2_2_autoEncoder regression for 1st floor.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn import preprocessing\n",
    "import keras\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Dropout, Activation\n",
    "from keras.optimizers import SGD, RMSprop, Adadelta, Adam\n",
    "import matplotlib.pyplot as plt\n",
    "from keras import regularizers\n",
    "import sklearn\n",
    "from sklearn import svm\n",
    "from sklearn import preprocessing\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "#train\n",
    "#test\n",
    "#load data and exchange the train and test data\n",
    "path = 'C:/Users/mys12/Desktop/northeastern/summer2018/data_Robust_Fingerprinting-master/DISTRIBUTED_OPENSOURCE/FINGERPRINTING_DB'\n",
    "\n",
    "test_rss = pd.read_csv(path + '/Training_rss_21Aug17.csv', header = 0)\n",
    "test_coord = pd.read_csv(path + '/Training_coordinates_21Aug17.csv', header = 0)\n",
    "test_rss = test_rss.replace(100, 0)\n",
    "\n",
    "train_rss = pd.read_csv(path + '/Test_rss_21Aug17.csv', header = 0)\n",
    "train_coord = pd.read_csv(path + '/Test_coordinates_21Aug17.csv', header = 0)\n",
    "train_rss = train_rss.replace(100, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "992\n"
     ]
    }
   ],
   "source": [
    "# combine the train_rss vaule and train_coord value into one matrix\n",
    "\n",
    "train = pd.concat([train_rss, train_coord], axis=1, ignore_index=True)\n",
    "test = pd.concat([test_rss, test_coord], axis=1, ignore_index=True)\n",
    "train = np.asarray(train)\n",
    "test = np.asarray(test)\n",
    "\n",
    "# get the first floor scaled Rss value and Coordination value \n",
    "train1 = train[train[:,-1]==0.0]\n",
    "normalizer = preprocessing.Normalizer().fit(train1[:,:-3])\n",
    "train1_r=normalizer.transform(train1[:,:-3])\n",
    "train1_c=train1[:,-3:-1]\n",
    "print(train1_r.shape[1])\n",
    "\n",
    "test1 = test[test[:,-1]==0.0]\n",
    "test1_r=normalizer.transform(test1[:,:-3])\n",
    "test1_c=test1[:,-3:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define a function that convert the locations into local ones.\n",
    "def predata(rss, locations):\n",
    "    # the origin of the room\n",
    "    origin = np.amin(locations,axis=0)\n",
    "    #size of the room\n",
    "    room_size = np.amax(locations, axis=0)-origin\n",
    "    # position respect to origin\n",
    "    train_Yy = locations - origin\n",
    "    train_Xx = np.asarray(rss, dtype=np.float64)\n",
    "    return train_Xx, train_Yy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_val(rss, locations):\n",
    "    train_Xx, train_Yy = predata(rss, locations)\n",
    "    train_x, val_x, train_y, val_y = train_test_split(train_Xx, train_Yy, test_size=0.25)\n",
    "    return train_x, val_x, train_y, val_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def accuracy(predictions, labels):\n",
    "    error = np.sqrt(np.sum((predictions - labels)**2, 1))\n",
    "    return error, np.mean(error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_X, val_X, train_Y, val_Y = train_val(train1_r, train1_c)\n",
    "test_X, test_Y = predata(test1_r, test1_c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "nb_epochs = 500\n",
    "batch_size = 64\n",
    "input_size = 992\n",
    "num_classes = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the encoder part of Autoencoder model\n",
    "def encoder():\n",
    "    model = Sequential()\n",
    "    model.add(Dense(512, input_dim=input_size, activation='relu', bias=True))\n",
    "    model.add(Dense(256, activation='relu', bias=True))\n",
    "    #model.add(Dense(128, activation='relu', bias=True))\n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the decoder part\n",
    "def decoder(e):   \n",
    "    #e.add(Dense(256, input_dim=128, activation='relu', bias=True))\n",
    "    e.add(Dense(512, input_dim=256, activation='relu', bias=True))\n",
    "    e.add(Dense(input_size, activation='relu', bias=True))\n",
    "    e.compile(optimizer='adam', loss='mse')\n",
    "    return e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\software\\WinPython-64bit-3.6.2.0Qt5\\python-3.6.2.amd64\\lib\\site-packages\\ipykernel_launcher.py:3: UserWarning: Update your `Dense` call to the Keras 2 API: `Dense(512, input_dim=992, activation=\"relu\", use_bias=True)`\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "C:\\software\\WinPython-64bit-3.6.2.0Qt5\\python-3.6.2.amd64\\lib\\site-packages\\ipykernel_launcher.py:4: UserWarning: Update your `Dense` call to the Keras 2 API: `Dense(256, activation=\"relu\", use_bias=True)`\n",
      "  after removing the cwd from sys.path.\n",
      "C:\\software\\WinPython-64bit-3.6.2.0Qt5\\python-3.6.2.amd64\\lib\\site-packages\\ipykernel_launcher.py:3: UserWarning: Update your `Dense` call to the Keras 2 API: `Dense(512, input_dim=256, activation=\"relu\", use_bias=True)`\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "C:\\software\\WinPython-64bit-3.6.2.0Qt5\\python-3.6.2.amd64\\lib\\site-packages\\ipykernel_launcher.py:4: UserWarning: Update your `Dense` call to the Keras 2 API: `Dense(992, activation=\"relu\", use_bias=True)`\n",
      "  after removing the cwd from sys.path.\n",
      "C:\\software\\WinPython-64bit-3.6.2.0Qt5\\python-3.6.2.amd64\\lib\\site-packages\\keras\\models.py:844: UserWarning: The `nb_epoch` argument in `fit` has been renamed `epochs`.\n",
      "  warnings.warn('The `nb_epoch` argument in `fit` '\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Epoch 497/500\n",
      "948/948 [==============================] - 0s - loss: 0.0010     \n",
      "Epoch 498/500\n",
      "948/948 [==============================] - 0s - loss: 0.0010     \n",
      "Epoch 499/500\n",
      "948/948 [==============================] - 0s - loss: 0.0010     \n",
      "Epoch 500/500\n",
      "948/948 [==============================] - 0s - loss: 0.0010     \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1ed51c03a58>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# combine and train\n",
    "e = encoder()\n",
    "d = decoder(e)\n",
    "d.fit(train_X, train_X, nb_epoch=nb_epochs, batch_size=batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define a regression model\n",
    "def regression(d):\n",
    "    num_to_remove = 2\n",
    "    regularzation_penalty = 0.02\n",
    "    initilization_method = 'he_normal' #'random_uniform' ,'random_normal','TruncatedNormal' ,'glorot_uniform', 'glorot_nomral', 'he_normal', 'he_uniform'\n",
    "    #Optimizer\n",
    "    adam = Adam(lr=0.0005, beta_1=0.9, beta_2=0.999, epsilon=1e-08, decay=0.0)\n",
    "    \n",
    "    for i in range(num_to_remove):\n",
    "        d.pop()\n",
    "    d.add(Dense(256, input_dim=256, activation='relu', kernel_initializer=initilization_method, kernel_regularizer=regularizers.l2(regularzation_penalty)))\n",
    "    d.add(Dropout(0.5))\n",
    "    d.add(Dense(256, activation='relu', kernel_initializer=initilization_method, kernel_regularizer=regularizers.l2(regularzation_penalty)))\n",
    "    d.add(Dropout(0.5))\n",
    "    d.add(Dense(num_classes, activation='linear', kernel_initializer=initilization_method, kernel_regularizer=regularizers.l2(regularzation_penalty)))\n",
    "\n",
    "    #Model compile\n",
    "    d.compile(loss='mean_squared_error',\n",
    "                  optimizer='adam')\n",
    "    \n",
    "    return d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\software\\WinPython-64bit-3.6.2.0Qt5\\python-3.6.2.amd64\\lib\\site-packages\\keras\\models.py:844: UserWarning: The `nb_epoch` argument in `fit` has been renamed `epochs`.\n",
      "  warnings.warn('The `nb_epoch` argument in `fit` '\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 948 samples, validate on 316 samples\n",
      "Epoch 1/500\n",
      "948/948 [==============================] - 0s - loss: 4518.2428 - val_loss: 3720.3163\n",
      "Epoch 2/500\n",
      "948/948 [==============================] - 0s - loss: 1936.9790 - val_loss: 595.4097\n",
      "Epoch 3/500\n",
      "948/948 [==============================] - 0s - loss: 585.6693 - val_loss: 323.7258\n",
      "Epoch 4/500\n",
      "948/948 [==============================] - 0s - loss: 378.7448 - val_loss: 231.8705\n",
      "Epoch 5/500\n",
      "948/948 [==============================] - 0s - loss: 311.5308 - val_loss: 213.9963\n",
      "Epoch 6/500\n",
      "948/948 [==============================] - 0s - loss: 272.1058 - val_loss: 193.4090\n",
      "Epoch 7/500\n",
      "948/948 [==============================] - 0s - loss: 258.2342 - val_loss: 186.5131\n",
      "Epoch 8/500\n",
      "948/948 [==============================] - 0s - loss: 259.8019 - val_loss: 185.4324\n",
      "Epoch 9/500\n",
      "948/948 [==============================] - 0s - loss: 240.7082 - val_loss: 178.3651\n",
      "Epoch 10/500\n",
      "948/948 [==============================] - 0s - loss: 252.5247 - val_loss: 168.7908\n",
      "Epoch 11/500\n",
      "948/948 [==============================] - 0s - loss: 228.6595 - val_loss: 168.9920\n",
      "Epoch 12/500\n",
      "948/948 [==============================] - 0s - loss: 217.1846 - val_loss: 155.6046\n",
      "Epoch 13/500\n",
      "948/948 [==============================] - 0s - loss: 203.8727 - val_loss: 138.6514\n",
      "Epoch 14/500\n",
      "948/948 [==============================] - 0s - loss: 179.4208 - val_loss: 110.9375\n",
      "Epoch 15/500\n",
      "948/948 [==============================] - 0s - loss: 156.6753 - val_loss: 91.4222\n",
      "Epoch 16/500\n",
      "948/948 [==============================] - 0s - loss: 140.3933 - val_loss: 85.0948\n",
      "Epoch 17/500\n",
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      "Epoch 26/500\n",
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      "Epoch 27/500\n",
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      "Epoch 28/500\n",
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      "Epoch 29/500\n",
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      "Epoch 30/500\n",
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      "Epoch 31/500\n",
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      "Epoch 32/500\n",
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      "Epoch 39/500\n",
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      "Epoch 41/500\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
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      "948/948 [==============================] - 0s - loss: 57.3324 - val_loss: 47.2417\n",
      "Epoch 396/500\n",
      "948/948 [==============================] - 0s - loss: 52.4193 - val_loss: 45.6979\n",
      "Epoch 397/500\n",
      "948/948 [==============================] - 0s - loss: 53.3097 - val_loss: 48.6518\n",
      "Epoch 398/500\n",
      "948/948 [==============================] - 0s - loss: 54.7260 - val_loss: 45.0961\n",
      "Epoch 399/500\n",
      "948/948 [==============================] - 0s - loss: 51.7903 - val_loss: 46.3702\n",
      "Epoch 400/500\n",
      "948/948 [==============================] - 0s - loss: 55.4510 - val_loss: 51.8196\n",
      "Epoch 401/500\n",
      "948/948 [==============================] - 0s - loss: 51.1815 - val_loss: 49.4169\n",
      "Epoch 402/500\n",
      "948/948 [==============================] - 0s - loss: 57.3992 - val_loss: 48.2906\n",
      "Epoch 403/500\n",
      "948/948 [==============================] - 0s - loss: 51.4108 - val_loss: 52.4594\n",
      "Epoch 404/500\n",
      "948/948 [==============================] - 0s - loss: 54.1786 - val_loss: 46.2795\n",
      "Epoch 405/500\n",
      "948/948 [==============================] - 0s - loss: 53.5384 - val_loss: 47.5687\n",
      "Epoch 406/500\n",
      "948/948 [==============================] - 0s - loss: 54.1831 - val_loss: 47.4685\n",
      "Epoch 407/500\n",
      "948/948 [==============================] - 0s - loss: 53.0959 - val_loss: 48.6086\n",
      "Epoch 408/500\n",
      "948/948 [==============================] - 0s - loss: 51.2995 - val_loss: 48.4483\n",
      "Epoch 409/500\n",
      "948/948 [==============================] - 0s - loss: 51.7362 - val_loss: 45.9690\n",
      "Epoch 410/500\n",
      "948/948 [==============================] - 0s - loss: 51.8377 - val_loss: 48.4448\n",
      "Epoch 411/500\n",
      "948/948 [==============================] - 0s - loss: 53.8649 - val_loss: 48.1553\n",
      "Epoch 412/500\n",
      "948/948 [==============================] - 0s - loss: 52.9063 - val_loss: 47.5561\n",
      "Epoch 413/500\n",
      "948/948 [==============================] - 0s - loss: 51.2293 - val_loss: 49.2606\n",
      "Epoch 414/500\n",
      "948/948 [==============================] - 0s - loss: 53.2570 - val_loss: 45.0491\n",
      "Epoch 415/500\n",
      "948/948 [==============================] - 0s - loss: 47.8437 - val_loss: 46.2083\n",
      "Epoch 416/500\n",
      "948/948 [==============================] - 0s - loss: 53.5233 - val_loss: 49.2777\n",
      "Epoch 417/500\n",
      "948/948 [==============================] - 0s - loss: 50.6000 - val_loss: 48.0858\n",
      "Epoch 418/500\n",
      "948/948 [==============================] - 0s - loss: 56.1356 - val_loss: 47.7024\n",
      "Epoch 419/500\n",
      "948/948 [==============================] - 0s - loss: 52.6264 - val_loss: 48.1556\n",
      "Epoch 420/500\n",
      "948/948 [==============================] - 0s - loss: 54.2165 - val_loss: 46.9066\n",
      "Epoch 421/500\n",
      "948/948 [==============================] - 0s - loss: 47.9213 - val_loss: 47.2319\n",
      "Epoch 422/500\n",
      "948/948 [==============================] - 0s - loss: 49.6107 - val_loss: 46.1707\n",
      "Epoch 423/500\n",
      "948/948 [==============================] - 0s - loss: 51.3813 - val_loss: 49.1189\n",
      "Epoch 424/500\n",
      "948/948 [==============================] - 0s - loss: 52.3464 - val_loss: 46.4611\n",
      "Epoch 425/500\n",
      "948/948 [==============================] - 0s - loss: 51.4836 - val_loss: 45.7959\n",
      "Epoch 426/500\n",
      "948/948 [==============================] - 0s - loss: 48.9589 - val_loss: 47.1824\n",
      "Epoch 427/500\n",
      "948/948 [==============================] - 0s - loss: 51.1996 - val_loss: 47.2909\n",
      "Epoch 428/500\n",
      "948/948 [==============================] - 0s - loss: 51.4245 - val_loss: 47.3305\n",
      "Epoch 429/500\n",
      "948/948 [==============================] - 0s - loss: 49.6989 - val_loss: 46.3154\n",
      "Epoch 430/500\n",
      "948/948 [==============================] - 0s - loss: 53.2020 - val_loss: 49.3361\n",
      "Epoch 431/500\n",
      "948/948 [==============================] - 0s - loss: 54.8779 - val_loss: 46.2159\n",
      "Epoch 432/500\n",
      "948/948 [==============================] - 0s - loss: 53.3296 - val_loss: 46.0043\n",
      "Epoch 433/500\n",
      "948/948 [==============================] - 0s - loss: 55.1354 - val_loss: 46.1275\n",
      "Epoch 434/500\n",
      "948/948 [==============================] - 0s - loss: 51.2162 - val_loss: 50.6866\n",
      "Epoch 435/500\n",
      "948/948 [==============================] - 0s - loss: 53.2599 - val_loss: 50.2919\n",
      "Epoch 436/500\n",
      "948/948 [==============================] - 0s - loss: 54.7859 - val_loss: 48.0901\n",
      "Epoch 437/500\n",
      "948/948 [==============================] - 0s - loss: 52.5575 - val_loss: 46.8194\n",
      "Epoch 438/500\n",
      "948/948 [==============================] - 0s - loss: 52.0143 - val_loss: 45.7064\n",
      "Epoch 439/500\n",
      "948/948 [==============================] - 0s - loss: 46.2396 - val_loss: 47.4858\n",
      "Epoch 440/500\n",
      "948/948 [==============================] - 0s - loss: 53.7150 - val_loss: 47.2441\n",
      "Epoch 441/500\n",
      "948/948 [==============================] - 0s - loss: 46.8834 - val_loss: 46.9702\n",
      "Epoch 442/500\n",
      "948/948 [==============================] - 0s - loss: 51.8492 - val_loss: 48.2562\n",
      "Epoch 443/500\n",
      "948/948 [==============================] - 0s - loss: 45.4330 - val_loss: 45.0799\n",
      "Epoch 444/500\n",
      "948/948 [==============================] - 0s - loss: 50.0832 - val_loss: 44.3850\n",
      "Epoch 445/500\n",
      "948/948 [==============================] - 0s - loss: 46.9679 - val_loss: 46.2879\n",
      "Epoch 446/500\n",
      "948/948 [==============================] - 0s - loss: 51.6319 - val_loss: 44.1870\n",
      "Epoch 447/500\n",
      "948/948 [==============================] - 0s - loss: 52.2737 - val_loss: 45.3383\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1ed6d8a9ba8>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# training \n",
    "earlyStopping=keras.callbacks.EarlyStopping(monitor='val_loss', patience=60, verbose=0, mode='auto')\n",
    "Model_best= keras.callbacks.ModelCheckpoint(filepath='best_model.h5', monitor='val_loss', save_best_only=True)\n",
    "\n",
    "c = regression(d)\n",
    "c.fit(train_X, train_Y, validation_data=(val_X, val_Y), nb_epoch=nb_epochs, callbacks=[earlyStopping, Model_best], batch_size=batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "948/948 [==============================] - 0s\n",
      "316/316 [==============================] - 0s\n",
      "226/226 [==============================] - 0s\n",
      "Loss for training data is 7.10064792633\n",
      "Loss for validation data is 45.3382949829\n",
      "Loss for test data is 73.4685821533\n"
     ]
    }
   ],
   "source": [
    "#model evaluate\n",
    "train_loss = c.evaluate(train_X,train_Y, batch_size=len(train_Y)) #calculate the data in test mode(Keras)\n",
    "val_loss = c.evaluate(val_X, val_Y, batch_size=len(val_Y))\n",
    "test_loss = c.evaluate(test_X, test_Y, batch_size=len(test_Y))\n",
    "print(\"Loss for training data is\",train_loss)\n",
    "print(\"Loss for validation data is\",val_loss)\n",
    "print(\"Loss for test data is\",test_loss)\n",
    "predict_Y = c.predict(test_X)\n",
    "error, accuracy1 = accuracy(predict_Y, test_Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average error: 8.82441610545\n"
     ]
    }
   ],
   "source": [
    "print('The average error:', accuracy1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum error: 0.656697212306 maximum error: 101.110358685 variance: 62.0252645697\n"
     ]
    }
   ],
   "source": [
    "print('minimum error:', np.amin(error), 'maximum error:', np.amax(error), 'variance:', np.var(error))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.4982784597270147"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GXYqISE5FOtwPdg0BsKl5ccCViIjkVqTDvaNvhCKDhpryoEsREcmprMLdzDabWZuZ7Tez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\nJIQU7iIiIaRwFxEJIYW7iEgI/X9L86Ht6DMAMgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ed66741978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# print the CDF of the error\n",
    "error_sorted= np.sort(error)\n",
    "p = 1. *np.arange(len(error))/(len(error)-1)\n",
    "plt.plot(error_sorted, p)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}