{
 "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": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-26T15:44:34.703366Z",
     "start_time": "2021-04-26T15:44:34.697471Z"
    }
   },
   "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": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-26T15:44:35.521771Z",
     "start_time": "2021-04-26T15:44:35.515581Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8.8 | packaged by conda-forge | (default, Feb 20 2021, 16:22:27) \n",
      "[GCC 9.3.0]\n"
     ]
    }
   ],
   "source": [
    "# Version information\n",
    "print(sys.version)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-26T15:44:35.902084Z",
     "start_time": "2021-04-26T15:44:35.894027Z"
    }
   },
   "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": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-26T15:44:36.724749Z",
     "start_time": "2021-04-26T15:44:36.714521Z"
    }
   },
   "outputs": [],
   "source": [
    "def gauss(x, sigma, mu):\n",
    "    \"\"\"Gaussian PDF\"\"\"\n",
    "    return (1 / (sigma * np.sqrt(2 * np.pi)) * np.exp(-1 / 2 * ((x - mu) / sigma)**2))\n",
    "    \n",
    "def multigauss(x, sigmas, mus):\n",
    "    \"\"\"Multimodal gaussian PDF as linear combination of gaussian PDFs\"\"\"\n",
    "    assert len(sigmas) == len(mus)\n",
    "    \n",
    "    out = np.zeros_like(x)\n",
    "    for s, m in zip(sigmas, mus):\n",
    "        out += gauss(x, s, m)\n",
    "    return out / len(sigmas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-26T15:44:37.088761Z",
     "start_time": "2021-04-26T15:44:37.082796Z"
    }
   },
   "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": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-26T15:44:37.435554Z",
     "start_time": "2021-04-26T15:44:37.430392Z"
    }
   },
   "outputs": [],
   "source": [
    "class multigauss_distribution(stats.rv_continuous):\n",
    "    \"\"\"Draw samples from a multimodal gaussian distribution\"\"\"\n",
    "           \n",
    "    def __init__(self, sigmas, mus, *args, **kwargs):\n",
    "        super().__init__(*args, **kwargs)\n",
    "        self._sigmas = sigmas\n",
    "        self._mus = mus\n",
    "\n",
    "    def _pdf(self, x):\n",
    "        return multigauss(x, sigmas=self._sigmas, mus=self._mus)"
   ]
  },
  {
   "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": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-26T15:44:38.643919Z",
     "start_time": "2021-04-26T15:44:38.388144Z"
    }
   },
   "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, sigmas=[1, 1.5], mus=[-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": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-26T15:44:39.661035Z",
     "start_time": "2021-04-26T15:44:39.475713Z"
    }
   },
   "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, sigmas=[1, 1.5], mus=[-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, sigmas=[1, 1.5], mus=[-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., sigmas=[1, 1.5], mus=[-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": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-04-26T15:45:22.979494Z",
     "start_time": "2021-04-26T15:45:22.749447Z"
    }
   },
   "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, sigmas=[1, 1.5], mus=[-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(\n",
    "            cut,\n",
    "            color=\"gray\",\n",
    "            alpha=0.5,\n",
    "            linewidth=1,\n",
    "            zorder=0\n",
    "            )\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": 32,
   "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",
    "    sigmas=[1, 1.5], mus=[-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, sigmas=[1, 1.5], mus=[-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": 33,
   "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, sigmas=[1, 1.5], mus=[-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": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Common nearest neighbour clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples2D = np.vstack([np.random.normal((-1, 0), (0.4, 0.4), (10, 2)), np.random.normal((1, 0), (0.4, 0.4), (10, 2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.save(\"algorithm_explained/samples\", samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.intersect1d([1], [1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 499.5x307.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Density criterion / Density reachability in 2D\n",
    "fig, ax = plt.subplots(figsize=(3.33, 2.05))\n",
    "r = 0.5\n",
    "c = 2\n",
    "\n",
    "neighbourhoods = np.array([\n",
    "    # Neighbour within r?\n",
    "    np.where((0 < x) & (x <= r))[0]\n",
    "    # distance matrix\n",
    "    for x in np.sqrt(np.subtract.outer(samples2D[:, 0], samples2D[:, 0])**2 + np.subtract.outer(samples2D[:, 1], samples2D[:, 1])**2)\n",
    "    ], dtype=object)\n",
    "\n",
    "for node, neighbours in enumerate(neighbourhoods):\n",
    "    for other_node in neighbours:\n",
    "        if np.intersect1d(neighbours, neighbourhoods[other_node]).shape[0] >= c:\n",
    "            # Density criterion fullfilled\n",
    "            ax.plot(*zip(samples2D[node], samples2D[other_node]), color=\"brown\", alpha=0.25, linewidth=0.75, zorder=0)\n",
    "\n",
    "source = 12\n",
    "member = 15\n",
    "intersection = [13, 18]\n",
    "classification = np.zeros(samples2D.shape[0])\n",
    "classification[source] = 1\n",
    "classification[member] = 2\n",
    "classification[intersection] = 3\n",
    "\n",
    "ax.plot(*zip(samples2D[source], samples2D[member]), color=\"brown\", alpha=1, linewidth=0.75, zorder=0)\n",
    "\n",
    "ax.annotate(\n",
    "    \"\", (samples2D[member][0] - r, samples2D[member][1]), samples2D[member],\n",
    "    arrowprops={\n",
    "        \"shrink\": 0, \"width\": 0.75, \"headwidth\": 3, \"headlength\": 3,\n",
    "        \"facecolor\": \"k\", \"linewidth\": 0\n",
    "        },\n",
    "    zorder=0\n",
    "    )\n",
    "\n",
    "ax.annotate(\n",
    "    \"$r$\", (samples2D[member][0] - r/2, samples2D[member][1] + 0.05),\n",
    "    fontsize=8\n",
    "    )\n",
    "\n",
    "ax.scatter(*samples2D.T, s=15, c=classification, linewidth=1, edgecolor=\"k\")\n",
    "neighbourhood = mpl.patches.Circle(\n",
    "    samples2D[source], r,\n",
    "    facecolor=\"None\",\n",
    "    edgecolor=\"k\", linewidth=0.75\n",
    "    )\n",
    "neighbourhood2 = mpl.patches.Circle(\n",
    "    samples2D[member], r,\n",
    "    facecolor=\"None\",\n",
    "    edgecolor=\"k\", linewidth=0.75\n",
    "    )\n",
    "ax.add_patch(neighbourhood)\n",
    "ax.add_patch(neighbourhood2)\n",
    "ax.set(**{\n",
    "    \"xticks\": (),\n",
    "    \"yticks\": (),\n",
    "    \"aspect\": \"equal\"\n",
    "})\n",
    "# fig.tight_layout(pad=0.1)\n",
    "# plt.savefig(\"/home/janjoswig/Documents/Projects/CNN/Manuscript/figures/density_criterion.png\")"
   ]
  },
  {
   "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": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:56:03.042701Z",
     "start_time": "2020-09-21T08:56:02.927063Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[], [], None]"
      ]
     },
     "execution_count": 13,
     "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": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:56:15.693273Z",
     "start_time": "2020-09-21T08:56:15.688379Z"
    }
   },
   "outputs": [],
   "source": [
    "r = 0.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:55:42.354214Z",
     "start_time": "2020-09-21T08:55:42.331259Z"
    }
   },
   "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": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:56:18.462760Z",
     "start_time": "2020-09-21T08:56:18.444603Z"
    }
   },
   "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": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:56:21.247309Z",
     "start_time": "2020-09-21T08:56:21.206190Z"
    }
   },
   "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": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:56:22.287028Z",
     "start_time": "2020-09-21T08:56:22.268185Z"
    }
   },
   "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": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:58:48.070955Z",
     "start_time": "2020-09-21T08:58:47.915781Z"
    }
   },
   "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": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:59:06.525528Z",
     "start_time": "2020-09-21T08:58:48.435835Z"
    }
   },
   "outputs": [],
   "source": [
    "Animation.animation.save('iteration.mp4', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:57:54.313923Z",
     "start_time": "2020-09-21T08:57:40.822150Z"
    }
   },
   "outputs": [
    {
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