{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Density based clustering explained"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Learn in this tutorial about the basics of density-based clustering and how common-nearest-neighbours\n",
    "clustering works compared to other methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pre-requirements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T14:43:18.762282Z",
     "start_time": "2020-06-18T14:43:18.760198Z"
    }
   },
   "source": [
    "### Import dependencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:34:09.925733Z",
     "start_time": "2020-08-20T15:34:09.105972Z"
    }
   },
   "outputs": [],
   "source": [
    "from collections import deque\n",
    "from itertools import islice\n",
    "import sys\n",
    "\n",
    "from IPython.display import HTML\n",
    "import matplotlib as mpl\n",
    "from matplotlib import animation\n",
    "import matplotlib.pyplot as plt\n",
    "# import networkx\n",
    "import numpy as np\n",
    "from scipy.integrate import quad\n",
    "from scipy import stats\n",
    "from scipy.spatial import cKDTree\n",
    "from sklearn import datasets\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook was created using Python 3.8."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:34:09.946708Z",
     "start_time": "2020-08-20T15:34:09.944690Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8.3 (default, Jun  4 2020, 11:17:16) \n",
      "[GCC 8.3.0]\n"
     ]
    }
   ],
   "source": [
    "# Version information\n",
    "print(sys.version)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:34:10.358307Z",
     "start_time": "2020-08-20T15:34:10.351256Z"
    }
   },
   "outputs": [],
   "source": [
    "# Matplotlib configuration\n",
    "mpl.rc_file(\n",
    "    \"matplotlibrc\",\n",
    "    use_default_template=False\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T10:29:23.385924Z",
     "start_time": "2020-06-19T10:29:23.361701Z"
    }
   },
   "outputs": [],
   "source": [
    "def gauss(x, sigma, mu):\n",
    "    \"\"\"Gaussian PDF\"\"\"\n",
    "    return (1 / (sigma * np.sqrt(2 * np.pi))\n",
    "            * np.exp(-1 / 2 * ((x - mu) / sigma)**2))\n",
    "    \n",
    "def multigauss(x, sigma, mu):\n",
    "    \"\"\"Multimodal gaussian PDF as linear combination of gaussian PDFs\"\"\"\n",
    "    assert len(sigma) == len(mu)\n",
    "    \n",
    "    out = np.zeros_like(x)\n",
    "    for s, m in zip(sigma, mu):\n",
    "        out += gauss(x, s, m)\n",
    "    return out / len(sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T09:17:31.926780Z",
     "start_time": "2020-06-19T09:17:31.910095Z"
    }
   },
   "outputs": [],
   "source": [
    "def determine_cuts(x, a, cutoff):\n",
    "    \"\"\"Find points in space where density cutoff is crossed\n",
    "    \n",
    "    Args:\n",
    "       x: coordinate\n",
    "       a: density\n",
    "       cutoff: density cutoff\n",
    "    \n",
    "    Returns:\n",
    "       cuts: Array of coordinates where cutoff is crossed\n",
    "    \"\"\"\n",
    "    \n",
    "    cuts = []\n",
    "    dense = False  # Assume low density on left border\n",
    "    for index, value in enumerate(a[1:], 1):\n",
    "        if dense:\n",
    "            if value < cutoff:\n",
    "                dense = False\n",
    "                cuts.append((x[index] + x[index - 1]) / 2)        \n",
    "        else:\n",
    "            if value >= cutoff:\n",
    "                dense = True\n",
    "                cuts.append((x[index] + x[index - 1]) / 2)\n",
    "    \n",
    "    return np.asarray(cuts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T10:53:19.319490Z",
     "start_time": "2020-06-19T10:53:19.308287Z"
    }
   },
   "outputs": [],
   "source": [
    "class multigauss_distribution(stats.rv_continuous):\n",
    "    \"\"\"Draw samples from a multimodal gaussian distribution\"\"\"\n",
    "           \n",
    "    def __init__(self, sigma, mu, *args, **kwargs):\n",
    "        super().__init__(*args, **kwargs)\n",
    "        self._sigma = sigma\n",
    "        self._mu = mu\n",
    "\n",
    "    def _pdf(self, x):\n",
    "        return multigauss(x, sigma=self._sigma, mu=self._mu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Density criteria"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Density-based clustering defines clusters as *dense* regions in space, separated by *sparse* regions. But what is dense and what is sparse? This is commonly defined by a threshold, that is a density criterion that determines the clustering. In the case where we have a density function defined on a continuous coordinate, the density criterion manifests itself as a density iso-surface. Regions in which the density is higher than a cutoff set as density criterion qualify as *dense*, and therefore represent a cluster. On the other hand, regions in which the density falls below the density criterion are considered *sparse* and do not constitute a part of a cluster. We can illustrate this on the example of a bimodal gaussian distribution in one dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T09:17:34.735108Z",
     "start_time": "2020-06-19T09:17:34.501583Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 750x450 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xlimit = (-8, 8)\n",
    "x = np.linspace(*xlimit, 101)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, multigauss(x, sigma=[1, 1.5], mu=[-2, 2]))\n",
    "ax.set(**{\n",
    "    \"xlim\": xlimit,\n",
    "    \"xlabel\": \"$x$\",\n",
    "    \"ylabel\": \"probability density\"\n",
    "})\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have two maxima in the distribution. An intuitive classification in clusters\n",
    "would separate the two peaks into two different clusters. In density based clustering we define the two clusters as the regions of high density where we have low density in between. By applying an iso-value cutoff on the density, we can specify what should be considered high or low density. In a dense region, the density is at least as high as the density criterion requires."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T09:33:25.448814Z",
     "start_time": "2020-06-19T09:33:25.100824Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 750x450 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "density_criterion = 0.1\n",
    "\n",
    "xlimit = (-8, 8)\n",
    "x = np.linspace(*xlimit, 1001)\n",
    "pdf = multigauss(x, sigma=[1, 1.5], mu=[-2, 2])\n",
    "cuts = determine_cuts(x, pdf, density_criterion)\n",
    "density_criterion_ = np.full_like(x, density_criterion)\n",
    "dense = np.maximum(pdf, density_criterion_)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, pdf)\n",
    "ax.plot(x, density_criterion_, linestyle=\"--\", color=\"k\")\n",
    "ax.fill_between(x, density_criterion_, dense)\n",
    "for cut in cuts:\n",
    "    ax.axvline(cut, color=\"gray\", alpha=0.5)\n",
    "\n",
    "ax.annotate(\n",
    "    \"density criterion\", (xlimit[0] * 0.975, density_criterion * 1.03),\n",
    "    fontsize=\"small\"\n",
    ")\n",
    "\n",
    "ax.annotate(\"0\", (cuts[0] * 1.2, 0))\n",
    "ax.annotate(\"1\", (cuts[1] * 2, 0))\n",
    "ax.annotate(\"0\", (cuts[2] * 0.2, 0))\n",
    "ax.annotate(\"2\", (cuts[3] * 0.8, 0))\n",
    "ax.annotate(\"0\", (cuts[3] * 1.2, 0))\n",
    "\n",
    "ax.annotate(\n",
    "    \"dense\",\n",
    "    xy=(2.2, multigauss(2.2, sigma=[1, 1.5], mu=[-2, 2])),\n",
    "    xytext=(cuts[3] * 1.2, density_criterion * 1.5),\n",
    "    arrowprops={\"arrowstyle\": \"->\"}\n",
    ")\n",
    "\n",
    "ax.annotate(\n",
    "    \"sparse\",\n",
    "    xy=(4, multigauss(4., sigma=[1, 1.5], mu=[-2, 2])),\n",
    "    xytext=(cuts[3] * 1.2, density_criterion * 1.2),\n",
    "    arrowprops={\"arrowstyle\": \"->\"}\n",
    ")\n",
    "\n",
    "ax.set(**{\n",
    "    \"xlim\": xlimit,\n",
    "    \"xlabel\": \"$x$\",\n",
    "    \"ylabel\": \"probability density\"\n",
    "})\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T09:13:41.465492Z",
     "start_time": "2020-06-19T09:13:41.442533Z"
    }
   },
   "source": [
    "Choosing the density criterion in this way, defines the two clusters exactly as we would have expected. We can label the regions, i.e. we can assign a number to them, that denotes their cluster membership. We use 0 to indicate that a region is not part of any cluster and positive integers as cluster numbers. When we vary the density criterion, we can influence the outcome of the clustering by changing the definition of what is dense enough to be a cluster. This could leave us with both density maxima in one cluster, clusters of different broadness, or not cluster at all."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T09:59:56.990875Z",
     "start_time": "2020-06-19T09:59:56.428979Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 750x450 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, Ax = plt.subplots(2, 2)\n",
    "ax = Ax.flatten()\n",
    "\n",
    "for i, d in enumerate([0.05, 0.09, 0.15, 0.22]):\n",
    "    density_criterion = d\n",
    "\n",
    "    xlimit = (-8, 8)\n",
    "    x = np.linspace(*xlimit, 1001)\n",
    "    pdf = multigauss(x, sigma=[1, 1.5], mu=[-2, 2])\n",
    "    cuts = determine_cuts(x, pdf, density_criterion)\n",
    "    density_criterion_ = np.full_like(x, density_criterion)\n",
    "    dense = np.maximum(pdf, density_criterion_)\n",
    "\n",
    "\n",
    "    ax[i].plot(x, pdf)\n",
    "    ax[i].plot(x, density_criterion_, linestyle=\"--\", color=\"k\")\n",
    "    ax[i].fill_between(x, density_criterion_, dense)\n",
    "    for cut in cuts:\n",
    "        ax[i].axvline(cut, color=\"gray\", alpha=0.5)\n",
    "\n",
    "\n",
    "    ax[i].set(**{\n",
    "        \"xlim\": xlimit,\n",
    "    })\n",
    "    \n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we operate on data sets (in maybe high dimensional spaces), however, we normally do not have a continuous description of the density, that we can directly use. Instead we may have sample points from an underlying (unknown) distribution. To apply a density based clustering on them, we need to approximate the density in some way. For this approximation, quite a number of different possibilities exist, which provide a different notion of what density is or how it could be estimated from scattered data. To illustrate this, let's draw samples from the above used bimodal distribution to emulate data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T11:53:24.610054Z",
     "start_time": "2020-06-19T11:53:23.646766Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 750x450 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "distribution = multigauss_distribution(\n",
    "    sigma=[1, 1.5], mu=[-2, 2], a=-8, b=8, seed=11\n",
    ")\n",
    "samples = distribution.rvs(size=20)\n",
    "\n",
    "xlimit = (-8, 8)\n",
    "x = np.linspace(*xlimit, 1001)\n",
    "pdf = multigauss(x, sigma=[1, 1.5], mu=[-2, 2])\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, pdf, color=\"gray\", linestyle=\"--\", alpha=0.5)\n",
    "\n",
    "ax.set(**{\n",
    "    \"xlim\": xlimit,\n",
    "    \"xlabel\": \"$x$\",\n",
    "    \"ylabel\": \"probability density\"\n",
    "})\n",
    "\n",
    "ax.plot(samples, np.zeros_like(samples), linestyle=\"\",\n",
    "        marker=\"|\", markeredgewidth=0.75, markersize=15) \n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following we look into how density is deduced from points in terms of the following methods:\n",
    "    \n",
    "  - DBSCAN\n",
    "  - Jarvis-Patrick\n",
    "  - CNN\n",
    "  \n",
    "In general, point density can be expressed in simple terms by the number of points $n$ found on an area $x$ $\\left(\\rho = \\frac{n}{x}\\right)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### DBSCAN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In DBSCAN local point density (so the density around a sample point) is accordingly expressed as the number of neighbouring points $k_r$ with respect to a neighbour search radius $r$.\n",
    "The density criterion is formulated as such: Points that have at least $k$ nearest neighbours in their neighbourhood $r$ qualify as part of a dense region, i.e. a cluster. Points that fulfill the density criterion can be also referred to as *core points*. Additionally it is possible to describe points that do not fulfill the density criterion themselves but are neighbours of those core points as *edge points*. For our samples above this could look as the followed if we choose the density criterion as $k=1$ and $r=0.5$. To determine the number of neighbours for each point, we calculated pairwise point distances and compare them to $r$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T12:57:51.133188Z",
     "start_time": "2020-06-19T12:57:51.126775Z"
    },
    "run_control": {
     "marked": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True,  True,  True,  True,  True, False,\n",
       "        True,  True,  True,  True,  True,  True, False,  True,  True,\n",
       "       False,  True])"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Density criterion\n",
    "r = 0.5  # Neighbour search radius\n",
    "k = 1    # Minimum number of neighbours\n",
    "\n",
    "n_neighbours = np.array([\n",
    "    # Neighbour within r?\n",
    "    len(np.where((0 < x) & (x <= r))[0])\n",
    "    # distance matrix\n",
    "    for x in np.absolute(np.subtract.outer(samples, samples))\n",
    "])\n",
    "\n",
    "dense = n_neighbours >= k  # Point is part of dense region?\n",
    "dense"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T12:58:14.716459Z",
     "start_time": "2020-06-19T12:58:14.478291Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 750x450 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xlimit = (-8, 8)\n",
    "x = np.linspace(*xlimit, 1001)\n",
    "pdf = multigauss(x, sigma=[1, 1.5], mu=[-2, 2])\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, pdf, color=\"gray\", linestyle=\"--\", alpha=0.5)\n",
    "\n",
    "ax.set(**{\n",
    "    \"xlim\": xlimit,\n",
    "    \"xlabel\": \"$x$\",\n",
    "    \"ylabel\": \"probability density\"\n",
    "})\n",
    "\n",
    "for i, s in enumerate(samples):\n",
    "    if dense[i]:\n",
    "        c = \"#396ab1\"\n",
    "    else:\n",
    "        c = \"gray\"\n",
    "    ax.plot(s, 0, linestyle=\"\",\n",
    "            marker=\"|\", markeredgewidth=0.75, markersize=15,\n",
    "            color=c)\n",
    "\n",
    "labels = [\n",
    "    (-4, \"1\"),\n",
    "    (-2.8, \"2\"),\n",
    "    (-1.8, \"0\"),\n",
    "    (-0.8, \"3\"),\n",
    "    (1, \"0\"),\n",
    "    (1.8, \"4\"),\n",
    "    (2.8, \"5\"),\n",
    "    (3.8, \"0\"),\n",
    "]\n",
    "\n",
    "for position, l in labels:\n",
    "    ax.annotate(l, (position, 0.02))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case we end up with 5 clusters, that are dense enough regions separated by low density areas. Like a change in the density iso-value as the density criterion for the continuous density function, a change of the cluster parameters $k$ and $r$ will determine the cluster result. Note, that we assigned the labels to the clusters by visual inspection. We will show later how to identify these isolated regions (connected components of core points) automatically."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Jarvis-Patrick"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "### CNN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary on density criteria"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A point is part of a dense region if the point ...\n",
    "\n",
    "  - DBSCAN: ... has at least $k_r$ neighbours within a radius $r$\n",
    "  - Jarvis-Patrick: ... shares at least $c$ common neighbours with a another point among their $k$ nearest neighbours\n",
    "  - CNN: ... shares at least $c$ common neighbours with a another point with respect to a radius $r$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T12:52:43.477733Z",
     "start_time": "2020-06-19T12:52:43.475271Z"
    }
   },
   "source": [
    "## Identify connected components of points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Classifying points as part of a dense or a sparse region according to a density criterion, is only one aspect of assigning points to clusters. We still need to identify groups of points that are part of the same region. In this context, we use the term *density reachable* to describe the situation where point is directly connected to a dense point. We also use the term *density connected* for points that are part of the same dense region, i.e. they are directly or indirectly connected to any other point in the region by a chain of density reachable points. In other words, it is not enough to know which points are dense but we also need to be aware of the relationship between dense points. When we express this relationship in a graph, the problem of identifying clusters of density connected points comes down to finding connected components of nodes within this graph. For the methods we considered above, points are density reachable if they are neighbours of a dense point (with respect to a radius *r* or one of the $k$ nearest neighbours). In the above example, we where only interested in the information if a point was part of a dense region by checking the density criterion. Let's now construct a density graph instead in which each dense point constitutes a node and each vertex represent the density reachability between two points. We neglect the concept of edge points (points that are not dense but density reachable from a dense point) for the sake of simplicity here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### DBSCAN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T13:59:03.310823Z",
     "start_time": "2020-06-19T13:59:02.861746Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 750x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Density criterion\n",
    "r = 0.5  # Neighbour search radius\n",
    "k = 1    # Minimum number of neighbours\n",
    "\n",
    "neighbourhoods = [\n",
    "    # Neighbour within r?\n",
    "    np.where((0 < x) & (x <= r))[0]\n",
    "    # distance matrix\n",
    "    for x in np.absolute(np.subtract.outer(samples, samples))\n",
    "]\n",
    "\n",
    "n_neighbours = np.asarray([len(x) for x in neighbourhoods])\n",
    "dense = n_neighbours >= k\n",
    "\n",
    "# Construct graph as dictionary\n",
    "# keys: dense points, values: density reachable points\n",
    "graph = {}\n",
    "for i, point in enumerate(neighbourhoods):\n",
    "    if dense[i]:\n",
    "        graph[i] = neighbourhoods[i][dense[neighbourhoods[i]]]\n",
    "\n",
    "G = networkx.Graph(graph)\n",
    "pos = networkx.spring_layout(G, iterations=10, seed=7)\n",
    "networkx.draw(G, pos=pos, with_labels=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T13:56:04.569929Z",
     "start_time": "2020-06-19T13:56:04.548535Z"
    }
   },
   "source": [
    "Once such a graph is constructed, graph traversal algorithms can be used to find the connected components of nodes within the graph. A generic way to do so using a breadth-first-search algorithm could look like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T14:13:17.940400Z",
     "start_time": "2020-06-19T14:13:17.917328Z"
    }
   },
   "outputs": [],
   "source": [
    "labels = {}                          # Cluster label assignments\n",
    "visited = {k: False for k in graph}  # Node has been assigned\n",
    "queue = deque()                      # First-in-first-out queue\n",
    "current = 1                          # Current cluster number\n",
    "\n",
    "for point, connected in graph.items():\n",
    "    # Source node\n",
    "    if visited[point]:\n",
    "        continue\n",
    "    \n",
    "    labels[point] = current\n",
    "    visited[point] = True\n",
    "    \n",
    "    while True:\n",
    "        for reachable in connected:\n",
    "            if visited[reachable]:\n",
    "                continue\n",
    "        \n",
    "            labels[reachable] = current\n",
    "            visited[reachable] = True\n",
    "            queue.append(reachable)\n",
    "        \n",
    "        if not queue:\n",
    "            break\n",
    "            \n",
    "        point = queue.popleft()\n",
    "        connected = graph[point]\n",
    "    \n",
    "    current += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T14:13:21.974227Z",
     "start_time": "2020-06-19T14:13:21.961449Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 1,\n",
       " 11: 1,\n",
       " 14: 1,\n",
       " 17: 1,\n",
       " 19: 1,\n",
       " 1: 2,\n",
       " 6: 2,\n",
       " 16: 2,\n",
       " 2: 3,\n",
       " 4: 3,\n",
       " 5: 3,\n",
       " 7: 3,\n",
       " 3: 4,\n",
       " 10: 4,\n",
       " 9: 5,\n",
       " 12: 5,\n",
       " 13: 5}"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T14:18:15.255407Z",
     "start_time": "2020-06-19T14:18:14.848982Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 750x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "networkx.draw(G, pos=pos, with_labels=True, node_color=[x[1] for x in sorted(labels.items())])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-19T14:35:24.454757Z",
     "start_time": "2020-06-19T14:35:23.935477Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 750x450 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xlimit = (-8, 8)\n",
    "x = np.linspace(*xlimit, 1001)\n",
    "pdf = multigauss(x, sigma=[1, 1.5], mu=[-2, 2])\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, pdf, color=\"gray\", linestyle=\"--\", alpha=0.5)\n",
    "\n",
    "ax.set(**{\n",
    "    \"xlim\": xlimit,\n",
    "    \"xlabel\": \"$x$\",\n",
    "    \"ylabel\": \"probability density\"\n",
    "})\n",
    "\n",
    "colors = ['#396ab1', '#da7c30', '#3e9651', '#cc2529', '#6b4c9a']\n",
    "for i, s in enumerate(samples):\n",
    "    if dense[i]:\n",
    "        c = colors[labels[i] - 1]\n",
    "    else:\n",
    "        c = \"gray\"\n",
    "    ax.plot(s, 0, linestyle=\"\",\n",
    "            marker=\"|\", markeredgewidth=0.75, markersize=15,\n",
    "            color=c)\n",
    "\n",
    "labels_ = [\n",
    "    (-4, \"2\"),\n",
    "    (-2.8, \"1\"),\n",
    "    (-1.8, \"0\"),\n",
    "    (-0.8, \"3\"),\n",
    "    (1, \"0\"),\n",
    "    (1.8, \"4\"),\n",
    "    (2.8, \"5\"),\n",
    "    (3.8, \"0\"),\n",
    "]\n",
    "\n",
    "for position, l in labels_:\n",
    "    ax.annotate(l, (position, 0.02))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CNN clustering in detail"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "\n",
    "**Note:** This section is currently under developement.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In practice, one does not necessarily need to construct a density connectivity graph in its entirety beforehand. It is also possible to start from another input structure and explore the connectivity while traversing the structure. We will now show a variant of the CNN clustering procedure, starting from pre-computed neighbourhoods in more detail. For this, we generate a small example data set of 200 points in 2D."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:34:18.819345Z",
     "start_time": "2020-08-20T15:34:18.761027Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[], [], None]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 750x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "noisy_circles, _ = datasets.make_circles(\n",
    "    n_samples=200,\n",
    "    factor=.5,\n",
    "    noise=.05,\n",
    "    random_state=8\n",
    "    )\n",
    "\n",
    "noisy_circles = StandardScaler().fit_transform(noisy_circles)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(*noisy_circles.T, \"k.\")\n",
    "ax.set(**{\n",
    "    \"xticks\": (),\n",
    "    \"yticks\": (),\n",
    "    \"aspect\": \"equal\"\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We expect to find two clusters (an inner and an outer ring) in this data set. We will at first compute the neighbourhoods for all points with respect to a radius of $r$. Below we show the neighbourhood for the first point in the set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:34:20.718879Z",
     "start_time": "2020-08-20T15:34:20.716946Z"
    }
   },
   "outputs": [],
   "source": [
    "r = 0.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:34:21.083285Z",
     "start_time": "2020-08-20T15:34:21.075537Z"
    }
   },
   "outputs": [],
   "source": [
    "def point_zoom(data, point, ax):\n",
    "    ax.plot(*data.T, \"k.\")\n",
    "    ax.plot(*data[point].T, \"r.\")\n",
    "    \n",
    "    neighbourhood = mpl.patches.Circle(\n",
    "        data[point], r,\n",
    "        edgecolor=\"k\",\n",
    "        facecolor=\"grey\"\n",
    "    )\n",
    "    ax.add_patch(neighbourhood)\n",
    "    \n",
    "    limit_factor = 1.2\n",
    "    ax.set_xlim(data[point][0] - r * limit_factor,\n",
    "                data[point][0] + r * limit_factor)\n",
    "    ax.set_ylim(data[point][1] - r * limit_factor,\n",
    "                data[point][1] + r * limit_factor)\n",
    "    ax.set(**{\n",
    "        \"xticks\": (),\n",
    "        \"yticks\": (),\n",
    "        \"aspect\": \"equal\"\n",
    "    })"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:34:22.034243Z",
     "start_time": "2020-08-20T15:34:21.989753Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 750x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "point_zoom(noisy_circles, 0, ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:34:22.524291Z",
     "start_time": "2020-08-20T15:34:22.513452Z"
    }
   },
   "outputs": [],
   "source": [
    "# Calculate neighbourhoods using a k-d tree\n",
    "tree = cKDTree(noisy_circles)\n",
    "neighbourhoods = [set(x) for x in tree.query_ball_point(noisy_circles, r)]\n",
    "for i, s in enumerate(neighbourhoods):\n",
    "    # Avoid neighbour self-counting\n",
    "    s.remove(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:34:23.194298Z",
     "start_time": "2020-08-20T15:34:23.184980Z"
    }
   },
   "outputs": [],
   "source": [
    "def check_similarity(a, b, c):\n",
    "    \"\"\"Check the CNN density criterion\"\"\"\n",
    "    if len(a & b) >= c:\n",
    "        return True\n",
    "    return False\n",
    "\n",
    "def cnn_from_neighbourhoods(\n",
    "        neighbourhoods, c, yield_iterations=False):\n",
    "    \"\"\"Apply CNN clustering\n",
    "    \n",
    "    neighbourhoods:\n",
    "        list of sets of point indices\n",
    "        (neighbours of each point)\n",
    "    c:\n",
    "        Density reachable points need at least this many common\n",
    "        nearest neighbours\n",
    "    yield_iterations:\n",
    "        Report state of clustering after each label assignment\n",
    "    \"\"\"\n",
    "    \n",
    "    n = len(neighbourhoods)              # Number of points\n",
    "    visited = [False for _ in range(n)]  # Track visited\n",
    "    labels = [0 for _ in range(n)]       # Output container\n",
    "    queue = deque()                      # FIFO queue    \n",
    "    current = 1                          # Cluster count\n",
    "    \n",
    "    for point in range(n):\n",
    "        # Source node\n",
    "        if visited[point]:\n",
    "            continue\n",
    "        \n",
    "        visited[point] = True\n",
    "\n",
    "        neighbours = neighbourhoods[point]\n",
    "        if len(neighbours) <= c:\n",
    "            continue\n",
    "\n",
    "        labels[point] = current\n",
    "\n",
    "        if yield_iterations:\n",
    "            # Get current state of clustering\n",
    "            yield (point, None, current, labels, visited)\n",
    "\n",
    "        while True:\n",
    "            for member in neighbours:\n",
    "                if visited[member]:\n",
    "                    continue\n",
    "                    \n",
    "                neighbour_neighbours = neighbourhoods[member]\n",
    "                if len(neighbour_neighbours) <= c:\n",
    "                    continue\n",
    "                    \n",
    "                if check_similarity(neighbours, neighbour_neighbours, c):\n",
    "                    labels[member] = current\n",
    "                    visited[member] = True\n",
    "                    queue.append(member)\n",
    "                    \n",
    "                    if yield_iterations:\n",
    "                        # Get current state of clustering\n",
    "                        yield (point, member, current, labels, visited)\n",
    "\n",
    "            if not queue:\n",
    "                break\n",
    "\n",
    "            point = queue.popleft()\n",
    "            neighbours = neighbourhoods[point]\n",
    "\n",
    "        current += 1\n",
    "    \n",
    "    if not yield_iterations:\n",
    "        yield labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:34:23.848579Z",
     "start_time": "2020-08-20T15:34:23.840758Z"
    }
   },
   "outputs": [],
   "source": [
    "def plt_iteration(\n",
    "        data, iteration=None, ax=None, ax_props=None, color_list=None):\n",
    "\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    else:\n",
    "        fig = ax.get_figure()\n",
    "        \n",
    "    ax_props_defaults = {\n",
    "        \"xticks\": (),\n",
    "        \"yticks\": (),\n",
    "        \"aspect\": \"equal\"\n",
    "    }\n",
    "    \n",
    "    if ax_props is not None:\n",
    "        ax_props_defaults.update(ax_props)\n",
    "    \n",
    "    if iteration is not None:\n",
    "        point, member, current, labels, visited = iteration\n",
    "        \n",
    "        if color_list is None:\n",
    "            color_list = [\n",
    "                \"black\"] + [i[\"color\"]\n",
    "                            for i in islice(mpl.rcParams[\"axes.prop_cycle\"],\n",
    "                                            current)]\n",
    "\n",
    "        for cluster in range(current + 1):\n",
    "            indices = np.where(np.asarray(labels) == cluster)[0]\n",
    "            ax.plot(*data[indices].T, c=color_list[cluster],\n",
    "                    linestyle=\"\", marker=\".\")\n",
    "        \n",
    "    else:\n",
    "        ax.plot(*data.T)    \n",
    "        \n",
    "    ax.set(**ax_props_defaults)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:36:30.745344Z",
     "start_time": "2020-08-20T15:36:23.230165Z"
    }
   },
   "outputs": [],
   "source": [
    "class AnimatedIterations:\n",
    "    \"\"\"An animated scatter plot using matplotlib.animations.FuncAnimation.\"\"\"\n",
    "    def __init__(self, data, iterations=None):\n",
    "        self.data = data\n",
    "        self.iterations = iter(iterations)\n",
    "        self.highlights = deque(maxlen=5)\n",
    "        self.sizes = np.ones(len(self.data)) * 10\n",
    "\n",
    "        self.fig, self.ax = plt.subplots()\n",
    "        self.animation = animation.FuncAnimation(\n",
    "            self.fig, self.update, frames=200, interval=100,\n",
    "            init_func=self.setup_plot, blit=True\n",
    "            )\n",
    "\n",
    "    def setup_plot(self):\n",
    "        \"\"\"Initial drawing of the scatter plot.\"\"\"\n",
    "        self.scatter = self.ax.scatter(\n",
    "            *self.data.T,\n",
    "            s=self.sizes,\n",
    "            c=np.asarray([0 for _ in range(len(self.data))]),\n",
    "            cmap=mpl.colors.LinearSegmentedColormap.from_list(\n",
    "                \"cluster_map\",\n",
    "                [\"black\"] + [i[\"color\"]\n",
    "                             for i in islice(mpl.rcParams[\"axes.prop_cycle\"],\n",
    "                                             2)]\n",
    "                ),\n",
    "            vmin=0, vmax=2\n",
    "            )\n",
    "        # self.ax.axis([-10, 10, -10, 10])\n",
    "        # For FuncAnimation's sake, we need to return the artist we'll be using\n",
    "        # Note that it expects a sequence of artists, thus the trailing comma.\n",
    "        return self.scatter,\n",
    "\n",
    "    def update(self, i):\n",
    "        \"\"\"Update the scatter plot.\"\"\"\n",
    "        point, member, current, labels, visited = next(self.iterations)\n",
    "        if member is None:\n",
    "            self.highlights.append(point)\n",
    "        else:\n",
    "            self.highlights.append(member)\n",
    "            \n",
    "        for c, p in enumerate(self.highlights, 1):\n",
    "            self.sizes[p] = c * 10\n",
    "        \n",
    "        # Set sizes\n",
    "        self.scatter.set_sizes(self.sizes)\n",
    "        \n",
    "        # Set colors\n",
    "        self.scatter.set_array(np.asarray(labels))\n",
    "\n",
    "        # We need to return the updated artist for FuncAnimation to draw..\n",
    "        # Note that it expects a sequence of artists, thus the trailing comma.\n",
    "        return self.scatter,\n",
    "\n",
    "\n",
    "Animation = AnimatedIterations(noisy_circles, cnn_from_neighbourhoods(neighbourhoods, 5, yield_iterations=True))\n",
    "# Animation.animation.save('iteration.mp4', dpi=150)\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-20T15:41:34.017597Z",
     "start_time": "2020-08-20T15:41:34.013015Z"
    }
   },
   "outputs": [
    {
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