{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:47:32.830267Z",
     "start_time": "2017-05-12T18:47:32.825599+02:00"
    }
   },
   "source": [
    "# Linkage Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modified version of \n",
    "\n",
    "https://joernhees.de/blog/2015/08/26/scipy-hierarchical-clustering-and-dendrogram-tutorial/\n",
    "\n",
    "by Jörn Hees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-15T06:39:27.481737Z",
     "start_time": "2017-05-15T08:39:27.476533+02:00"
    }
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from scipy.cluster.hierarchy import dendrogram, linkage\n",
    "import numpy as np\n",
    "\n",
    "# some setting for this notebook to actually show the graphs inline, you probably won't need this\n",
    "%matplotlib inline\n",
    "np.set_printoptions(precision=5, suppress=True)  # suppress scientific float notation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-15T06:39:28.032301Z",
     "start_time": "2017-05-15T08:39:27.914444+02:00"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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31vyf7hrunosP4ApgUfn1nwB/ErHeC8CZbWhPP/AL4MPAKcCTwK9VrfNfgP9R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\nyRkFdhGRnFFgFxHJGQV2EZGc+f87lFsf/ZGpIAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3ec05b3110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate two clusters: a with 100 points, b with 50:\n",
    "np.random.seed(4711)  # for repeatability of this tutorial\n",
    "a = np.random.multivariate_normal([10, 0], [[3, 1], [1, 4]], size=[100,])\n",
    "b = np.random.multivariate_normal([0, 20], [[3, 1], [1, 4]], size=[50,])\n",
    "X = np.concatenate((a, b),)\n",
    "print X.shape  # 150 samples with 2 dimensions\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perform the Hierarchical Clustering\n",
    "\n",
    "Now that we have some very simple sample data, let's do the actual clustering on it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-15T06:39:29.302548Z",
     "start_time": "2017-05-15T08:39:29.297667+02:00"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# generate the linkage matrix\n",
    "Z = linkage(X, 'single') # also 'max' ' ward'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:16:20.880113Z",
     "start_time": "2017-05-12T18:16:20.873750+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 52.     ,  53.     ,   0.04151,   2.     ])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that ach row of the resulting array has the format [idx1, idx2, dist, sample_count].\n",
    "\n",
    "In its first iteration the linkage algorithm decided to merge the two clusters (original samples here) with indices 52 and 53, as they only had a distance of 0.04151. This created a cluster with a total of 2 samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:16:39.950594Z",
     "start_time": "2017-05-12T18:16:39.943834+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 14.     ,  79.     ,   0.05914,   2.     ])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:16:33.711697Z",
     "start_time": "2017-05-12T18:16:33.703018+02:00"
    }
   },
   "source": [
    "In the second iteration the algorithm decided to merge the clusters (original samples here as well) with indices 14 and 79, which had a distance of 0.04914. This again formed another cluster with a total of 2 samples.\n",
    "\n",
    "The indices of the clusters until now correspond to our samples. Remember that we had a total of 150 samples, so indices 0 to 149. Let's have a look at the first 20 iterations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:19:06.050245Z",
     "start_time": "2017-05-12T18:19:06.039065+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  52.     ,   53.     ,    0.04151,    2.     ],\n",
       "       [  14.     ,   79.     ,    0.05914,    2.     ],\n",
       "       [  33.     ,   68.     ,    0.07107,    2.     ],\n",
       "       [  17.     ,   73.     ,    0.07137,    2.     ],\n",
       "       [   1.     ,    8.     ,    0.07543,    2.     ],\n",
       "       [  85.     ,   95.     ,    0.10928,    2.     ],\n",
       "       [ 108.     ,  131.     ,    0.11007,    2.     ],\n",
       "       [   9.     ,   66.     ,    0.11302,    2.     ],\n",
       "       [  15.     ,   69.     ,    0.11429,    2.     ],\n",
       "       [  63.     ,   98.     ,    0.1212 ,    2.     ],\n",
       "       [ 107.     ,  115.     ,    0.12167,    2.     ],\n",
       "       [  65.     ,   74.     ,    0.1249 ,    2.     ],\n",
       "       [  41.     ,  158.     ,    0.13314,    3.     ],\n",
       "       [  58.     ,   61.     ,    0.14028,    2.     ],\n",
       "       [  62.     ,  152.     ,    0.14862,    3.     ]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z[:15]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:17:34.471964Z",
     "start_time": "2017-05-12T18:17:34.463364+02:00"
    }
   },
   "source": [
    "We can observe that until iteration 13 the algorithm only directly merged original samples. We can also observe the monotonic increase of the distance.\n",
    "\n",
    "In iteration 13 the algorithm decided to merge cluster indices 62 with 158. If you paid attention the 152 should astonish you as we only have original sample indices 0 to 149 for our 150 samples. All indices idx >= len(X) actually refer to the cluster formed in Z[idx - len(X)].\n",
    "\n",
    "This means that while idx 149 corresponds to X[149] that idx 150 corresponds to the cluster formed in Z[0], idx 151 to Z[1], 152 to Z[2], ...\n",
    "\n",
    "Hence, the merge iteration 13 merged sample 41 to our samples 15 and 69 that were previously merged in iteration 8.\n",
    "\n",
    "Let's check out the points coordinates to see if this makes sense:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:22:15.678823Z",
     "start_time": "2017-05-12T18:22:15.673902+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8.81583, -0.56394],\n",
       "       [ 8.72437, -0.73102],\n",
       "       [ 8.6953 , -0.62049]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[[41, 15, 69]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:23:27.008498Z",
     "start_time": "2017-05-12T18:23:27.001613+02:00"
    }
   },
   "source": [
    "Seems pretty close..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting a Dendrogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:23:44.976982Z",
     "start_time": "2017-05-12T18:23:44.969408+02:00"
    }
   },
   "source": [
    "A dendrogram is a visualization in form of a tree showing the order and distances of merges during the hierarchical clustering."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:24:09.981641Z",
     "start_time": "2017-05-12T18:24:09.249043+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3ec09f18d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calculate full dendrogram\n",
    "plt.figure(figsize=(25, 10))\n",
    "plt.title('Hierarchical Clustering Dendrogram')\n",
    "plt.xlabel('sample index')\n",
    "plt.ylabel('distance')\n",
    "dendrogram(\n",
    "    Z,\n",
    "    leaf_rotation=90.,  # rotates the x axis labels\n",
    "    leaf_font_size=8.,  # font size for the x axis labels\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:24:52.050124Z",
     "start_time": "2017-05-12T18:24:52.040471+02:00"
    }
   },
   "source": [
    "If this is the first time you see a dendrogram, it's probably quite confusing, so let's take this apart...\n",
    "\n",
    "On the x axis you see labels. If you don't specify anything else they are the indices of your samples in X.\n",
    "On the y axis you see the distances (of the 'single linkage' method in our case).\n",
    "Starting from each label at the bottom, you can see a vertical line up to a horizontal line. The height of that horizontal line tells you about the distance at which this label was merged into another label or cluster. You can find that other cluster by following the other vertical line down again. If you don't encounter another horizontal line, it was just merged with the other label you reach, otherwise it was merged into another cluster that was formed earlier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Summarizing:__\n",
    "\n",
    "- horizontal lines are cluster merges\n",
    "- vertical lines tell you which clusters/labels were part of merge forming that new cluster\n",
    "- heights of the horizontal lines tell you about the distance that needed to be \"bridged\" to form the new cluster\n",
    "- You can also see that from distances > 25 up there's a huge jump of the distance to the final merge at a distance of approx. 180. Let's have a look at the distances of the last 4 merges:\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:28:20.913687Z",
     "start_time": "2017-05-12T18:28:20.908499+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  2.01561,   2.0993 ,   3.78363,  15.44509])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z[-4:,2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Such distance jumps / gaps in the dendrogram are pretty interesting for us. They indicate that something is merged here, that maybe just shouldn't be merged. In other words: maybe the things that were merged here really don't belong to the same cluster, telling us that maybe there's just 2 clusters here.\n",
    "\n",
    "Looking at indices in the above dendrogram also shows us that the green cluster only has indices >= 100, while the red one only has such < 100. This is a good thing as it shows that the algorithm re-discovered the two classes in our toy example.\n",
    "\n",
    "In case you're wondering about where the colors come from, you might want to have a look at the color_threshold argument of dendrogram(), which as not specified automagically picked a distance cut-off value of 70 % of the final merge and then colored the first clusters below that in individual colors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dendrogram Truncation\n",
    "\n",
    "As you might have noticed, the above is pretty big for 150 samples already and you probably have way more in real scenarios, so let me spend a few seconds on highlighting some other features of the dendrogram() function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:31:03.723362Z",
     "start_time": "2017-05-12T18:31:03.455384+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vLDDGscBDpOs8vgi8C9gv//9iHv4Q8LGC4t0J/BB4AzC0ZdxQYJ88/o4Cl3Fx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\nIjAzqzknAjOzmnMiMDOruf8P9d5kLc5syMoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3ec0373550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Hierarchical Clustering Dendrogram (truncated)')\n",
    "plt.xlabel('sample index')\n",
    "plt.ylabel('distance')\n",
    "dendrogram(\n",
    "    Z,\n",
    "    truncate_mode='lastp',  # show only the last p merged clusters\n",
    "    p=12,  # show only the last p merged clusters    \n",
    "    leaf_rotation=90.,\n",
    "    leaf_font_size=12.,\n",
    "    show_contracted=True,  # to get a distribution impression in truncated branches\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:31:59.746665Z",
     "start_time": "2017-05-12T18:31:59.739414+02:00"
    }
   },
   "source": [
    "## Selecting a Distance Cut-Off aka Determining the Number of Clusters\n",
    "\n",
    "As explained above already, a huge jump in distance is typically what we're interested in if we want to argue for a certain number of clusters. If you have the chance to do this manually, i'd always opt for that, as it allows you to gain some insights into your data and to perform some sanity checks on the edge cases. In our case i'd probably just say that our cut-off is 50, as the jump is pretty obvious:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:36:13.683268Z",
     "start_time": "2017-05-12T18:36:13.397934+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3ec0699890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set cut-off to 6\n",
    "max_d = 6  # max_d as in max_distance\n",
    "# Let's visualize this in the dendrogram as a cut-off line:\n",
    "dendrogram(\n",
    "    Z,\n",
    "    truncate_mode='lastp',\n",
    "    p=12,\n",
    "    leaf_rotation=90.,\n",
    "    leaf_font_size=12.,\n",
    "    show_contracted=True,    \n",
    ")\n",
    "plt.axhline(y=max_d, c='k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:36:21.010633Z",
     "start_time": "2017-05-12T18:36:21.004589+02:00"
    }
   },
   "source": [
    "As we can see, we (\"surprisingly\") have two clusters at this cut-off."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:36:53.819164Z",
     "start_time": "2017-05-12T18:36:53.810408+02:00"
    }
   },
   "source": [
    "## Automated Cut-Off Selection is doomed to fail\n",
    "\n",
    "See more on the original blog post cited above.\n",
    "\n",
    "Now while this manual selection of a cut-off value offers a lot of benefits when it comes to checking for a meaningful clustering and cut-off, there are cases in which you want to automate this.\n",
    "\n",
    "The problem again is that there is no golden method to pick the number of clusters for all cases (which is why i think the investigative & backtesting manual method is preferable). Wikipedia lists a couple of common methods. Reading this, you should realize how different the approaches and how vague their descriptions are.\n",
    "\n",
    "I honestly think it's a really bad idea to just use any of those methods, unless you know the data you're working on really really well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## more clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:39:11.837416Z",
     "start_time": "2017-05-12T18:39:11.639833+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0UsY7ZyemHc/nBA/evAKvb70Wcy5o7+xlqViYtkAakV2sQC8ilwC4FsB3jcsC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3ec09143d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = np.random.multivariate_normal([40, 40], [[20, 1], [1, 30]], size=[200,])\n",
    "d = np.random.multivariate_normal([80, 80], [[30, 1], [1, 30]], size=[200,])\n",
    "e = np.random.multivariate_normal([0, 100], [[100, 1], [1, 100]], size=[200,])\n",
    "X2 = np.concatenate((X, c, d, e),)\n",
    "plt.scatter(X2[:,0], X2[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see we have 5 clusters now, but they have increasing variances... let's have a look at the dendrogram again and how you can use it to spot the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:50:10.384750Z",
     "start_time": "2017-05-12T18:50:09.644076+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAMCBMAUAAOBAmAIAAHAgTAEAADgQpgAAABwIUwAAAA6EKQAAAAfCFAAAgANhCgAAwIEw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\npmo9U4cOHXLX6un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r672k35b0nQJt6lecsudnivNeDStOYfCA4nbvKQVqXZWtk89TPJq+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3ec08cd550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z2 = linkage(X2, 'single')\n",
    "plt.figure(figsize=(10,10))\n",
    "dendrogram(\n",
    "    Z2,\n",
    "    truncate_mode='lastp',\n",
    "    p=30,\n",
    "    leaf_rotation=90.,\n",
    "    leaf_font_size=12.,\n",
    "    show_contracted=True,    \n",
    ")\n",
    "plt.axhline(y=15, c='k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:42:51.486567Z",
     "start_time": "2017-05-12T18:42:51.479637+02:00"
    }
   },
   "source": [
    "## Performing Clustering (with stopping) and Visualize clusters\n",
    "\n",
    "If you're lucky enough and your data is very low dimensional, you can actually visualize the resulting clusters very easily:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:43:25.983156Z",
     "start_time": "2017-05-12T18:43:25.979298+02:00"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.cluster.hierarchy import fcluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:46:04.016183Z",
     "start_time": "2017-05-12T18:46:03.980337+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,\n",
       "       4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,\n",
       "       4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,\n",
       "       4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,\n",
       "       4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,\n",
       "       4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,\n",
       "       4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,\n",
       "       3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_d = 20\n",
    "clusters = fcluster(Z2, max_d, criterion='distance')\n",
    "clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-05-12T16:46:05.542005Z",
     "start_time": "2017-05-12T18:46:05.285137+02:00"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5qXOK7nnp1BXaFHwvyfN0Bh2mQCNfrh1E/lJ5UvQMIYQQ/17JDbIkJ+sR3Lke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1RMwtsnUIUswPljj+nfmxKRQU89WSIy6D2w6TVS+xT/TOPYFW9gce36TssgvFG7gdvefoZl9ZsJ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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3ecc070410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 8))\n",
    "plt.scatter(X2[:,0], X2[:,1], c=clusters)  # plot points with cluster dependent colors\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}