]\n",
    "X_test, y_test = X_digits[1400:], y_digits[1400:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "80b463ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7481108312342569"
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     "execution_count": 33,
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   ],
   "source": [
    "#We will pretend we only have labels for 50 instances. To get a \n",
    "#baseline performance, let’s train a logistic regression model on \n",
    "#these 50 labeled instances:\n",
    "\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "n_labeled = 50\n",
    "log_reg = LogisticRegression(max_iter=10000)\n",
    "log_reg.fit(X_train[:n_labeled], y_train[:n_labeled])\n",
    "\n",
    "#We can then measure the accuracy of this model on the test set \n",
    "#(note that the test set must be labeled):\n",
    "log_reg.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "9689ae3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#The model’s accuracy is just 74.8%. That’s not great: indeed, if you\n",
    "#try training the model on the full training set, you will find that\n",
    "#it will reach about 90.7% accuracy. Let’s see how we can do better.\n",
    "#First, let’s cluster the training set into 50 clusters. Then, for\n",
    "#each cluster, we’ll find the image closest to the centroid. We’ll\n",
    "#call these images the representative images:\n",
    "\n",
    "\n",
    "k = 50\n",
    "kmeans = KMeans(n_clusters=k, random_state=42)\n",
    "X_digits_dist = kmeans.fit_transform(X_train)\n",
    "representative_digit_idx = np.argmin(X_digits_dist, axis=0)\n",
    "X_representative_digits = X_train[representative_digit_idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "b333d201",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1400, 50)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_digits_dist.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "857d224f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1400, 64)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "86f310c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[53.8347602 , 41.42507119, 40.38645515, ..., 46.70298587,\n",
       "        43.32913642, 41.73144964],\n",
       "       [22.96665235, 50.3636375 , 45.70161035, ..., 48.27458499,\n",
       "        43.06000537, 50.03512655],\n",
       "       [29.42934195, 50.1412468 , 43.36356873, ..., 50.49457617,\n",
       "        47.66591091, 53.60050269],\n",
       "       ...,\n",
       "       [49.57764931, 56.45575913, 36.34319282, ..., 46.91590586,\n",
       "        54.17253975, 56.99134925],\n",
       "       [49.46706914, 55.89670767, 33.61503416, ..., 46.99966903,\n",
       "        53.61297942, 54.25569607],\n",
       "       [38.3721188 , 43.90294928, 48.93405716, ..., 43.3609143 ,\n",
       "        41.15263129, 37.04745455]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_digits_dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "01428bb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  5., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ..., 10.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ..., 16.,  9.,  0.],\n",
       "       ...,\n",
       "       [ 0.,  0.,  1., ...,  6.,  0.,  0.],\n",
       "       [ 0.,  0.,  2., ..., 12.,  0.,  0.],\n",
       "       [ 0.,  0., 10., ..., 12.,  1.,  0.]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "fc7e4aa6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 64)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_representative_digits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "574d41e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1120,  708,  582,  925,  597,  384,  798,  970,  768,  815,  885,\n",
       "       1387,  870,  141, 1084,   88, 1030,  310, 1312,  972,  410, 1168,\n",
       "        213,  579,  612, 1315,  463, 1075, 1005,  199,  558,  613,  877,\n",
       "       1352, 1327,  259, 1114,  652,  983,  115, 1328, 1050, 1336,  543,\n",
       "        938, 1227,  881,  685,  345,  438])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "representative_digit_idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "a0cadd78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8488664987405542"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Let’s look at each image and manually label them:\n",
    "y_representative_digits = np.array([\n",
    "    1, 3, 6, 0, 7, 9, 2, 4, 8, 9,\n",
    "    5, 4, 7, 1, 2, 6, 1, 2, 5, 1,\n",
    "    4, 1, 3, 3, 8, 8, 2, 5, 6, 9,\n",
    "    1, 4, 0, 6, 8, 3, 4, 6, 7, 2,\n",
    "    4, 1, 0, 7, 5, 1, 9, 9, 3, 7\n",
    "])\n",
    "\n",
    "\n",
    "#Now we have a dataset with just 50 labeled instances, but \n",
    "#instead of being random instances, each of them is a representative\n",
    "#image of its cluster. Let’s see if the performance is any better:\n",
    "\n",
    "\n",
    "log_reg = LogisticRegression(max_iter=10000)\n",
    "log_reg.fit(X_representative_digits, y_representative_digits)\n",
    "log_reg.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "be88289e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Wow! We jumped from 74.8% accuracy to 84.9%, although we are \n",
    "#still only training the model on 50 instances. Since it is often \n",
    "#costly and painful to label instances, especially when it has to \n",
    "#be done manually by experts, it is a good idea to label representative\n",
    "#instances rather than just random instances.\n",
    "\n",
    "#But perhaps we can go one step further: what if we propagated the \n",
    "#labels to all the other instances in the same cluster? This is \n",
    "#called label propagation:\n",
    "        \n",
    "        \n",
    "y_train_propagated = np.empty(len(X_train), dtype=np.int64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "89f8704d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1400,)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_propagated.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "113b378b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1400,)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans.labels_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "747ecb31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50,)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_representative_digits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "56099cf3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([32, 41, 39, ..., 40, 40, 43], dtype=int32)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "af3977f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_propagated = np.empty(len(X_train), dtype=np.int64)\n",
    "\n",
    "for i in range(k):\n",
    "    y_train_propagated[kmeans.labels_ == i] = y_representative_digits[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "c810cd06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1400,)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_propagated.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "35d1e8e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, ..., False, False, False])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans.labels_ == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "f40ba8d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 6, 0, 7, 9, 2, 4, 8, 9, 5, 4, 7, 1, 2, 6, 1, 2, 5, 1, 4, 1,\n",
       "       3, 3, 8, 8, 2, 5, 6, 9, 1, 4, 0, 6, 8, 3, 4, 6, 7, 2, 4, 1, 0, 7,\n",
       "       5, 1, 9, 9, 3, 7])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_representative_digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "907e52d2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rokosango/miniforge3/envs/homl3/lib/python3.10/site-packages/sklearn/linear_model/_logistic.py:444: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "  n_iter_i = _check_optimize_result(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.8967254408060453"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Now let’s train the model again and look at its performance:\n",
    "\n",
    "\n",
    "log_reg = LogisticRegression()\n",
    "log_reg.fit(X_train, y_train_propagated)\n",
    "log_reg.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "44cd45c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DBSCAN(eps=0.05)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">DBSCAN</label><div class=\"sk-toggleable__content\"><pre>DBSCAN(eps=0.05)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "DBSCAN(eps=0.05)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#DBSCAN\n",
    "#The density-based spatial clustering of applications with noise \n",
    "#(DBSCAN) algorithm defines clusters as continuous regions of high \n",
    "#density. Here is how it works:\n",
    "    \n",
    "    \n",
    "#For each instance, the algorithm counts how many instances are \n",
    "#located within a small distance ε (epsilon) from it. This region \n",
    "#is called the instance’s ε-neighborhood.\n",
    "\n",
    "\n",
    "#If an instance has at least min_samples instances in its \n",
    "#ε-neighborhood (including itself), then it is considered a core \n",
    "#instance. In other words, core instances are those that are located\n",
    "#in dense regions.\n",
    "\n",
    "#All instances in the neighborhood of a core instance belong to the\n",
    "#same cluster. This neighborhood may include other core instances; \n",
    "#therefore, a long sequence of neighboring core instances forms a \n",
    "#single cluster.\n",
    "\n",
    "\n",
    "#Any instance that is not a core instance and does not have one in \n",
    "#its neighborhood is considered an anomaly.\n",
    "\n",
    "\n",
    "\n",
    "#This algorithm works well if all the clusters are well separated by \n",
    "#low- density regions. The DBSCAN class in Scikit-Learn is as simple\n",
    "#to use as you might expect. Let’s test it on the moons dataset, \n",
    "#introduced in Chapter 5:\n",
    "\n",
    "\n",
    "from sklearn.cluster import DBSCAN\n",
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X, y = make_moons(n_samples=1000, noise=0.05)\n",
    "dbscan = DBSCAN(eps=0.05, min_samples=5)\n",
    "\n",
    "dbscan.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "dba7f781",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, -1,  0,  3,  1,  2,  2,  0,  0,  3])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The labels of all the instances are now available in the labels_ \n",
    "#instance variable:\n",
    "\n",
    "dbscan.labels_[:10]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "30e382dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  4,  6,  7,  8,  9, 10, 12, 13, 14])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Notice that some instances have a cluster index equal to –1, \n",
    "#which means that they are considered as anomalies by the algorithm.\n",
    "#The indices of the core instances are available in the \n",
    "#core_sample_indices_ instance variable, and the core instances \n",
    "#themselves are available in the components_ instance variable:\n",
    "\n",
    "dbscan.core_sample_indices_[:10]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "82fe9ab2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(791, 2)"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dbscan.components_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "83feec3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<style>#sk-container-id-4 {color: black;background-color: white;}#sk-container-id-4 pre{padding: 0;}#sk-container-id-4 div.sk-toggleable {background-color: white;}#sk-container-id-4 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-4 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-4 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-4 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-4 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-4 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-4 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-4 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-4 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-4 div.sk-item {position: relative;z-index: 1;}#sk-container-id-4 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-4 div.sk-item::before, #sk-container-id-4 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-4 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-4 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-4 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-4 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-4 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-4 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-4 div.sk-label-container {text-align: center;}#sk-container-id-4 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-4 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KNeighborsClassifier(n_neighbors=50)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" checked><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">KNeighborsClassifier</label><div class=\"sk-toggleable__content\"><pre>KNeighborsClassifier(n_neighbors=50)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "KNeighborsClassifier(n_neighbors=50)"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#This clustering is represented in the lefthand plot of Figure 9-14. \n",
    "#As you can see, it identified quite a lot of anomalies, plus seven \n",
    "#different clusters. How disappointing! Fortunately, if we widen each \n",
    "#instance’s neighborhood by increasing eps to 0.2, we get the clustering\n",
    "#on the right, which looks perfect. Let’s continue with this model.\n",
    "\n",
    "\n",
    "#Surprisingly, the DBSCAN class does not have a predict() method, \n",
    "#although it has a fit_predict() method. In other words, it cannot \n",
    "#predict which cluster a new instance belongs to. This decision was \n",
    "#made because different classification algorithms can be better for \n",
    "#different tasks, so the authors decided to let the user choose which\n",
    "#one to use. Moreover, it’s not hard to implement. For example, let’s \n",
    "#train a KNeighborsClassifier:\n",
    "\n",
    "\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "knn = KNeighborsClassifier(n_neighbors=50)\n",
    "knn.fit(dbscan.components_, dbscan.labels_[dbscan.core_sample_indices_])\n",
    "# x=core instances, y=labels of those core instances\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "7ee92384",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 4, 0, 2])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Now, given a few new instances, we can predict which clusters they most\n",
    "#likely belong to and even estimate a probability for each cluster:\n",
    "\n",
    "X_new = np.array([[-0.5, 0], [0, 0.5], [1, -0.1], [2, 1]])\n",
    "knn.predict(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "246ca78d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.  , 0.14, 0.  , 0.  , 0.28, 0.58, 0.  ],\n",
       "       [0.06, 0.  , 0.  , 0.  , 0.94, 0.  , 0.  ],\n",
       "       [0.74, 0.  , 0.26, 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 1.  , 0.  , 0.  , 0.  , 0.  ]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn.predict_proba(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "cde4f5e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1,  4,  0, -1])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Note that we only trained the classifier on the core instances, but\n",
    "#we could also have chosen to train it on all the instances, or all \n",
    "#but the anomalies: this choice depends on the final task.\n",
    "\n",
    "\n",
    "y_dist, y_pred_idx = knn.kneighbors(X_new, n_neighbors=1)\n",
    "y_pred = dbscan.labels_[dbscan.core_sample_indices_][y_pred_idx]\n",
    "y_pred[y_dist > 0.2] = -1\n",
    "y_pred.ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d10cf012",
   "metadata": {},
   "outputs": [],
   "source": [
    "#In short, DBSCAN is a very simple yet powerful algorithm capable of \n",
    "#identifying any number of clusters of any shape. It is robust to \n",
    "#outliers, and it has just two hyperparameters (eps and min_samples).\n",
    "#If the density varies significantly across the clusters, however, or\n",
    "#if there’s no sufficiently low-density region around some clusters,\n",
    "#DBSCAN can struggle to capture all the clusters properly. Moreover,\n",
    "#its computational complexity is roughly O(m2n), so it does not scale\n",
    "#well to large datasets.\n",
    "\n",
    "\n",
    "#TIP\n",
    "#You may also want to try hierarchical DBSCAN (HDBSCAN), which is \n",
    "#implemented in the scikit-learn-contrib project, as it is usually \n",
    "#better than DBSCAN at finding clusters of varying densities.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e729ecd0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {color: black;background-color: white;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GaussianMixture(n_components=3, n_init=10)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">GaussianMixture</label><div class=\"sk-toggleable__content\"><pre>GaussianMixture(n_components=3, n_init=10)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "GaussianMixture(n_components=3, n_init=10)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Gaussian Mixtures\n",
    "\n",
    "#A Gaussian mixture model (GMM) is a probabilistic model that \n",
    "#assumes that the instances were generated from a mixture of several\n",
    "#Gaussian distributions whose parameters are unknown. All the instances\n",
    "#generated from a single Gaussian distribution form a cluster that \n",
    "#typically looks like an ellipsoid. Each cluster can have a different\n",
    "#ellipsoidal shape, size, density, and orientation, just like in\n",
    "#Figure 9-11. When you observe an instance, you know it was generated\n",
    "#from one of the Gaussian distributions, but you are not told which\n",
    "#one, and you do not know what the parameters of these distributions are.\n",
    "\n",
    "\n",
    "\n",
    "#There are several GMM variants. In the simplest variant, implemented\n",
    "#in the GaussianMixture class, you must know in advance the number k \n",
    "#of Gaussian distributions. The dataset X is assumed to have been \n",
    "#generated through the following probabilistic process:\n",
    "\n",
    "\n",
    "#So what can you do with such a model? Well, given the dataset X, you \n",
    "#typically want to start by estimating the weights φ and all the \n",
    "#distribution parameters μ(1) to μ(k) and Σ(1) to Σ(k). \n",
    "#Scikit-Learn’s GaussianMixture class makes this super easy:\n",
    "\n",
    "from sklearn.mixture import GaussianMixture\n",
    "\n",
    "gm = GaussianMixture(n_components=3, n_init=10)\n",
    "gm.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "37af5ae1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.60004901, 0.20538315, 0.19456785])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm.weights_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e712f10c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.51575815,  0.23655838],\n",
       "       [-0.73913692,  0.56405816],\n",
       "       [ 1.76252366, -0.03852565]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm.means_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f5e468ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0.17551545, -0.10705901],\n",
       "        [-0.10705901,  0.29020979]],\n",
       "\n",
       "       [[ 0.05416888,  0.06121707],\n",
       "        [ 0.06121707,  0.08695673]],\n",
       "\n",
       "       [[ 0.04457658,  0.05661628],\n",
       "        [ 0.05661628,  0.08603756]]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm.covariances_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8ada8943",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7e3a2dc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Great, it worked fine! Indeed, two of the three clusters were \n",
    "#generated with 500 instances each, while the third cluster only \n",
    "#contains 250 instances. So the true cluster weights are 0.4, 0.4, \n",
    "#and 0.2, respectively, and that’s roughly what the algorithm found. \n",
    "#Similarly, the true means and covariance matrices are quite close to \n",
    "#those found by the algorithm. But how? This class relies on the\n",
    "#expectation-maximization (EM) algorithm, which has many similarities\n",
    "#with the k-means algorithm: it also initializes the cluster parameters \n",
    "#randomly, then it repeats two steps until convergence, first assigning \n",
    "#instances to clusters (this is called the expectation step) and then\n",
    "#updating the clusters (this is called the maximization step). Sounds \n",
    "#familiar, right? In the context of clustering, you can think of EM\n",
    "#as a generalization of k-means that not only finds the cluster centers\n",
    "#(μ(1) to μ(k)), but also their size, shape, and orientation (Σ(1) to\n",
    "#Σ(k)), as well as their relative weights (φ(1) to φ(k)). Unlike\n",
    "#k-means, though, EM uses soft cluster assignments, not hard \n",
    "#assignments. For each instance, during the expectation step, the\n",
    "#algorithm estimates the probability that it belongs to each cluster\n",
    "#(based on the current cluster parameters). Then, during the \n",
    "#maximization step, each cluster is updated using all the instances \n",
    "#in the dataset, with each instance weighted by the estimated \n",
    "#probability that it belongs to that cluster. These probabilities are\n",
    "#called the responsibilities of the clusters for the instances. During \n",
    "#the maximization step, each cluster’s update will mostly be impacted\n",
    "#by the instances it is most responsible for.\n",
    "\n",
    "\n",
    "#Unfortunately, just like k-means, EM can end up converging to poor \n",
    "#solutions, so it needs to be run several times, keeping only the \n",
    "#best solution. This is why we set n_init to 10. Be careful: by \n",
    "#default n_init is set to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e1fe0ee2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm.converged_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "17de7f75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm.n_iter_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "3edd8305",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 0, 0, 2, 2, 2, 0, 0, 0])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Now that you have an estimate of the location, size, shape, \n",
    "#orientation, and relative weight of each cluster, the model can \n",
    "#easily assign each instance to the most likely cluster (hard clustering)\n",
    "#or estimate the probability that it belongs to a particular cluster \n",
    "#(soft clustering). Just use the predict() method for hard clustering,\n",
    "#or the predict_proba() method for soft clustering:\n",
    "\n",
    "gm.predict(X)[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a7e254ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.   , 0.   , 0.   ],\n",
       "       [0.001, 0.   , 0.999],\n",
       "       [1.   , 0.   , 0.   ],\n",
       "       ...,\n",
       "       [1.   , 0.   , 0.   ],\n",
       "       [1.   , 0.   , 0.   ],\n",
       "       [1.   , 0.   , 0.   ]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm.predict_proba(X).round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "9d3dafb2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.4550797 ,  0.2370624 ],\n",
       "       [ 1.15955566,  0.12094283],\n",
       "       [ 0.81360972,  0.40495105],\n",
       "       [ 1.19270785,  0.03126418],\n",
       "       [ 1.80071991, -0.00677528],\n",
       "       [ 1.72123542,  0.09811061]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#A Gaussian mixture model is a generative model, meaning you can \n",
    "#sample new instances from it (note that they are ordered by cluster\n",
    "#index):\n",
    "\n",
    "X_new, y_new = gm.sample(6)\n",
    "X_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "346b5ec7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 2, 2])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "70384637",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.5 , -0.24, -1.85, -1.53,  0.01,  0.12, -0.65, -1.29, -1.56,\n",
       "       -1.9 ])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#It is also possible to estimate the density of the model at any \n",
    "#given location. This is achieved using the score_samples() method:\n",
    "#for each instance it is given, this method estimates the log of \n",
    "#the probability density function (PDF) at that location. The greater\n",
    "#the score, the higher the density:\n",
    "\n",
    "gm.score_samples(X).round(2)[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "76f981d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "#If you compute the exponential of these scores, you get the value \n",
    "#of the PDF at the location of the given instances. These are not \n",
    "#probabilities, but probability densities: they can take on any \n",
    "#positive value, not just a value between 0 and 1. To estimate \n",
    "#the probability that an instance will fall within a particular\n",
    "#region, you would have to integrate the PDF over that region \n",
    "#(if you do so over the entire space of possible instance locations,\n",
    "#the result will be 1).\n",
    "\n",
    "#Figure 9-16 shows the cluster means, the decision boundaries \n",
    "#(dashed lines), and the density contours of this model.\n",
    "\n",
    "\n",
    "\n",
    "#Nice! The algorithm clearly found an excellent solution. Of course, \n",
    "#we made its task easy by generating the data using a set of 2D Gaussian\n",
    "#distributions (unfortunately, real-life data is not always so Gaussian\n",
    "#and low-dimensional). We also gave the algorithm the correct number of \n",
    "#clusters. When there are many dimensions, or many clusters, or few \n",
    "#instances, EM can struggle to converge to the optimal solution. You\n",
    "#might need to reduce the difficulty of the task by limiting the number\n",
    "#of parameters that the algorithm has to learn. One way to do this is\n",
    "#to limit the range of shapes and orientations that the clusters can \n",
    "#have. This can be achieved by imposing constraints on the covariance \n",
    "#matrices. To do this, set the covariance_type hyperparameter to one\n",
    "#of the following values:\n",
    "\n",
    "#\"spherical\"\n",
    "#All clusters must be spherical, but they can have different diameters\n",
    "#(i.e., different variances).\n",
    "\n",
    "#\"diag\"\n",
    "#Clusters can take on any ellipsoidal shape of any size, but the \n",
    "#ellipsoid’s axes must be parallel to the coordinate axes (i.e., the covariance matrices must be diagonal).\n",
    "\n",
    "\n",
    "#\"tied\"\n",
    "#All clusters must have the same ellipsoidal shape, size, and \n",
    "#orientation (i.e., all clusters share the same covariance matrix).\n",
    "\n",
    "\n",
    "#By default, covariance_type is equal to \"full\", which means that\n",
    "#each cluster can take on any shape, size, and orientation (it has\n",
    "#its own unconstrained covariance matrix). Figure 9-17 plots the \n",
    "#solutions found by the EM algorithm when covariance_type is set\n",
    "#to \"tied\" or \"spherical\".\n",
    "\n",
    "\n",
    "#NOTE\n",
    "#The computational complexity of training a GaussianMixture model \n",
    "#depends on the number of instances m, the number of dimensions n, \n",
    "#the number of clusters k, and the constraints on the covariance \n",
    "#matrices. If covariance_type is \"spherical\" or \"diag\", it is O(kmn), \n",
    "#assuming the data has a clustering structure. If covariance_type is \n",
    "#\"tied\" or \"full\", it is O(kmn2 + kn3), so it will not scale to large\n",
    "#numbers of features.\n",
    "\n",
    "\n",
    "#Gaussian mixture models can also be used for anomaly detection. \n",
    "#We’ll see how in the next section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "e7dd303f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using Gaussian Mixtures for Anomaly Detection\n",
    "#Using a Gaussian mixture model for anomaly detection is quite simple:\n",
    "#any instance located in a low-density region can be considered an \n",
    "#anomaly. You must define what density threshold you want to use. For \n",
    "#example, in a manufacturing company that tries to detect defective \n",
    "#products, the ratio of defective products is usually well known. Say\n",
    "#it is equal to 2%. You then set the density threshold to be the value\n",
    "#that results in having 2% of the instances located in areas below that\n",
    "#threshold density. If you notice that you get too many false positives\n",
    "#(i.e., perfectly good products that are flagged as defective), you can\n",
    "#lower the threshold. Conversely, if you have too many false negatives\n",
    "#(i.e., defective products that the system does not flag as defective),\n",
    "#you can increase the threshold. This is the usual precision/recall\n",
    "#trade-off (see Chapter 3). Here is how you would identify the outliers\n",
    "#using the fourth percentile lowest density as the threshold (i.e.,\n",
    "#approximately 4% of the instances will be flagged as anomalies):\n",
    "        \n",
    "        \n",
    "densities = gm.score_samples(X)\n",
    "density_threshold = np.percentile(densities, 2)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2917271b",
   "metadata": {},
   "outputs": [],
   "source": [
    "density_threshold = np.percentile(densities, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f56548f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.3648379305947973"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "density_threshold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "9bcd6e7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "densities.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "518eb088",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.3648379305947973"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(densities, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "e2400f94",
   "metadata": {},
   "outputs": [],
   "source": [
    "anomalies = X[densities < density_threshold]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6e8e81d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "#A closely related task is novelty detection: it differs from anomaly\n",
    "#detection in that the algorithm is assumed to be trained on a “clean”\n",
    "#dataset, uncontaminated by outliers, whereas anomaly detection does \n",
    "#not make this assumption. Indeed, outlier detection is often used to \n",
    "#clean up a dataset.\n",
    "\n",
    "\n",
    "\n",
    "#Gaussian mixture models try to fit all the data, including the \n",
    "#outliers; if you have too many of them this will bias the model’s \n",
    "#view of “normality”, and some outliers may wrongly be considered as \n",
    "#normal. If this happens, you can try to fit the model once, use it\n",
    "#to detect and remove the most extreme outliers, then fit the model\n",
    "#again on the cleaned-up dataset. Another approach is to use robust\n",
    "#covariance estimation methods (see the EllipticEnvelope class).\n",
    "\n",
    "\n",
    "#Just like k-means, the GaussianMixture algorithm requires you to specify\n",
    "#the number of clusters. So how can you find that number?   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "757f9dea",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Selecting the Number of Clusters\n",
    "#With k-means, you can use the inertia or the silhouette score to select\n",
    "#the appropriate number of clusters. But with Gaussian mixtures, it is\n",
    "#not possible to use these metrics because they are not reliable when \n",
    "#the clusters are not spherical or have different sizes. Instead, you \n",
    "#can try to find the model that minimizes a theoretical information \n",
    "#criterion, such as the Bayesian information criterion (BIC) or the \n",
    "#Akaike information criterion (AIC), defined in Equation 9-1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cd34c0a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Both the BIC and the AIC penalize models that have more parameters to\n",
    "#learn (e.g., more clusters) and reward models that fit the data well.\n",
    "#They often end up selecting the same model. When they differ, the model\n",
    "#selected by the BIC tends to be simpler (fewer parameters) than the one\n",
    "#selected by the AIC, but tends to not fit the data quite as well \n",
    "#(this is especially true for larger datasets)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e4bcac64",
   "metadata": {},
   "outputs": [],
   "source": [
    "#In short, the PDF is a function of x (with θ fixed), while the likelihood\n",
    "#function is a function of θ (with x fixed). It is important to understand\n",
    "#that the likelihood function is not a probability distribution: if you\n",
    "#integrate a probability distribution over all possible values of x, you\n",
    "#always get 1, but if you integrate the likelihood function over all\n",
    "#possible values of θ the result can be any positive value.\n",
    "#Given a dataset X, a common task is to try to estimate the most likely\n",
    "#values for the model parameters. To do this, you must find the values\n",
    "#that maximize the likelihood function, given X. In this example, if you\n",
    "#have observed a single instance x=2.5, the maximum likelihood estimate\n",
    "#is possible to take it into account by maximizing L(θ|x)g(θ) rather than \n",
    "#just maximizing L(θ|x). This is called maximum a-posteriori (MAP) (MLE) \n",
    "#of θ is 𝛉=1.5. If a prior probability distribution g over θ exists, it ˆ\n",
    "#estimation. Since MAP constrains the parameter values, you can think\n",
    "#of it as a regularized version of MLE.\n",
    "#Notice that maximizing the likelihood function is equivalent to\n",
    "#maximizing its logarithm (represented in the lower-right plot in\n",
    "#Figure 9-19). Indeed, the logarithm is a strictly increasing function, so\n",
    "#if θ maximizes the log likelihood, it also maximizes the likelihood. It\n",
    "#turns out that it is generally easier to maximize the log likelihood. For\n",
    "#example, if you observed several independent instances x(1) to x(m), you\n",
    "#would need to find the value of θ that maximizes the product of the\n",
    "#individual likelihood functions. But it is equivalent, and much simpler,\n",
    "#to maximize the sum (not the product) of the log likelihood functions,\n",
    "#thanks to the magic of the logarithm which converts products into sums:\n",
    "#log(ab) = log(a) + log(b).\n",
    "\n",
    "#Once you have estimated 𝛉, the value of θ that maximizes the\n",
    "#likelihood function, then you are ready to compute 𝛉 ,\n",
    "#which is the value used to compute the AIC and BIC; you can think of \n",
    "#it as a measure of how well the model fits the data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "357fe207",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2767.095745566612"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm.bic(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "5250fc73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2683.6639058239157"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm.aic(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4d0280a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Figure 9-20 shows the BIC for different numbers of clusters k. As you can see, both the BIC and the\n",
    "#AIC are lowest when k=3, so it is most likely the best choice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9885e00d",
   "metadata": {},
   "outputs": [
    {
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       "<style>#sk-container-id-4 {color: black;background-color: white;}#sk-container-id-4 pre{padding: 0;}#sk-container-id-4 div.sk-toggleable {background-color: white;}#sk-container-id-4 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-4 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-4 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-4 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-4 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-4 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-4 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-4 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-4 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-4 div.sk-item {position: relative;z-index: 1;}#sk-container-id-4 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-4 div.sk-item::before, #sk-container-id-4 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-4 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-4 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-4 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-4 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-4 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-4 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-4 div.sk-label-container {text-align: center;}#sk-container-id-4 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-4 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>BayesianGaussianMixture(n_components=10, n_init=10, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" checked><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">BayesianGaussianMixture</label><div class=\"sk-toggleable__content\"><pre>BayesianGaussianMixture(n_components=10, n_init=10, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "BayesianGaussianMixture(n_components=10, n_init=10, random_state=42)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Bayesian Gaussian Mixture Models\n",
    "#Rather than manually searching for the optimal number of clusters, you can use the\n",
    "#BayesianGaussianMixture class, which is capable of giving weights equal (or close) to zero \n",
    "#to unnecessary clusters. Set the number of clusters n_components to a value that you have \n",
    "#good reason to believe is greater than the optimal number of clusters (this assumes some \n",
    "#minimal knowledge about the problem at hand), and the algorithm will eliminate the unnecessary \n",
    "#clusters automatically. For example, let’s set the number of clusters to 10 and see what happens:\n",
    "    \n",
    "from sklearn.mixture import BayesianGaussianMixture\n",
    "bgm = BayesianGaussianMixture(n_components=10, n_init=10, random_state=42)\n",
    "bgm.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "6bdd7d40",
   "metadata": {},
   "outputs": [
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   "source": [
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  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fdda113a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Perfect: the algorithm automatically detected that only three clusters are needed, and the resulting \n",
    "#clusters are almost identical to the ones in Figure 9-16.\n",
    "\n",
    "\n",
    "#A final note about Gaussian mixture models: although they work great on clusters with \n",
    "#ellipsoidal shapes, they don’t do so well with clusters of very different shapes. For example,\n",
    "#let’s see what happens if we use a Bayesian Gaussian mixture model to cluster the moons dataset (see Figure 9-21).\n",
    "\n",
    "#Oops! The algorithm desperately searched for ellipsoids, so it found eight different clusters instead \n",
    "#of two. The density estimation is not too bad, so this model could perhaps be used for anomaly detection,\n",
    "#but it failed to identify the two moons. To conclude this chapter, let’s take a quick look at a few \n",
    "#algorithms capable of dealing with arbitrarily shaped clusters.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
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