Seeds Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Seeds Clustering\n",
    "____\n",
    "\n",
    "In this example, we would implement Unsupervised Learning techniques to cluster seeds into groups based on the attributes in the dataset.\n",
    "\n",
    "You can download the dataset from : https://archive.ics.uci.edu/ml/datasets/seeds\n",
    "\n",
    "To construct the data, seven geometric parameters of wheat kernels were measured: \n",
    "\n",
    "1. area A, \n",
    "2. perimeter P, \n",
    "3. compactness C = 4*pi*A/P^2, \n",
    "4. length of kernel, \n",
    "5. width of kernel, \n",
    "6. asymmetry coefficient \n",
    "7. length of kernel groove. \n",
    "8. The 3 Classes - three different varieties of wheat\n",
    "\n",
    "All of these parameters are real-valued continuous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn import cross_validation, metrics\n",
    "from sklearn import preprocessing\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cols = ['Area', 'Perimeter','Compactness','Kernel_Length','Kernel_Width','Assymetry_Coefficient','Kernel_Groove_Length', 'Class']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# read .csv from provided dataset\n",
    "csv_filename=\"seeds_dataset.txt\"\n",
    "\n",
    "# df=pd.read_csv(csv_filename,index_col=0)\n",
    "df=pd.read_csv(csv_filename,delim_whitespace=True,names=cols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Area</th>\n",
       "      <th>Perimeter</th>\n",
       "      <th>Compactness</th>\n",
       "      <th>Kernel_Length</th>\n",
       "      <th>Kernel_Width</th>\n",
       "      <th>Assymetry_Coefficient</th>\n",
       "      <th>Kernel_Groove_Length</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>15.26</td>\n",
       "      <td>14.84</td>\n",
       "      <td>0.8710</td>\n",
       "      <td>5.763</td>\n",
       "      <td>3.312</td>\n",
       "      <td>2.221</td>\n",
       "      <td>5.220</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14.88</td>\n",
       "      <td>14.57</td>\n",
       "      <td>0.8811</td>\n",
       "      <td>5.554</td>\n",
       "      <td>3.333</td>\n",
       "      <td>1.018</td>\n",
       "      <td>4.956</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14.29</td>\n",
       "      <td>14.09</td>\n",
       "      <td>0.9050</td>\n",
       "      <td>5.291</td>\n",
       "      <td>3.337</td>\n",
       "      <td>2.699</td>\n",
       "      <td>4.825</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13.84</td>\n",
       "      <td>13.94</td>\n",
       "      <td>0.8955</td>\n",
       "      <td>5.324</td>\n",
       "      <td>3.379</td>\n",
       "      <td>2.259</td>\n",
       "      <td>4.805</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>16.14</td>\n",
       "      <td>14.99</td>\n",
       "      <td>0.9034</td>\n",
       "      <td>5.658</td>\n",
       "      <td>3.562</td>\n",
       "      <td>1.355</td>\n",
       "      <td>5.175</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Area  Perimeter  Compactness  Kernel_Length  Kernel_Width  \\\n",
       "0  15.26      14.84       0.8710          5.763         3.312   \n",
       "1  14.88      14.57       0.8811          5.554         3.333   \n",
       "2  14.29      14.09       0.9050          5.291         3.337   \n",
       "3  13.84      13.94       0.8955          5.324         3.379   \n",
       "4  16.14      14.99       0.9034          5.658         3.562   \n",
       "\n",
       "   Assymetry_Coefficient  Kernel_Groove_Length  Class  \n",
       "0                  2.221                 5.220      1  \n",
       "1                  1.018                 4.956      1  \n",
       "2                  2.699                 4.825      1  \n",
       "3                  2.259                 4.805      1  \n",
       "4                  1.355                 5.175      1  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Area', 'Perimeter', 'Compactness', 'Kernel_Length', 'Kernel_Width',\n",
       "       'Assymetry_Coefficient', 'Kernel_Groove_Length'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = df.columns[:-1]\n",
    "features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = df[features]\n",
    "y = df['Class']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Area</th>\n",
       "      <th>Perimeter</th>\n",
       "      <th>Compactness</th>\n",
       "      <th>Kernel_Length</th>\n",
       "      <th>Kernel_Width</th>\n",
       "      <th>Assymetry_Coefficient</th>\n",
       "      <th>Kernel_Groove_Length</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>15.26</td>\n",
       "      <td>14.84</td>\n",
       "      <td>0.8710</td>\n",
       "      <td>5.763</td>\n",
       "      <td>3.312</td>\n",
       "      <td>2.221</td>\n",
       "      <td>5.220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14.88</td>\n",
       "      <td>14.57</td>\n",
       "      <td>0.8811</td>\n",
       "      <td>5.554</td>\n",
       "      <td>3.333</td>\n",
       "      <td>1.018</td>\n",
       "      <td>4.956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14.29</td>\n",
       "      <td>14.09</td>\n",
       "      <td>0.9050</td>\n",
       "      <td>5.291</td>\n",
       "      <td>3.337</td>\n",
       "      <td>2.699</td>\n",
       "      <td>4.825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13.84</td>\n",
       "      <td>13.94</td>\n",
       "      <td>0.8955</td>\n",
       "      <td>5.324</td>\n",
       "      <td>3.379</td>\n",
       "      <td>2.259</td>\n",
       "      <td>4.805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>16.14</td>\n",
       "      <td>14.99</td>\n",
       "      <td>0.9034</td>\n",
       "      <td>5.658</td>\n",
       "      <td>3.562</td>\n",
       "      <td>1.355</td>\n",
       "      <td>5.175</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Area  Perimeter  Compactness  Kernel_Length  Kernel_Width  \\\n",
       "0  15.26      14.84       0.8710          5.763         3.312   \n",
       "1  14.88      14.57       0.8811          5.554         3.333   \n",
       "2  14.29      14.09       0.9050          5.291         3.337   \n",
       "3  13.84      13.94       0.8955          5.324         3.379   \n",
       "4  16.14      14.99       0.9034          5.658         3.562   \n",
       "\n",
       "   Assymetry_Coefficient  Kernel_Groove_Length  \n",
       "0                  2.221                 5.220  \n",
       "1                  1.018                 4.956  \n",
       "2                  2.699                 4.825  \n",
       "3                  2.259                 4.805  \n",
       "4                  1.355                 5.175  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# split dataset to 60% training and 40% testing\n",
    "X_train, X_test, y_train, y_test = cross_validation.train_test_split(X, y, test_size=0.4, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((126, 7), (126,))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape, y_train.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "# Unsupervised Learning\n",
    "<hr>\n",
    "## Feature Transformation\n",
    "\n",
    "The first PCA dimension is the dimension in the data with highest variance. Intuitively, it corresponds to the 'longest' vector one can find in the 6-dimensional feature space that captures the data, that is, the eigenvector with the largest eigenvalue.\n",
    "ICA, as opposed to PCA, finds the subcomponents that are statistically independent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3], dtype=int64)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No of components will be equal to no of feature variables i.e. 7."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.8842285   0.39540542  0.00431132  0.12854448  0.11105914 -0.12761562\n",
      "   0.1289665 ]\n",
      " [ 0.10080577  0.05648963 -0.00289474  0.03062173  0.00237229  0.98941048\n",
      "   0.08223339]\n",
      " [ 0.26453354 -0.28251995  0.05903584 -0.40014946  0.31923869  0.06429754\n",
      "  -0.76193973]\n",
      " [-0.19944949  0.57881686 -0.05776023  0.43610024 -0.23416358  0.02514736\n",
      "  -0.61335659]\n",
      " [-0.13717297  0.57475603 -0.05310454 -0.78699776 -0.1448029  -0.00157564\n",
      "   0.08765361]\n",
      " [ 0.28063956 -0.30155864 -0.04522905 -0.11343761 -0.89626785  0.003288\n",
      "  -0.10992364]\n",
      " [ 0.02539824 -0.0658399  -0.99412565 -0.00143143  0.0815499  -0.00114269\n",
      "  -0.00897193]]\n",
      "[  8.29385197e-01   1.63632452e-01   5.65790880e-03   9.90306086e-04\n",
      "   2.11180347e-04   1.20677139e-04   2.27879552e-06]\n"
     ]
    }
   ],
   "source": [
    "# Apply PCA with the same number of dimensions as variables in the dataset\n",
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=7) #7 components for 7 variables\n",
    "pca.fit(X)\n",
    "\n",
    "# Print the components and the amount of variance in the data contained in each dimension\n",
    "print(pca.components_)\n",
    "print(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The explained variance is high for the first two dimensions, but drops significantly beginning with the third dimension. Thus, the first two components explain already 86.5 % of the variation in the data.\n",
    "\n",
    "How many dimension to choose for the analysis really depends on the goal of the analysis. Even though PCA reduces the feature space (with all advantages that brings, such as faster computations) and makes interpreting the data easier for us by projecting them down to a lower dimension, it necessarily comes with a loss of information that may or may not be desired.\n",
    "\n",
    "It the case at hand, assuming interpretation is the goal (creating seed clusters) and given the sharp drop of the explained variance after the second component, we would choose the first two dimensions for analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Rjqtb0gEUwbHAi+5en8/MtbW19O3bt0lZTU0NNTU1WeevqoLzzoO774aRI1sd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\nDDMzM6sIJxlmZmZWEU4yzMzMrCL+H48HXnXTM+JJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5d51c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(list(pca.explained_variance_ratio_),'-o')\n",
    "plt.title('Explained variance ratio as function of PCA components')\n",
    "plt.ylabel('Explained variance ratio')\n",
    "plt.xlabel('Component')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Area', 'Perimeter', 'Compactness', 'Kernel_Length', 'Kernel_Width',\n",
       "       'Assymetry_Coefficient', 'Kernel_Groove_Length'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first dimension seems to basically represent only the 'Area'-feature, as this feature has a strong negative projection on the first dimension. The other features have rather weak (mostly negative) projections on the first dimension. That is, the first dimension basically tells us whether the 'area'-feature value is high or low, mixed with a little bit of information from the other features.\n",
    "\n",
    "The second dimension is mainly represented by the features 'Perimeter' and 'Compactness', in the order of decreasing importance, and has rather low correlation with the other features. \n",
    "\n",
    "There are two main uses of this information. The first use is feature interpretation and hypothesis formation. We could form initial conjectures about the seed clusters contained in the data. One conjecture could be that the bulk of seeds can be split into clusters ordering mainly by 'Area wise' and seeds mainly ordering by 'Perimeter' and 'Compactness' from the datasource. The second use is that, given knowledge of the PCA components, new features can be engineered for further analysis of the problem. These features could be generated by applying an exact PCA-transformation or by using some heuristic based on the feature combinations recovered in PCA. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Applying PCA to visualize high-dimensional data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = df[features].values\n",
    "y= df['Class'].values\n",
    "pca = PCA(n_components=2)\n",
    "reduced_X = pca.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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R4KXgHW2sEjpXqsIut+4dcu8tfbdu9BN+dK/vXvq8zQxY0MH/beAvW5YWrgJf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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9faee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "red_x, red_y = [], []\n",
    "blue_x, blue_y = [], []\n",
    "green_x, green_y = [], []\n",
    "\n",
    "for i in range(len(reduced_X)):\n",
    "    if y[i] == 1:\n",
    "        red_x.append(reduced_X[i][0])\n",
    "        red_y.append(reduced_X[i][1])\n",
    "    elif y[i] == 2:\n",
    "        blue_x.append(reduced_X[i][0])\n",
    "        blue_y.append(reduced_X[i][1])\n",
    "    else:\n",
    "        green_x.append(reduced_X[i][0])\n",
    "        green_y.append(reduced_X[i][1])\n",
    "\n",
    "plt.scatter(red_x, red_y, c='r', marker='x')\n",
    "plt.scatter(blue_x, blue_y, c='b', marker='D')\n",
    "plt.scatter(green_x, green_y, c='g', marker='.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering\n",
    "\n",
    "In this section we will choose either K Means clustering or Gaussian Mixed Models clustering, which implements expectation-maximization. Then we will sample elements from the clusters to understand their significance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing a Cluster Type\n",
    "\n",
    "K Means Clustering or Gaussian Mixture Models?\n",
    "\n",
    "Before discussing the advantages of K Means vs Gaussian Mixture models, it is helpful to observe that both methods are actually very similar. The main difference is that Gaussian Mixture models make a probabilistic assignment of points to classes depending on some distance metric, whereas K Means makes a deterministic assignment depending on some metric. Now, when the variance of the Gaussian mixtures is very small, this method becomes very similar to K Means, since the assignment probabilities to a specific cluster converge to 0 or 1 for any point in the domain. Because of the probabilistic assignment, Gaussian Mixtures (in contrast to K Means) are often characterized as soft clustering algorithms. \n",
    "\n",
    "An advantage of Gaussian Mixture models is that, if there is some a priori uncertainty about the assignment of a point to a cluster, this uncertainty is inherently reflected in the probabilistic model (soft assignment) and assignment probabilities can be computed for any data point after the model is trained. On the other hand, if a priori the clusters assignments are expected to be deterministic, K Means has advantages. An example would be a data generating process that actually is a mixture of Gaussians. Applying a Gaussian mixture model is more natural given this data generating process. When it comes to processing speed, the EM algorithm with Gaussian mixtures is generally slightly slower than Lloyd's algorithm for K Means, since computing the normal probability (EM) is generally slower than computing the L2-norm (K Means). A disadvantage of both methods is that they can get stuck in local minima (this can be considered as the cost of solving NP-hard problems (global min for k-means) approximately).\n",
    "\n",
    "Since there is no strong indication that the data are generated from a mixture of normals (this assesment may be different given more information about the nature of the spending data) and the goal is to \"hard\"-cluster them (and not assign probabilities), I decided the use the general-purpose k-means algorithm.\n",
    "\n",
    "A decision on the number of clusters will be made by visualizing the final clustering and deciding whether k equals the number of data centers found by visual inspection. Note that many other approaches for this task could be utilized, such as silhoutte analysis (see for example http://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is some starter code to help you visualize some cluster data. The visualization is based on [this demo](http://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_digits.html) from the sklearn documentation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import clustering modules\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.mixture import GMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.66344838 -1.41732098]\n",
      " [ 0.31566651 -2.68922915]\n",
      " [-0.6604993  -1.13150635]\n",
      " [-1.0552759  -1.62119002]\n",
      " [ 1.61999921 -2.18338442]\n",
      " [-0.47693801 -1.33649437]\n",
      " [-0.18483472 -0.15036441]\n",
      " [-0.78062962 -1.12979883]\n",
      " [ 2.2821081  -1.3600169 ]\n",
      " [ 1.97854147 -1.49468793]]\n"
     ]
    }
   ],
   "source": [
    "# First we reduce the data to two dimensions using PCA to capture variation\n",
    "pca = PCA(n_components=2)\n",
    "reduced_data = pca.fit_transform(X)\n",
    "print(reduced_data[:10])  # print upto 10 elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
      "    n_clusters=3, n_init=10, n_jobs=1, precompute_distances='auto',\n",
      "    random_state=None, tol=0.0001, verbose=0)\n"
     ]
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=3)\n",
    "clusters = kmeans.fit(reduced_data)\n",
    "print(clusters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Plot the decision boundary by building a mesh grid to populate a graph.\n",
    "x_min, x_max = reduced_data[:, 0].min() - 1, reduced_data[:, 0].max() + 1\n",
    "y_min, y_max = reduced_data[:, 1].min() - 1, reduced_data[:, 1].max() + 1\n",
    "hx = (x_max-x_min)/1000.\n",
    "hy = (y_max-y_min)/1000.\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, hx), np.arange(y_min, y_max, hy))\n",
    "\n",
    "# Obtain labels for each point in mesh. Use last trained model.\n",
    "Z = clusters.predict(np.c_[xx.ravel(), yy.ravel()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*** K MEANS CENTROIDS ***\n",
      "[[ 4.33639856  0.46609094]\n",
      " [-0.11491258 -1.08548863]\n",
      " [-3.32787801  0.64576148]]\n",
      "*** CENTROIDS TRANSFERED TO ORIGINAL SPACE ***\n",
      "[[ 18.72887568  16.3002505    0.88834498   6.20022594   3.74130716\n",
      "    3.607964     6.00564981]\n",
      " [ 14.63649131  14.45252981   0.87364536   5.58052241   3.24326757\n",
      "    2.64087177   5.30398814]\n",
      " [ 11.9700157   13.27990355   0.8547817    5.22052733   2.89054543\n",
      "    4.76381335   5.03198981]]\n"
     ]
    }
   ],
   "source": [
    "# Find the centroids for KMeans or the cluster means for GMM \n",
    "\n",
    "centroids = kmeans.cluster_centers_\n",
    "print('*** K MEANS CENTROIDS ***')\n",
    "print(centroids)\n",
    "\n",
    "# TRANSFORM DATA BACK TO ORIGINAL SPACE FOR ANSWERING 7\n",
    "print('*** CENTROIDS TRANSFERED TO ORIGINAL SPACE ***')\n",
    "print(pca.inverse_transform(centroids))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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UFTou+l4f97t0LDT9f6HvfXpBszJ+UefWSGiAPdoY82ffNoaHrSwi3QH8PzSzQxeaPzHI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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa0982b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Put the result into a color plot\n",
    "Z = Z.reshape(xx.shape)\n",
    "plt.figure(1)\n",
    "plt.clf()\n",
    "plt.imshow(Z, interpolation='nearest',\n",
    "           extent=(xx.min(), xx.max(), yy.min(), yy.max()),\n",
    "           cmap=plt.cm.Paired,\n",
    "           aspect='auto', origin='lower')\n",
    "\n",
    "plt.plot(reduced_data[:, 0], reduced_data[:, 1], 'k.', markersize=2)\n",
    "plt.scatter(centroids[:, 0], centroids[:, 1],\n",
    "            marker='x', s=169, linewidths=3,\n",
    "            color='w', zorder=10)\n",
    "plt.title('Clustering on the seeds dataset (PCA-reduced data)\\n'\n",
    "          'Centroids are marked with white cross')\n",
    "plt.xlim(x_min, x_max)\n",
    "plt.ylim(y_min, y_max)\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "## Elbow Method\n",
    "\n",
    "### Using the elbow method to find the optimal number of clusters \n",
    "\n",
    "One of the main challenges in unsupervised learning is that we do not know the definitive answer. We don't have the ground truth class labels in our dataset that allow us to apply the techniques in order to evaluate the performance of a supervised model. Thus, in order to quantify the quality of clustering, we need to use intrinsic metrics—such as the within-cluster SSE (distortion) to compare the performance of different k-means clusterings. Conveniently, we don't need to compute the within-cluster SSE explicitly as it is already accessible via the inertia_ attribute after fitting a KMeans model.\n",
    "\n",
    "Based on the within-cluster SSE, we can use a graphical tool, the so-called elbow method, to estimate the optimal number of clusters k for a given task. Intuitively,\n",
    "we can say that, if k increases, the distortion will decrease. This is because the\n",
    "samples will be closer to the centroids they are assigned to. The idea behind the elbow method is to identify the value of k where the distortion begins to increase most rapidly, which will become more clear if we plot distortion for different\n",
    "values of k:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ziKQ5kt6T9Jqkf2/rays3Q4fCQQclw3URkXU5ZmZmHUpZBCegN/BH4Dxgm9/m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\nktSRwUmSJKkjg5MkSVJHvwB/4J5ynAJNwQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa088198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distortions = []\n",
    "for i in range(1, 11):\n",
    "    km = KMeans(n_clusters=i, \n",
    "                init='k-means++', \n",
    "                n_init=10, \n",
    "                max_iter=300, \n",
    "                random_state=0)\n",
    "    km.fit(X)\n",
    "    distortions .append(km.inertia_)\n",
    "plt.plot(range(1,11), distortions , marker='o')\n",
    "plt.xlabel('Number of clusters')\n",
    "plt.ylabel('Distortion')\n",
    "plt.tight_layout()\n",
    "#plt.savefig('./figures/elbow.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see in the following plot, the elbow is located at k = 3, which provides evidence that k = 3 is indeed a good choice for this dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantifying the quality of clustering via silhouette plots\n",
    "\n",
    "Another intrinsic metric to evaluate the quality of a clustering is silhouette analysis, which can also be applied to clustering algorithms other than k-means that we will discuss later in this chapter. Silhouette analysis can be used as a graphical tool to plot a measure of how tightly grouped the samples in the clusters are. To calculate the silhouette coefficient of a single sample in our dataset, we can apply the following three steps:\n",
    "1. Calculate the cluster cohesion a(i) as the average distance between a sample x(i) and all other points in the same cluster.\n",
    "2. Calculate the cluster separation b(i) from the next closest cluster as the average distance between the sample x(i) and all samples in the nearest cluster.\n",
    "3. Calculate the silhouette s(i) as the difference between cluster cohesion and separation divided by the greater of the two as shown : \n",
    "\n",
    "s(i) = b(i) - a(i) / max(b(i),a(i))\n",
    "\n",
    "The silhouette coefficient is bounded in the range -1 to 1. Based on the preceding formula, we can see that the silhouette coefficient is 0 if the cluster separation and cohesion are equal (b(i)=a(i)). Furthermore, we get close to an ideal silhouette coefficient of 1 if (b(i)>>a(i)) since b(i) quantifies how dissimilar a sample is to other clusters, and a(i) tells us how similar it is to the other samples in its own cluster, respectively.\n",
    "The silhouette coefficient is available as silhouette_samples from scikit-learn's metric module, and optionally the silhouette_scores can be imported. This calculates the average silhouette coefficient across all samples, which is equivalent to numpy.mean(silhouette_samples(…)). By executing the following code, we will now create a plot of the silhouette coefficients for a k-means clustering with k=3:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6ytWs32dB1aVIlag8OAHHUZxF992m9a8Fzu55NZKkWU2NzGPd/ouqLqPv2W3qX5UHp5RS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\nEghMvsUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9fda198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import cm\n",
    "from sklearn.metrics import silhouette_samples\n",
    "\n",
    "km = KMeans(n_clusters=3, \n",
    "            init='k-means++', \n",
    "            n_init=10, \n",
    "            max_iter=300,\n",
    "            tol=1e-04,\n",
    "            random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "\n",
    "cluster_labels = np.unique(y_km)\n",
    "n_clusters = cluster_labels.shape[0]\n",
    "silhouette_vals = silhouette_samples(X, y_km, metric='euclidean')\n",
    "y_ax_lower, y_ax_upper = 0, 0\n",
    "yticks = []\n",
    "for i, c in enumerate(cluster_labels):\n",
    "    c_silhouette_vals = silhouette_vals[y_km == c]\n",
    "    c_silhouette_vals.sort()\n",
    "    y_ax_upper += len(c_silhouette_vals)\n",
    "    color = cm.jet(i / n_clusters)\n",
    "    plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, \n",
    "            edgecolor='none', color=color)\n",
    "\n",
    "    yticks.append((y_ax_lower + y_ax_upper) / 2)\n",
    "    y_ax_lower += len(c_silhouette_vals)\n",
    "    \n",
    "silhouette_avg = np.mean(silhouette_vals)\n",
    "plt.axvline(silhouette_avg, color=\"red\", linestyle=\"--\") \n",
    "\n",
    "plt.yticks(yticks, cluster_labels + 1)\n",
    "plt.ylabel('Cluster')\n",
    "plt.xlabel('Silhouette coefficient')\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/silhouette.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our clustering with 3 centroids is good."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "## Applying agglomerative clustering via scikit-learn\n",
    "\n",
    "In this section, we saw how to perform agglomerative hierarchical clustering\n",
    "using SciPy. However, there is also an AgglomerativeClustering implementation in scikit-learn, which allows us to choose the number of clusters that we want to return. This is useful if we want to prune the hierarchical cluster tree. By setting\n",
    "the n_cluster parameter to 3, we will now cluster the samples into three groups using the complete linkage approach based on the Euclidean distance metric:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster labels: [2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 0 2 2 2 0 2 2 0 0 2 2 0 2 2 2 2 2 2\n",
      " 2 2 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 0 2 2 2 1\n",
      " 2 2 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1\n",
      " 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 1 1 1 2 1 1 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "ac = AgglomerativeClustering(n_clusters=3, affinity='euclidean', linkage='complete')\n",
    "labels = ac.fit_predict(X)\n",
    "print('Cluster labels: %s' % labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "X = df[features]\n",
    "y = df['Class']\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y ,test_size=0.25, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "## Clustering using K Means:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(157,)\n",
      "[0 1 0 0 0 0 0 1 0 2 2 2 1 1 0 0 0 0 0 2 2 1 0 2 1 2 0 1 2 0 0 1 1 0 0 2 0\n",
      " 2 2 2 2 1 0 2 1 0 0 2 0 0 1 1 0 0 1 0 1 0 0 2 1 2 1 2 0 1 1 1 1 0 1 1 2 1\n",
      " 0 0 0 0 2 0 1 1 2 1 1 0 2 1 0 1 0 2 0 0 1 1 1 0 2 0 0 2 2 2 1 1 2 0 0 0 1\n",
      " 2 0 1 2 1 0 1 1 1 0 2 0 1 1 1 0 0 2 0 0 1 1 2 2 1 1 0 0 1 2 1 2 2 2 2 2 2\n",
      " 1 0 1 2 2 0 2 0 2]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import cluster\n",
    "clf = cluster.KMeans(init='k-means++', n_clusters=3, random_state=5)\n",
    "clf.fit(X_train)\n",
    "print( clf.labels_.shape)\n",
    "print (clf.labels_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Predict clusters on testing data\n",
    "y_pred = clf.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Addjusted rand score:0.71\n",
      "Homogeneity score:0.69 \n",
      "Completeness score: 0.69 \n",
      "Confusion matrix\n",
      "[[ 0  0  0  0]\n",
      " [11  3  0  0]\n",
      " [ 2  0 16  0]\n",
      " [ 1 20  0  0]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "print (\"Addjusted rand score:{:.2}\".format(metrics.adjusted_rand_score(y_test, y_pred)))\n",
    "print (\"Homogeneity score:{:.2} \".format(metrics.homogeneity_score(y_test, y_pred)) )\n",
    "print (\"Completeness score: {:.2} \".format(metrics.completeness_score(y_test, y_pred)))\n",
    "print (\"Confusion matrix\")\n",
    "print (metrics.confusion_matrix(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "## Affinity Propogation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10,)\n"
     ]
    }
   ],
   "source": [
    "# Affinity propagation\n",
    "aff = cluster.AffinityPropagation()\n",
    "aff.fit(X_train)\n",
    "print (aff.cluster_centers_indices_.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y_pred = aff.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Addjusted rand score:0.31\n",
      "Homogeneity score:0.84 \n",
      "Completeness score: 0.42 \n",
      "Confusion matrix\n",
      "[[0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 2 4 0 0 1 0 7 0]\n",
      " [5 7 1 0 0 1 0 0 0 4]\n",
      " [0 0 0 2 3 0 9 7 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "print (\"Addjusted rand score:{:.2}\".format(metrics.adjusted_rand_score(y_test, y_pred)))\n",
    "print (\"Homogeneity score:{:.2} \".format(metrics.homogeneity_score(y_test, y_pred)) )\n",
    "print (\"Completeness score: {:.2} \".format(metrics.completeness_score(y_test, y_pred)))\n",
    "print (\"Confusion matrix\")\n",
    "print (metrics.confusion_matrix(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "## MeanShift"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 12.90285714  13.6938961    0.86236364   5.35018182   3.01996104\n",
      "    3.46636364   5.0844026 ]\n",
      " [ 17.32053571  15.67982143   0.88386429   5.98578571   3.57646429\n",
      "    3.34401786   5.801875  ]]\n"
     ]
    }
   ],
   "source": [
    "ms = cluster.MeanShift()\n",
    "ms.fit(X_train)\n",
    "print( ms.cluster_centers_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred = ms.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Addjusted rand score:0.55\n",
      "Homogeneity score:0.51 \n",
      "Completeness score: 0.84 \n",
      "Confusion matrix\n",
      "[[ 0  0  0  0]\n",
      " [12  2  0  0]\n",
      " [ 0 18  0  0]\n",
      " [21  0  0  0]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "print (\"Addjusted rand score:{:.2}\".format(metrics.adjusted_rand_score(y_test, y_pred)))\n",
    "print (\"Homogeneity score:{:.2} \".format(metrics.homogeneity_score(y_test, y_pred)) )\n",
    "print (\"Completeness score: {:.2} \".format(metrics.completeness_score(y_test, y_pred)))\n",
    "print (\"Confusion matrix\")\n",
    "print (metrics.confusion_matrix(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "## Mixture of Guassian Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adjusted rand score for covariance=spherical:0.63\n",
      "Adjusted rand score for covariance=tied:0.85\n",
      "Adjusted rand score for covariance=diag:0.65\n",
      "Adjusted rand score for covariance=full:0.69\n"
     ]
    }
   ],
   "source": [
    "from sklearn import mixture\n",
    "\n",
    "# Define a heldout dataset to estimate covariance type\n",
    "X_train_heldout, X_test_heldout, y_train_heldout, y_test_heldout = train_test_split(\n",
    "        X_train, y_train,test_size=0.25, random_state=42)\n",
    "for covariance_type in ['spherical','tied','diag','full']:\n",
    "    gm=mixture.GMM(n_components=3, covariance_type=covariance_type, random_state=42, n_init=5)\n",
    "    gm.fit(X_train_heldout)\n",
    "    y_pred=gm.predict(X_test_heldout)\n",
    "    print (\"Adjusted rand score for covariance={}:{:.2}\".format(covariance_type, \n",
    "                                                               metrics.adjusted_rand_score(y_test_heldout, y_pred)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GMM(covariance_type='tied', init_params='wmc', min_covar=0.001,\n",
       "  n_components=3, n_init=1, n_iter=100, params='wmc', random_state=42,\n",
       "  tol=0.001, verbose=0)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm = mixture.GMM(n_components=3, covariance_type='tied', random_state=42)\n",
    "gm.fit(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Addjusted rand score:0.94\n",
      "Homogeneity score:0.94 \n",
      "Completeness score: 0.93 \n",
      "Confusion matrix\n",
      "[[ 0  0  0  0]\n",
      " [ 0  0 14  0]\n",
      " [ 0 18  0  0]\n",
      " [20  0  1  0]]\n"
     ]
    }
   ],
   "source": [
    "# Print train clustering and confusion matrix\n",
    "y_pred = gm.predict(X_test)\n",
    "print (\"Addjusted rand score:{:.2}\".format(metrics.adjusted_rand_score(y_test, y_pred)))\n",
    "print (\"Homogeneity score:{:.2} \".format(metrics.homogeneity_score(y_test, y_pred)) )\n",
    "print (\"Completeness score: {:.2} \".format(metrics.completeness_score(y_test, y_pred)))\n",
    "\n",
    "print (\"Confusion matrix\")\n",
    "print (metrics.confusion_matrix(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UPx/vM7OdE9v/g7zab7a08fj3O84hhKcT//vP4O1xknaN67qtyL4U7kuF72mxay3rh+hQ\nCj9mshrgS9rY9GMreabvo0XKWPhe7jBI+YYyQaV/l2Rmb5b39n+DPNhPlmdLDREwxx81M+VVq5Pl\nmc/C8s9kLZL4vCQVB1TRNfKbxSRJvwghlPwLIOGd8e9o+YX29xKXK7aTw4tMfzFjWiFD9yl5O5Ms\npdWd5uN78mq7b8nbGz0nPy4/Vv8OByUfqxDCB8xsX3ngc6i8qvGTZvaGEEJPCGFlzOwdKr/g3yXp\nZDO7MoQwoMGitPGXyG/kX9Kvyb8sa+QPgCs1sHPEhqF2fAjFli82vZ691YbJH47vjH/Til5flRzr\nCtXruJSy3mHyFP1ZRbaXFextFEI428zmyKs5D5Fnh//LzPYLIfxLpR//Uu8FA8YqGqRsvZIOMLOD\n5I2w3ylvL/hbMztkiKCqVKXeAzLFIPFOeUbrc/LsVq+8OvfryXXU8FiX69m4T4MF+AtCCM9mfRBC\neCH+IHldGds8Nv79XWp6kCQz2zFmdf9dXlWf/Dx5X12bse5hcb7jtal9T1IlwwuV+zwcTOGc/6+K\nDz3Q0GFSzGwn+TNksfxe8ZQ8QH+3PEgqpbat0L7vMvm1/qz8Ov12keUL11tWsJWp2oDqRnnVzH7q\n37C4JLFx3OflD+29JV1mZnumArNiF8oq+Q14q9T0HcsoQuEX4AshhFsHnTPb39X/13bBlMTnlaxz\nmDyCTv5C3TVj3qPk6eBCg2WZ95pMH5NV8bNxoX8D6B2zChCry+6V9HnzUYl/JP/Fdnn8fL28gezP\n43pnS/qImX05hJDVW2fPWP4PhRA2VgubNwBvJoXztXvGZ6+R9EwIYa2ZvSi/UWadk3RvwMfk1+kT\nIYSsX2KDquBYS74fbzezLVJZqmquy8zi1WAdj0naK4SQ9Wu9tEKE8JD8F/dXzewN8ofgx+SZ1lKP\nf0n3AjNbqdLPfaF8t8mzEf9hZv8lbyx7kDb1REsr3AN2Vv8MeNb6S70HFDtXB8ofHEeGEO5OrGPn\nrJlrdKwHK0/WNjeY2WPa1GOvEjdLmhGDv0EbppsPsVDo+HFn6uNh8kDjWElflTcqL/c+VjhOK4d4\n7hS+p1nXWvoeVerzsHDPGCy4XCnP9gwv4bn4d3mvurTM70LGdkr9Lr1HPmbYe5LVg2b29oxli11b\nR8nbVvXrRWhmWyk7Qz5ZHnBl1VhkqurVM/Fm/TF5W6ibylk2ttGZI68WOFPem2ai/JdW0po4/7jU\n9L8rNnpLTT9dpX9ZF8kv7v8wsy0yyjhU3ektkiaa2cZg0syGy3vTvCBv/Feu+fIvxump6Z/QwP3a\noIHn8AwN/FVS+AInhzHYQj5yuxLT0l9GadOv9VFxnm0y5nkwOU+GQqYiXdaZaqKxcYL38rhP0onJ\n6828J8ohikFN8PHU5svHpUl2B58S50uaK/9SzsraZpHjOdhnQx1rya/LEZI+npp+VizLLwZZthyF\nYC3ruinV9ZJeZWYz0h+YDx9SdLw4M3tZ/L4lPSTfx8LxKfX4l3QvKOfcm1lWRuV++XdxsPP3izhP\neniMrO9LqfeANcp+4G6I0zeuw3y4in73nxof60J5ymmW8HtJ08qYP+0b8vYyl5n3YEuXbWfbNBzJ\n8fLjfEEIYW7q3w3y+/pxklfvhRBuTf4roSzz5dWQn7GMtqqJay15P3pZ4vOD5Q39k0p6HoYQnpEH\niafEZhgDxGv8p5KOMrMBwVLquXiLpFeY2VGJz8fIO/wMqsz76IBnSMyunpSx6jXKvicVrvXkvrxf\nXlOSZaqkh8qpeaskQ5VuFFnpK1Q+L+/N8rYYmD1oZl+S9BUz+2kIoXDTXxS3+V0zmy9v+f/j2C7m\nJ5LOiO1jHpM3jJ9QagFCCMHMTpVfFA+Zj3v1T/kBPkiePh9sHIofyOuY55jZNG0aNuGNks7MaMNS\nSpn+ZGY/lTQzXrj3yBu3F6L45A31ZkkfMh9X669xu2/XwBTlr+Ttii43swu0qTv4CknJL9WJZna6\nPPP4mLzNwQz5cbglznNZvDHeqk3dtD8u6c/Bh+wvSF4nD8f1XRi/OM/Lfy1U8yCul7Pl+3qP+fhb\nY+T7t0r9R+ufJa/auMvMLpb3YPu4vFvvxnFNQgiPm9nn5L/oJ8vbpL0gb8vwXnmGt9h7HUs91mk3\nyTMi58VtFoZNeI+kb4UyRv4dwmPyqqKPmVm3/EZ2TwihnAzY1fJGvrNj1djd8mBgivy7dIiKd5d/\nm6TvxfvAEvn97AR5lclPpdKPf5n3gpLOvaQvmI8L9HP5A+/l8vYbT8obfWcKIdxvZtdKOj3+yPmd\n/Hu9swZWi5Z6D7hP/kA5J67zRXlj+9/Jr+2rzKwwFEchoEiq2bGO61sk6QPm7bL+KO/AcHOxYyLv\nKn+8me1SYab3cTM7Vj58wWIzS46U/ib5tXZ5nP04SfcN0mh7nvx5tHcI4b4KyvKC+RAuV0n6k5ld\nJ8+QbC+vwrpLm4Lp/5Kf47vN7HJ5T8bCtTY2sc5ynodnyDv5/MnMfiBvrztZ0mEhhEK7rE/Ls5d/\nMLNL5dfWNvIg423a1FD70lieq+MzsDBsQqnPvlK/S7+St4+72cwukT+bTpVXmU5MrXOR/J70WXn7\nrBUxS3yzvNblcvl1v6f8XKfbKhYSPm+VV6mXLpTXjfRExWEThpjvcUn/LzVtg6TPx//eR/6F/lZq\nnmHyRn9PSRqXmHaRfNyT9erfLXm8/BfuC/IbyP/Ib8QbNHDYhOcGKe9e8rEpVsh/xTwuH9flwBKO\nybbyOtmn5enL++RVW0Mek0HWOVqebl4pv5HfIG/w2Sfp7MR84xLbfk5+4941buuHqXXuLb+I1sq/\nQGdo4LAJe8vT2UvjcVgmvynuk1jP++S/oJcl1vU/krZLzDOgC688RT0/lvNpeaPO15V6ruRfvPUl\nHLvM4xy38+3UtB3i9LNS0w+S/4rrlj9sbpS0e8Y695dXja6VV83MUPEhKt4r/2X7fPz3kLzufpfU\nvj9WzrEe5DiMkfRN+XepVx7UnlXKcUkcxx+WsJ3D5VmzF5PnUh7Q3Z8xf799jNOGy8eieyBed8/E\n4/pZJbqLZ6xrR/kNfYn8Br5S3s5iwPe2lONfzr2glHMvfyDNjedgbfx7taSdSzium8mz9StieW+U\nj8m38T5awT3glFjWl5T4fsob+d4tv96fkldlvSM1T02Pdbw+r5aPSbdBQwyhIH/QrtDA4VRmxeW3\nGeqYxvl3lvf2fiyek9Xy7/ppcRv7xPXNGmQd28d5vjnEtjK/A4nPD5AH8M/GY7pEPv7YPqn53isP\nMHrk37Ujlf09Kul5GOedIn+udMVt/zW9z/Jn23fkiYJe+Q+MX0k6JTXfq+L1+UK8Di+U92QcctiE\nUr9Lcb53y4eRWBPP36fkGaqNz7A433byoHd1/OzWxHfqG/Ifp93xGt1X/oP1t6ltvTMuu1Mp11Xh\nn8WF0eTMGyf/ST62zLV5lwcAGilmv06WB2Y8uFA3ZvYz+Q/4o8tZrqo2VKgPy3jrubz9xAYNbCQJ\nAJ3gW/Ihej6Yd0HQvsxfM3aYvFlSWart5Yf6+E8zmypPGa+Xn9xDJV0SBh+MDQDaUvA2qen2MkBN\nhRAellcPlo0qvyYUhxP4grwnx1h5I9arJH01eM8IAADQRAioAAAAqkQbKgAAgCoRUAEAAFSJgApA\n3ZjZF82sb7AR4Wu5nTquv8/MvlDGvN8Zes7aMbM5ZlbSiM7l7Es91PtcAXkhoELDmNmJ8WbeZ2Zv\nKjLPU/HzeY0uH+oiqDGvF6r3dvqt38zeaGazbOArsfJSzv7nvS8VnyszO83MTqxxeYCaIKBCHtZq\n09vcNzKzt8pf9dHb8BIBg9tc0nmJ/3+TvCduM74+aSitvC+ny9/wADQdAirk4RZJ7zez9PV3rKSF\n8tcMdSwzG25mI/MuRzUGe6lxKwohvJQasiT9Tr2W0U77AjQTAio0WpC/G228/H1PkqQYQBwt6Rpl\n3ODNzTSzv5jZWjNbbmbfjy96Tc53hJndbGb/NLNeM/ubmX0uHbyZ2e1m9oCZTTGz28xsjZn9w8zO\nztj2J+J215jZs2b2RzMbdLRmMxtpZl8ys4VmttrMus3sTjM7MDXfDrGK85NmdqaZ/U2eoZsSP9/M\nzM41s0fj/jxpZueb2ZADzyX2cc/432vieo6Kn7/VzO4xsx4ze9jM3p5afnszuzh+1mNmz5jZ9Wa2\nQ2q+QlXuAXH+p+XvhCtWrh3ieXnAzCYkpu9nZr+Mx2tNLPOAqmEz2z+eg7Vxfz4y1LGIy33CzNYn\nq7bM7FOx7N9MTBtmZi+Y2dcS0za2OzKzWfJ3gknSE/GzDWa2fWp7R5rZg/G8/cXMDi2hjCtTZbF4\nPNalyn1OnDYmtfwrzOxnsfwrzOwCM7PUPGXti5kdH6/jHjPrMrNrzV9yPqRSz5X5j4jPx+ui18yW\nmtl5yevczJZKeq2kA21T04Fb42cjzKstl8RtPWNmC9LXNFBPjJSOPDwh6R5Jx8hfmCz5aPDj5G+D\nPzNjmR/I325/ufxFq5MlfULS3mb25hDChjjfSfKXdF4ofwHm2yR9Sf528nMS6wvyt6f/Qv4C2+vk\nAd3XzeyBEMJ8STKzGXF718tf0j1a/gLd/eIyxYyTv4z22lj2l0n6sKRfmtm+IYQHUvOfImmUpEvk\nLxp+Nj4Ib5JXyVwif8HxnpLOkr8Ad/og20/u402xrNfLXwJ7rZkdH/fnYkk/kvSfkn5iZq+OI1JL\n0r/JX5x7rfyFojvKq1xuM7M9QgjpqtmL5S+wPVf+ipABzGxn+ctIV0o6OISwKk5/mzxzuVDSF+Uv\nAj9Z0q1mtn8IYWGc73Xya2aFvJpqZJx/xRDHQpIWyIP1/eO2FP97g6S3JObbR/7y3juKrGeupN3k\nr0A5U/6CWcV9KniL/PxcLL8ez5B0g5ltX9jnIu6WvzS3YC/5tbRB0pvl12uh3H8KIfQk5h0hPzb3\nyF8c+w5Jn5T0N/n1U/a+mNln5d+f6+QvR54Q9+UOM9snhPB8sR0p81z9UP79vl7+Uu/9JP2XpNdI\nOirOc6ak78mP51fk5/Lp+Nm5kj4t/679UX7Mpkl6vaTfFisjUFPlvEmZf/yr5p+87cMG+U3udPnb\nwEfFz34s6Tfxv5dKmpdYbn/5A/bfU+s7OE7/YGLaqIztzpbfhEcmpt0Wy3JsYtpISf+SdH1i2o2S\nHqhgX03SiNS0cZKWSbo0MW2HuA+rJG2Tmv94SeskvTE1/SOx7G8YogyFffxAYtpucXvrJE3LOJYn\nJKZlHct943zHpc5rn6TbFQcLTnw2K5ZhG/nD8R+Sfi9py9R8j0j6eWraKPlb5X+ZOh9rJL0yMW33\nuD8bhjgeFq+5ryWmrZQHCy9JGhOnnRXXNy4xX5+kLyT+/1NKveU+Ne9aSTsmpu0Zp58+RBk/Fcuy\nRfz/j0t6PB6zryb241lJ30wsd0Usz2dS61sk6d6M8g25L5K2j8fhnNT0PWIZPz3EvpR0ruRBY5+k\n76eW/0Ys11sT0x6UdGvGtv6sxD2Df/zL4x9VfsjL9fIswOFmNlbS4fJMSZaj5Q/C35rZ+MI/+U20\nW9JBhRlDCC8W/tvMxsb57orbek1qvd0hhGsSy66TdK+knRLzrJb0KjObVs7OBbc+lsPMbGv5+6EW\nygPKtBtCCM9m7PdiSUtS+32b/KF6UHolGbpDCNcnyrUk7tPiELM+0R/i350S8yaP5QjzoQ8ej8un\n9yHIA8Vivbf2lAdcj8szU88l1r23PON2bWo/XybPLhwQ5xsm6RBJN4bEOy1DCI9oU6azqFi23yXW\nt4c80Pu6vPnDG+Os+0v6Sxgk+1KCX4cQnkhs+0FJz6v/tZVlgTzTVKjqfEuctkCbsmh7yhuQL8hY\nPp2JWlDCNos5Sn6d/SR1XlZIelSDXH9lnqvD5NfPt1LTL4zbf3cJZV0t6bVmtksJ8wJ1QUCFXIQQ\nnpH0G3lD9Onya/GGIrPvKn+ArJBnFAr/VsirlrYrzGhme5jZjWa2Wv4AWynp6vjxlqn1/iNjW6sk\nbZ34//PlQdu9sX3G96zIkA9p5m2L7pe3ieqK5X13RjkkrwZN21XeZmRl6t8j8gfQdhnLpGXt43NK\ntXFKBA8d1nTDAAAf8ElEQVQb993MRpu3A3tSXg35TNyHLcvYB8kfijfJz8c7Qwjdqc93jX+v0sDz\ne6qkzcxsS3l10+byKqy0R4psO22BpKlmNkoeoCwLIdwn6X5tClj2V3awUo6sNmTpayvLnyT1JMqS\nDKimxTZFb5Gf/7tSy/aGELpS00rZZjG7yL+Xf9PA8/IaDX79lXOuClnafvOGEJ6WB0o7aGiFXopL\nzNvmfcPM9ixhOaBmaEOFPF0jb5cxSdIvQgjFBiYcJm8rcayyeyQV2ntsKelO+U34c/JsSK+kqdqU\nhUjaoGwbtxFCeNjMdpdn0N4pD/5ON7NzQwjnFtux2EbpCnkblW/IH0IbJH1G2RmDtRnThsmrOM5S\n9n4XbfidUGwfh9x3eXuVE+WZg3vkgViQV89m/RjL2gfFZW6I6zpe3s4lqbCuT8kDmyzd8vZr1bpL\nXrX7RvUPnBZIeks81xNUfUBVyvEdIISw3sz+IOmA2N5sovyaXhnLvV8s98MZwVOxbVZqmDzQeWf8\nm5YOjKtV8ThiIYQF8XgdKc+MfVjSWWb20RDC5bUqIDAYAirk6UZ5FcV+kv59kPkek/R2Sb9LVkNl\nOFD+a/zIEMLdhYnxRluxEMJaST+RV32MiOX+rJl9LYTwUpHFjpL0WAjh6OREM/tSGZt+TNJeIYTb\nKil3DRwlaU4I4T8LE2Jmp5Lxis6WP/AvNrPnQwjJBv2Pxb8vhBBuLbYCM1spD9p2zfg4XZ1bzL3y\nNjwHyDM9hR5ud0qaIb/OQvz/wdRzENEF8k4C75C0MlbTyswe0qZy31TD7RXbl8fkAeATIYSsTNNg\nyjlXf5cHb7sqkb0ys+3k19rfSyirQgirJV0p6crY+3GBvBE8ARUagio/5CZ4b7KPyW96gz0grpcH\n/wNelxG7WxeqnzbIHwDDEp9vJm8AXxFLvTIltotaHLcz2FhRA7IFZrafNrXTKcX18vZbMzLWNdrq\nP9bTBg28R5whaXgF6wryxvQ3SLrKzA5PfLZI/vD+DzMb0DvQzLaVpOBjJ82X9N5kt30zmyLPSgxd\nCA/I/yjvYfpq9c9QbS7fv8diddNgCj0h6zEY5gJ5Nm6m+lfr3SXpQ/KMbrUZtKRi+zJXnpmalbVQ\n+ruRVOa5ukX+fZqZmv4p+XXz81RZBxzzjO9pj7wKcVSxMgK1RoYKjdavyiOEcHWxGRPz3Glml0j6\ndGzA/Ct5lmE3ecPtM+Q3/9/J24xcZZvepXa8qssm/MrMlsu7sz8t7+H0fyXdHDYNL5DlZknTzexn\n8gfCTpI+KukhSWNL3PbVkj4gabaZHRTLMFw+RtX75Q+mP5W9R6W7WdKHzOx5SX+VB4Nvl7elShty\ncMgQQohVoT+TZ/sOCyHcFqefKn+wPmRmV0j6p3zU/IPkVY1HxtXMkldB3WVmF8uD2o9L+ou8t1gp\nFsi72K+OjcUVQlhpZo/Ie6FdUcI6FsV9/qqZXSe/HufFbGa1fi9pvfz6TjYyv1M+7EVQbQOqYvvy\nuJl9Lk6fLD9vL8iv5ffGsv33IOst6VyFEB4wsyslfSR23rhDnrU+QdLcEEJy+IpFkj4Wh3P4m6QV\nMYP7VzO7PX7+rHzIj6MlNfSdiuhsBFRotFKCmwHv+gohnGZmC+VByXnyB84T8obMd8d5njWzd8t7\nB31ZHlxdLR/3KKsXWLGyJKd/X9Jx8nZMY+WNvC9S/1d3DFxBCHPM7OWxvIfIA5Lj5AHSAenZs8oS\nA40j47ZPkD/EeuRtw74laclgZcjYl0G3lzH9DPlxPlaeMblLXg01P2P5koLW2EboaHnw9DMze0cI\n4Y8hhDvM7I2SPi8PWMfKR8z/gxJBRQjhQTM7RP4gP1d+Pr4g6RUqL6A6R/G6SU3fTdnVff2OTQhh\nYQw2PibpUHkmb7KkJ9PzFltHMSGEHjP7s7ztXzJDtSAu/2QIIav9XCnXc1n7EkI4PwaaZ2lThvgp\nSb+UNOj7Nss8Vx+WZylPkl/ny+XfsXQV+ZfkwzmcLe8Feoe81+u3JR0hH/5jlLya8DPyMa2AhrDi\nvZwBAABQCtpQAQAAVImACgAAoEoEVAAAAFUioAIAAKgSvfwkxfdTHSrvNdabb2kAAGgpoyXtKGl+\nxgj+HYOAyh2q4i/mBQAAQztO/kqxjkRA5Z6QpE++cZJeNY6BdYFaWXvCxblu/80//3Ku2wc6wZJn\nu/WRXz4oFX9BekcgoHK9kvSqcaO08za1eP8qAElaM2XPXLe/9x/H5bp9oMN0dJMZGqUDqIs1Z/86\n7yLolhMuy7sIADoEARWAmmuGYAoAGomACgAAoEoEVABqiuwUgE5EQAWgZgimAHQqAioAbY2G6QAa\ngYAKQE2QnQLQyQioAAAAqkRABaBqZKcAdDoCKgBVIZgCAAIqAACAqhFQAagY2SkAcARUyFVXzzpd\numi5unrW5V0UAAAqRkCFXM1d3KWbl6zW3MVdeRcFZWql7BRjUQGotxF5FwCdbfqU8f3+ojW0UjAF\nAI1AQIVcjR8zUjOmTsy7GAAAVIUqPwBlITsFAAMRUAHoCLSjAlBPBFQAAABVIqACUDKq+wAgGwEV\ngJIQTAFAcQRUAAAAVSKgAjAkslMAMDgCKgCDaqdgip5+AOqFgCoHvL8OAID2QkCVA95fh1bRTtkp\nAKgnXj2TA95fh1ZAMAUApSNDlYPC++vGjxmZd1GAjkM7KqB2lnX36jsLl+ZdjKZAQAVgALJTAEpx\n0cKlmrtked7FaAoEVEAZ6FAAAJvMnDZZ03ebmHcxmgIBFVCGTuhQQHYKQKkmjR2tM6ZNzrsYTYFG\n6UAZ6FAAAMhChgooQ7t3KOiU7BQN0wHUGgEVAEmdE0wBQD0QUAEAAFSJgAoA2SkAqBIBFQAAQJUI\nqIAOR3YKAKpHQAWgI9HTD0AtEVABHYzsFADUBgEVAABAlQiogA5FdgoAaoeACuhABFOOdlQAaoWA\nCgAAoEoEVECHITsFALVHQAV0EIIpAKgPAioAAIAqEVABHYLsFADUDwEVgI5GTz8AtUBABXQAslMA\nUF8EVAAAAFUioALaHNkpAKg/AiqgjRFMlYZ2VACqRUAFAABQJQIqoE2RnQKAxiGgAtoQwRQANBYB\nFQAAQJUIqABANEwHUB0CKqDNUN0HAI1HQAUAAFAlAiqgjZCdAoB8EFABbYJgCgDyQ0AFAABQJQIq\noA2QnaoNevoBqBQBFdDiCKYAIH8EVAAAAFUioEJFunrW6dJFy9XVsy7vonQ0slMA0BwIqFCRuYu7\ndPOS1Zq7uCvvogAAkLsReRcArWn6lPH9/qLxyE4BQPMgoEJFxo8ZqRlTJ+ZdDAAAmgJVfkALIjtV\nPwydAKASBFRAiyGYAoDmQ0AFAABQJQIqoIWQnQKA5kRABbQIgimgPpZ19+qc2xdrWXdv3kVBCyOg\nAoAUGqZ3losWLtUl9z2pixYuzbsoaGEMmwAAVVjW3auLFi7VzGmTNWns6LyLgwrMnDa531+gEgRU\nQAuguq95FbIbknT+gVNyLg0qMWnsaM4dqkZABQBVILsBQCKgApoe2anmRnYDgESjdKCpEUzlh4bp\nAMpBQAU0KYIpNBJDBwDVIaAC0BRWrVyuKy+YpVUrl+ddlI7E0AFAdWhDBTShTsxOzZszW/OvvVyS\ndOLZ5+Zcms5D43qgOmSoADSFI046TYcec4qOOOm0vIuyUSe1oyo0rmcsrdqgCrXzkKECmkwnZqck\naesJE8lMoW0wPlnnIaACAKDGqELtPARUQBPp1OwU0G4Yn6zz0IYKaBIEUwDQugioAAAAqkRABTQB\nslPNq5N6+gGoHAEVAABAlQiogJyRnQKA1kdABeSIYArIFwNwolYIqAAAHYt3GKJWCKgAYAg0TG9f\nM6dN1kf33p4BOFE1BvZMeK53fd5FQAehug/IHwNwolbIUCXcunR13kUAAAAtiIAq4W2Tt8q7COgQ\nZKcAoL0QUCVsOZoaUNQfwVRroh0VgMEQUAENRDAFAO2JgAoAAKBKBFRAg5CdAoD2RUAFAABQJQKq\nFtPVs06XLlqurp51eRcFZSA7BQDtjYCqxcxd3KWbl6zW3MVdeRcFJSKYah/09ANQDOMEtJjpU8b3\n+wsAAPJHQNVixo8ZqRlTJ+ZdDJSI7BQAdAaq/AAAAKpEQAXUCdmp9kQ7KgBZCKgAAACqREAF1AHZ\nKQDoLARUQI0RTAFA5yGgAgAAqBIBVYtghPTWQHaqM9AwHUAaAVWLYIR0AACaFwFVi5g+ZbwO322r\nthghvV2zbWSnKrdq5XJdecEsrVq5PO+iAEBFCKhaRGGE9PFjRuZdlKqRbUPavDmzNf/ayzVvzuy8\niwIAFeHVM2i4dnwfIdmp6hxx0mn9/gJAqyFDhYZrp2ybRDBVC1tPmKgTzz5XW09onfdU0jAdQBIB\nFQAAQJUIqIAqkJ0CAEgEVAAAAFUjoAIqRHYKjbKsu1fn3L5Yy7p78y4KgCIIqIAKEEyhkS5auFSX\n3PekLlq4NO+iACiCYRMAoMnNnDa5318AzYeACigT2Sk02qSxo3X+gVPyLgaAQVDlBwAVYiwqAAUE\nVEAZyE4BaAZ0VGg+BFQAALQYOio0H9pQASUiO4V2say7VxctXKqZ0yZr0tjReRcHFaCjQvMhQwWU\ngGAK7YTsRm3lUf1W6KhAQNw8CKgAoAqt2DB95rTJ+uje25PdqBECVEhU+QFDIjtVH6tWLte8ObN1\nxEmnaesJE/MuTkdhGIbaovoNEhkqADmZN2e25l97uebNmZ13UYCqUP0GiQwVMCiyU/VzxEmn9fsL\nAK2MgApALraeMFEnnn1u3sUAgJqgyg8oguwUStWKDdMB1BYBFZCBYAoAUA4CKgAAgCoRUAEpZKcA\nAOUioOoAXT3rdOmi5erqWZd3UZoewRQqRTsqoLMRUHWAuYu7dPOS1Zq7uCvvogAA0JYYNqEDTJ8y\nfuPfrp51mru4S9OnjNf4MSNzLllzITsFAKgUGaoOMH7MSM2YOlHjx4wkWwUAQB2QoeowyWwVNiE7\nBQCoBhmqnAwbuZk2G7eNho3crKHbTWargFpZtXK5rrxgllatXJ53UQAgF2SoGslMk/Y9RJMPPlbj\nXzNVNmy4Qt8GdT28SEt/fY2W3fsrKYS8S7lRp7S3IjtVvcKLjiV19OtkbjnhMh121al5FwNADgio\nGmTE5lto2pnf1nZ7vbnfdBs2XNvusa+23WNfrXjgbi389plav3ZNTqXsr9DeSpJmTJ2Yc2nqg2Cq\nNnjRMYBOR5VfI5jp32Z+Z0AwlbbdXm/WtDO/LZk1qGCDmz5lvA7fbSvaW2FIhRcdbz2hPQNvABgK\nAVUDTNr3EE3Y800lzbvdXm/WpH0PKWv99Rq4s93bW5GdAgDUCgFVA0w++Njy5n/HMWXNz1AIAADk\ni4CqzoaN3EzjXzO1rGXGT5lWVu8/qubKR3YKpaik9yKvoNlkWXevzrl9sZZ19+ZdFKDuCKjqbMTm\nY2XDhpe1jA0brhGbjy15/qyqOd7fB1Rn1crlOv8TJ2r+tZdr3pzZeRenJV20cKkuue9JXbRwad5F\nAeqOXn51tn5tt0LfhrKCqtC3QevXdle13U7ooVcpslMoxbw5s/Xkkr9q+932oPdihWZOm9zvL9DO\nCKjqrG/dS+p6eJG23WPfkpfpWrxQfeteqmq7jIgOVCc5FAS9FyszaexonX/glLyLATQEVX4NsPTX\n15Q3/2+urXqb7d5Dr1Jkp1CqaoaCoB0V0HkIqBpg2b2/0ooH7i5p3hUP3O0jpqPmCKYAAPVCQNUI\nIWjht88cMqgqjJTeTK+fAQAAQ6MNVYOsX7tG95w/w9/l945jNH7KtE3v8lu8UEt/c23TvcuvnZCd\nAgDUEwFVI4WgZX+Yr2V/mK9hIzfTiM3Hav3a7qoboGNwBFMAgHojoMpJ37qX9NK6Z/MuBgAAqAHa\nUKGtkZ1CXujpB3QWAioAAJoEr+tpXQRUaFtkp9AueMh2jkpf18M1kj/aUAFAkys8ZCUx8nibq/R1\nPVwj+SOgQlsiO4VmcMsJl+mwq06tej28E69zVPq6Hq6R/BFQoe0QTKHd8E48DIVrJH+0oQIAYCgj\nRsrGbimN4P2oyEaGCm2F7BSAmjHTiL3216j936PhO71249stNjz+kF686yatf+Au3m6BjQioAACZ\nlnX36qKFSzVz2mRNGjs67+I01qgxGnPyZzVy96n9Jtuw4Rqxy14ascteWvfIIvVccZ70Yk9OhUQz\nocoPbYPsFFBblXbhb3lmGnPy5wYEU2kjd5+qMSd/VjLbOI3hCzoXARUA1FErj5g+c9pkfXTv7Tuu\n59iIvfbXyN1fX9K8I3efqhF77b/x/zs2CAUBFTbp6lmnSxctV1fPuryLUjayU0DtFXqOlVPd1w4Z\nmlH7v6e8+d98+Mb/7tQgFARUuWumIGbu4i7dvGS15i7uyrsoAFpUy2doRozU8J1eW9Yiw3d+3cbe\nf5UEoWgPNErPWSGIkaQZUyfmWpbpU8b3+9sqOjU7tWrlcs2bM1tHnHSatp6Q77UDFLT6AJM2eoxs\n2PDylhk2XDZ6jEL3c3UqFVoBGaqcTZ8yXofvtlVTBDHjx4zUjKkTNX5M64yz0qnBlCTNmzNb86+9\nXPPmzM67KBhCK7ejKlejMzS1rmIMvT0KfRvKW6Zvg0IvPf06HRmqnBWCGKBcR5x0Wr+/QCeq+Tvs\n1q/Thscf0ohd9ip5kQ2P/UVan3+zDeSLgAotq5OzU5K09YSJOvHsc/MuBpCrelQxvnjXTWUFVC/e\nfXPNto3WRZVfzpqpUXor6fRgCoCrRxXj+gfu0rpHFpU077pHFvmI6eh4BFQ5o2cdADSZENRzxXlD\nBlUbR0rn9TMQAVXumqlReqsgO4W8rFq5XFdeMEurVi4ve9lOapjeFl7sUc8ln9OaOedp/aP3b2yo\nHvo2aP2j92vNnPPUc8nneO0MNqINVc5olA60jkLPSkm0X+sEIWj9/Qu0/v4F0oiRPjRCbw8N0JGJ\ngAothewU8kTPyg62fl3u40x19MuqWwBVfi2gExuuZ+0zwRTyVuhZyUCqyEPLj0Lf5shQtYBmGk29\nUTpxnwFgMK0+Cn27I6BqAa36SphqpPe5U7NTvF4GQEFhiAg0JwKqFtCJDdc7cZ+z0AgaAFoDARWa\nXqdmpyQaQQNAq6BROtDEaATdXhiLCmhfBFRoau2UnapmUEgAQHMjoELTaqdgStrUHmrenNl5FwUA\nUGMEVChJp42FVY9s0hEnnaZDjzmF9lAA0IYIqFCSTnuJcz2ySbSHAoD2RUDVQvLMEjX6Jc55V/eR\nTUK90DC9vS3r7tU5ty/Wsu7evIuCBmPYhBaS5+jhjRwXKu9gStqUTQKAchReDyOJQTg7DAFVC+nE\nEdMBoJXwepjORUDVQjph9PBmyE4BQKV4PUznog0VmgbBFDoF7aiA9kNABQAAUCUCqjrotDGbaoHs\nFACglRFQ1UGnjdlULYKp9sYrdwB0AgKqQVSaaWr0mE1AM+OVO2h3jD0FiV5+g6p03KdO6I1XK2Sn\n2l9hcFQGSUW7YuwpSGSoBtVOmSbadSEvvHInGz392sfMaZP10b23Z+ypDkeGahDtlGnKc5T1YshO\nAWgHjD0FiYCqYzDKOgAA9UOVX4coZNvGjxmZd1EkkZ1qBHrXAUDjEFCh4QimGoPedc2PdlRA+6DK\nD2hT9K4DgMYhoEJDkZ1qnELvOgBA/VHlB6Bp0O4LQKsioELDkJ3CUGj3BaBVEVABaBpHnHSaDj3m\nFNp9oa7yelUMr6hpbwRUaAiyUyhFLUdVb5XqQ3r6NV7hVTEXLVzaEdtFY9AoHUBbKlQfSqJxPvop\nvCKm0a+KyWu7aAwCKtQd2SnkgWEjUExer4rhFTXtjSo/1BXBFPLCS5mRN9pMdRYCKgAA6oA2U52F\ngAp10wzZqVZpmIzORsP0xmh0xmjmtMn66N7b02aqQxBQtaGunnW6dNFydfWsy60MzRBMSYxrBGCT\nRmeMCm2mJo0d3ZDtIV80Sm9Dcxd36eYlqyVJM6Z2dvsRGiYDKKCXHeqJgKoNTZ8yvt/fRmuW7JTE\n++wAbEIvO9QTVX5taPyYkZoxdaLGjxmZd1EAlIh2VLVHLzs0EgFVi2qGdlJZmik7BaCz0csOjURA\n1aIK7aTmLu7KuyioMXomArVBLzs0EgFVi5o+ZbwO322r3NpJZSE7VRv0TES1qOpy9LJDI9EoPWdd\nPes0d3GXpk8ZX1abp0I7qWZBMFU79ExEtQpVXZJohA00CAFVzhjiAGn0TES1GB4AaDyq/HLWjFV3\n5SI7BdRGrXr6UdUFNB4BVc4Y4gBAI9G+CqgPAipUhexU56EXYmtjKAGgPmhDBaAshV6Ikmjr1YJo\nXwXUBxkqVKza7BSZjtZ0xEmn6dBjTqEXYp3Ue8R02lcB9UGGCrkh09Ga6IUIAAMRUCXcuPgZnbzP\ny2kgXoJatJ1ivCUAQLugyi9hwZPdvMq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      "text/plain": [
       "<matplotlib.figure.Figure at 0xafbfb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl=plt\n",
    "from sklearn import decomposition\n",
    "# In this case the seeding of the centers is deterministic,\n",
    "# hence we run the kmeans algorithm only once with n_init=1\n",
    "\n",
    "pca = decomposition.PCA(n_components=2).fit(X_train)\n",
    "reduced_X_train = pca.transform(X_train)\n",
    "\n",
    "# Step size of the mesh. Decrease to increase the quality of the VQ.\n",
    "h = .01     # point in the mesh [x_min, m_max]x[y_min, y_max].\n",
    "\n",
    "# Plot the decision boundary. For that, we will asign a color to each\n",
    "x_min, x_max = reduced_X_train[:, 0].min() + 1, reduced_X_train[:, 0].max() - 1\n",
    "y_min, y_max = reduced_X_train[:, 1].min() + 1, reduced_X_train[:, 1].max() - 1\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
    "\n",
    "gm.fit(reduced_X_train)\n",
    "#print np.c_[xx.ravel(),yy.ravel()]\n",
    "Z = gm.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "\n",
    "# Put the result into a color plot\n",
    "Z = Z.reshape(xx.shape)\n",
    "pl.figure(1)\n",
    "pl.clf()\n",
    "pl.imshow(Z, interpolation='nearest',\n",
    "          extent=(xx.min(), xx.max(), yy.min(), yy.max()),\n",
    "          cmap=pl.cm.Paired,\n",
    "          aspect='auto', origin='lower')\n",
    "#print reduced_X_train.shape\n",
    "\n",
    "pl.plot(reduced_X_train[:, 0], reduced_X_train[:, 1], 'k.', markersize=2)\n",
    "# Plot the centroids as a white X\n",
    "centroids = gm.means_\n",
    "\n",
    "pl.scatter(centroids[:, 0], centroids[:, 1],\n",
    "           marker='.', s=169, linewidths=3,\n",
    "           color='w', zorder=10)\n",
    "\n",
    "pl.title('Mixture of gaussian models on the seeds dataset (PCA-reduced data)\\n'\n",
    "         'Means are marked with white dots')\n",
    "pl.xlim(x_min, x_max)\n",
    "pl.ylim(y_min, y_max)\n",
    "pl.xticks(())\n",
    "pl.yticks(())\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "### Summary\n",
    "\n",
    "Thus we looked at another unsupervised learning examples where we clustered seed based on its properties. Feel free to search similar datasets from UCI ML repository or any other sources you would like and apply these codes to them. This way you would get a better understanding of how and when to apply unsupervised learning techniques on different datasets.\n",
    "\n",
    "\n",
    "___"
   ]
  }
 ],
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