{
 "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": "2020-09-21T08:54:50.375128Z",
     "start_time": "2020-09-21T08:54:49.382085Z"
    }
   },
   "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": "2020-09-21T08:54:50.380827Z",
     "start_time": "2020-09-21T08:54:50.376974Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8.5 | packaged by conda-forge | (default, Aug 21 2020, 18:21:27) \n",
      "[GCC 7.5.0]\n"
     ]
    }
   ],
   "source": [
    "# Version information\n",
    "print(sys.version)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:55:12.862057Z",
     "start_time": "2020-09-21T08:55:12.851591Z"
    }
   },
   "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": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:55:15.494203Z",
     "start_time": "2020-09-21T08:55:15.477639Z"
    }
   },
   "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": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:55:15.856309Z",
     "start_time": "2020-09-21T08:55:15.842765Z"
    }
   },
   "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": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-21T08:55:16.907338Z",
     "start_time": "2020-09-21T08:55:16.894581Z"
    }
   },
   "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": 24,
   "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, 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": 26,
   "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, 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": 27,
   "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, 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(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": 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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