4ma-da/tp/clustering/agglomerative.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "063e4e3e",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       ".output_png {\n",
       "    display: table-cell;\n",
       "    text-align: center;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "\n",
    "HTML(\n",
    "    \"\"\"\n",
    "<style>\n",
    ".output_png {\n",
    "    display: table-cell;\n",
    "    text-align: center;\n",
    "    vertical-align: middle;\n",
    "}\n",
    "</style>\n",
    "\"\"\"\n",
    ")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "370d673f",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 5)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "019ab614",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# A connectivity-based algorithm: Agglomerative clustering\n",
    "\n",
    "## Outline\n",
    "\n",
    "- Algorithm\n",
    "- scikit-learn implementation\n",
    "- Choose K\n",
    "- Linkage"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec775a8c",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Toy data generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "13f522d1",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "means = [np.array([1, 1]), np.array([5, 5]), np.array([5, 1])]\n",
    "covariance = np.array([[0.25, 0], [0, 0.25]])\n",
    "n_points = 10\n",
    "\n",
    "data = [\n",
    "    np.random.multivariate_normal(mean=means[i], cov=covariance, size=n_points)\n",
    "    for i in range(3)\n",
    "]\n",
    "all_data = np.r_[data[0], data[1], data[2]]\n",
    "\n",
    "plt.scatter(all_data[:, 0], all_data[:, 1])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "babc0d81",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Agglomerative clustering algorithm\n",
    "\n",
    "__Objective__: Recursively merges pair of clusters of sample data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f77e30b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## K-means using scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "58cc2222",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "ac = AgglomerativeClustering(n_clusters=3)\n",
    "clusters = ac.fit_predict(all_data)\n",
    "\n",
    "plt.scatter(all_data[:, 0], all_data[:, 1], c=clusters)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1abc56c1",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Visualize dendrogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d52284a0",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plot Dendrogram\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.cluster.hierarchy import dendrogram\n",
    "\n",
    "print(\"Plot Dendrogram\")\n",
    "\n",
    "ac = AgglomerativeClustering(n_clusters=3, compute_distances=True)\n",
    "clusters = ac.fit(all_data)\n",
    "\n",
    "children = ac.children_\n",
    "distances = ac.distances_\n",
    "n_observations = np.arange(2, children.shape[0] + 2)\n",
    "\n",
    "linkage_matrix = np.c_[children, distances, n_observations]\n",
    "\n",
    "dendrogram(linkage_matrix, labels=ac.labels_)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc1f919a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Choose optimal number of clusters K\n",
    "\n",
    "Plot the height of the different successive merges.\\\n",
    "Find the elbow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7676f1a2",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dfzRZwim2LxPo7lu6+/rF719Lciw73zph/53AnWxfJtI7vr54eI/Ff5017MNzD6jdvi7GzjatTvL+qrpucdd41uNB3X1LsvOPaJIH7vM8Z6IXVdXHF6f4nGJaUVUdTvK4JNfG/ju5k7ZvYv+dTFWdVVU3JDmR5OruXss+PPeAql2Wzfec48H05O5+fJIfTfLLi9MjcNC8Ickjkjw2yS1Jfm9fpzngquq+Sd6R5Fe7+6v7Pc+ZZpfta/+dUHf/b3c/NjvfkPLEqnr0Ot5n7gF1Wl8Xw/K6+0uLnyeSvCs7p02Z3pcX1z/cfh3EiX2e54zS3V9e/KP5zSR/HPvx0hbXjbwjyZXd/c7FYvvvRHbbvvbf9ejuf0/ygSQXZg378NwDytfFrFFVnb24kDFVdXaSZyW58c5fxZLem+TSxe+XJnnPPs5yxrn9H8aFn4j9eCmLC3DflORYd7/2Dk/Zfydwqu1r/51OVW1U1f0Xv987yTOSfCpr2Idn/Sm8JFl8nPN1+dbXxfzO/k505qiqh2fnqFOyc1f6P7d9V1dVVyV5ana+AfzLSV6Z5N1J3pbk/CRfSPLT3e1C6CWcYvs+NTunPzrJzUl+8fbrHTh9VfUDSf4xySeSfHOx+Dezc52O/XdFd7J9L4n9dxJV9ZjsXCR+VnYOEr2tu3+7qr4jE+/Dsw8oAIC5mfspPACA2RFQAACDBBQAwCABBQAwSEABAAwSUAAAgwQUAMAgAQUAMOj/AG0pGBSxCUW4AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(3 * n_points - 1, 0, -1)\n",
    "y = ac.distances_\n",
    "\n",
    "plt.bar(x, y)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b95a0d2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "source": [
    "## Linkage\n",
    "\n",
    "The linkage represent how the similarity between different groups of points is computed.\n",
    "\n",
    "Different linkages in scikit-learn:\n",
    "- __average__: uses the average of the distances of each observation of the two sets.\n",
    "- __complete__: linkage uses the maximum distances between all observations of the two sets.\n",
    "- __single__: uses the minimum of the distances between all observations of the two sets.\n",
    "- __ward__: minimizes the variance of the clusters being merged."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f823699e",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Visualization of the influence of different linkage strategies\n",
    "\n",
    "<img src=\"images/aggloClustering_linkage_comparison.png\" width=\"500px\"/>"
   ]
  }
 ],
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