{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Working With Image Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "digits_data = load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'target_names', 'images', 'DESCR'])"
      ]
     },
     "execution_count": 331,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits_data.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels = pd.Series(digits_data['target'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>54</th>\n",
       "      <th>55</th>\n",
       "      <th>56</th>\n",
       "      <th>57</th>\n",
       "      <th>58</th>\n",
       "      <th>59</th>\n",
       "      <th>60</th>\n",
       "      <th>61</th>\n",
       "      <th>62</th>\n",
       "      <th>63</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 64 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    0    1    2     3    4    5    6    7    8    9  ...    54   55   56   57  \\\n",
       "0  0.0  0.0  5.0  13.0  9.0  1.0  0.0  0.0  0.0  0.0 ...   0.0  0.0  0.0  0.0   \n",
       "\n",
       "    58    59    60   61   62   63  \n",
       "0  6.0  13.0  10.0  0.0  0.0  0.0  \n",
       "\n",
       "[1 rows x 64 columns]"
      ]
     },
     "execution_count": 333,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame(digits_data['data'])\n",
    "data.head(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x106f352b0>"
      ]
     },
     "execution_count": 334,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "first_image = data.iloc[0]\n",
    "np_image = first_image.values\n",
    "np_image = np_image.reshape(8,8)\n",
    "\n",
    "plt.imshow(np_image, cmap='gray_r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a1780fd68>"
      ]
     },
     "execution_count": 335,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axarr = plt.subplots(2, 4)\n",
    "\n",
    "axarr[0, 0].imshow(data.iloc[0].values.reshape(8,8), cmap='gray_r')\n",
    "axarr[0, 1].imshow(data.iloc[99].values.reshape(8,8), cmap='gray_r')\n",
    "axarr[0, 2].imshow(data.iloc[199].values.reshape(8,8), cmap='gray_r')\n",
    "axarr[0, 3].imshow(data.iloc[299].values.reshape(8,8), cmap='gray_r')\n",
    "\n",
    "axarr[1, 0].imshow(data.iloc[999].values.reshape(8,8), cmap='gray_r')\n",
    "axarr[1, 1].imshow(data.iloc[1099].values.reshape(8,8), cmap='gray_r')\n",
    "axarr[1, 2].imshow(data.iloc[1199].values.reshape(8,8), cmap='gray_r')\n",
    "axarr[1, 3].imshow(data.iloc[1299].values.reshape(8,8), cmap='gray_r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-Nearest Neighbors Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9677233358079684"
      ]
     },
     "execution_count": 336,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.model_selection import KFold\n",
    "\n",
    "# 50% Train / test validation\n",
    "def train_knn(nneighbors, train_features, train_labels):\n",
    "    knn = KNeighborsClassifier(n_neighbors = nneighbors)\n",
    "    knn.fit(train_features, train_labels)\n",
    "    return knn\n",
    "\n",
    "def test(model, test_features, test_labels):\n",
    "    predictions = model.predict(test_features)\n",
    "    train_test_df = pd.DataFrame()\n",
    "    train_test_df['correct_label'] = test_labels\n",
    "    train_test_df['predicted_label'] = predictions\n",
    "    overall_accuracy = sum(train_test_df[\"predicted_label\"] == train_test_df[\"correct_label\"])/len(train_test_df)    \n",
    "    return overall_accuracy\n",
    "\n",
    "def cross_validate(k):\n",
    "    fold_accuracies = []\n",
    "    kf = KFold(n_splits = 4, random_state=2)\n",
    "    for train_index, test_index in kf.split(data):\n",
    "        train_features, test_features = data.loc[train_index], data.loc[test_index]\n",
    "        train_labels, test_labels = labels.loc[train_index], labels.loc[test_index]\n",
    "        model = train_knn(k, train_features, train_labels)\n",
    "        overall_accuracy = test(model, test_features, test_labels)\n",
    "        fold_accuracies.append(overall_accuracy)\n",
    "    return fold_accuracies\n",
    "        \n",
    "knn_one_accuracies = cross_validate(1)\n",
    "np.mean(knn_one_accuracies)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a16f77ac8>]"
      ]
     },
     "execution_count": 337,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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53P7qQto2qM6ofq2YOH8dQ5/4jI079YudiBw7CvNjIK1eNa7olcYr89aSuWFX2OXIMZaf70z4bDXnPjydjNXb+NPgzrwyqhd3DezI2OEnkbV5Dz8aPZN5X28Pu1QRKacU5sfIzf3bUKNyMn95O1P3TcuxVTl7GDr2M37/1hK6t6jNu7f05creaSQkGADndG7EGzf2oWpKIpeNncUrGWtDrlhEyiOF+TFSq2oKPz+zLTNWbGHa8pywy5ESlpuXz+PTVjLgHzNYtnE391/cjQlX96BZnar/s267hqm8dWMfTmlVh1+99gV/nLSEw3n5IVQtIuWVwvwYGt6zBWl1q3Lv5Exy9cO73Fi6fhcXPvYpf3vnS85oX58PbuvHJenNMLPv3KZW1RSeHnEy157akn99upornpyjmfZEpMQozI+hlKQE7hzYgazNe3hprrpX493B3DwefG8Zg0fPZMPO/YwZ1p1/Xn4SDWpUjmn7pMQEfnt+Jx685HjmrdnO4NEz9UyFiJQIhfkxdm7nRvRIq8PD7y9n94HDYZcjxTR/zXbOe2Qmj36UxeDjj+P9W/txXrfG33s1/l2GnNSUV0f14nBePhc99ilTFm04BhWLSEWiMD/GzIzfnt+RrXsP8fi0lWGXIz/QvkO53PPvpQx5/FP2Hszl6REn89DQE6hdLeWo9nt8s1r8+6ZT6dg4leufn89D7y3TmP4iUmwK81LQrWktfnzCcTw58yvW7dgfdjkSo0+ztjDg7zN46pOv+OkpzXnv1r6c0aFBie2/QY3KvDiyJz9Jb8ojH2Ux8tl56r0RkWJRmJeSOwZ0AOD+d74MuRI5kl0HDnPn618wbPxsEgxeHtmTP/+4K6mVk0v8WJWSEvnbkG78aXBnpi7bzEWPfcrqLXtL/DgiUr7FFOZmNsDMlplZlpndWUR7CzP70My+MLNpZtY0qq25mb1nZplmttTM0gpt+6iZ7TnaEynrmtSqwjWntuTNz9fz+dodYZcj3+GDpZs4+6GPeSVjLaP6tuKdW/pySqu6x/SYZsaVvdN49uoebNlzkMGjZzJdH2cUkR/giGFuZonAGGAg0Am4zMw6FVrtAWCCu3cD7gH+GtU2Abjf3TsCPYDNUftOB2od1RnEketPb0296incO3mpBpIpY7buOcjPX1zAtRMyqF01hTdu6MNdgzpSOTmx1Gro3aYek246leNqVWHE03MYP2OV/p2ISExiuTLvAWS5+yp3PwS8BFxQaJ1OwIfB66kF7UHoJ7n7+wDuvsfd9wVticD9wK+O+iziRGrlZG49ux1zV2/n3SUbwy5HiEyM8tbn6zj74elMWbyBW89qx6SbTuX4ZuH8jtmsTlVev74353ZuxJ8nZ/LLVzRRi4gcWSxh3gSI/pB0drAs2kJgSPD6QiDVzOoC7YAdZjbRzBaY2f1BiAPcBExy9+/9XI6ZjTSzDDPLyMmJ/67HoenNaNugOvdN+ZJDuRpIJkwbdx7g2mcy+MVLn9OsTlX+c/Np/OKstqQkhfsoSbVKSTz20+788ux2TFygiVpE5Mhi+alV1AdpC/f93Q70M7MFQD9gHZALJAGnBe0nA62AEWZ2HHAJ8OiRDu7uY9093d3T69evH0O5ZVtSYgJ3n9eR1Vv38eysr8Mup0Jyd16cs4azH/qYT1Zu4TeDOjLx+t60b5QadmnfMDNuPrOtJmoRkZjEEubZQLOo902B9dEruPt6d7/I3U8EfhMs2xlsuyDoos8F3gS6AycCbYAsM1sNVDWzrKM9mXhxerv6nNa2Ho98uIId+zSkZ2n6euteho2bzV0TF9G5SQ3e+UVfruvbisSEHz74S2koPFHLy3PXhF2SiJRBsYT5XKCtmbU0sxTgUmBS9ApmVs/MCvZ1F/BU1La1zazgkro/sNTdJ7t7I3dPc/c0YJ+7tznak4kXZsbdgzqy68BhHvmwwvwOE6q8fGf8jFWc+/fpLFq3k79c2JUXru1JWr1qYZd2RNETtfz69UX84a3FmqhFRL7liGEeXFHfBLwLZAKvuPsSM7vHzAYHq50OLDOz5UBD4N5g2zwiXewfmtkiIl3240r8LOJQx8Y1GJrejGdnrdbnio+xFZt2c/E/P+XPkzPp3boe79/Wl2GnNP9mmtJ4UDBRy3WnteSZz75m+JOzNVGLiHzD4umjL+np6Z6RkRF2GSVm8+4DnH7/NPq2rc8/h58UdjnlzqHcfP758UpGf5RFtUqJ/HFwZwYff1yxxlMvSybOz+bOiYtokFqJscPT6XRcjbBLEpFjxMzmuXv6kdbTCHAhapBamZ/1a807SzYy56ttYZdTrnyRvYPBo2fy0PvLOadzQ96/rR8XnNAk7oMc4KLukYlacvOcIY9/ytuaqEWkwlOYh+y601rRqEZl7p28VBNtlIADh/P465RMfjzmE7btPcTY4Scxelh36lWvFHZpJer4ZrWYdHMfOjZO5Ybn5/OgJmoRqdAU5iGrkpLI7ee2Z2H2Tv79xfojbyDfac5X2xj4jxk88fEqLjmpGe/f1o9zOjcKu6xjpkFqZKKWoenNeFQTtYhUaArzMuCiE5vQpUkN/jblS432VQx7DubyuzcX85MnPuNwXj7PXXMKf7u4GzWrlPzEKGVNpaRE7hvS9ZuJWi587FO+0gOVIhWOwrwMSEgwfjOoE+t3HuDJmV+FXU5c+Xh5Duc+PJ3nZn/NVX3SePeWvpzatl7YZZWqbyZquaYHW/cc5ILRM/lYE7WIVCgK8zKiV+u6nNWxIY9PW8mWPQfDLqfM27HvELe98jlXPjWHyskJvPazXvzhR52pVikp7NJC07v1fydquerpOYybrolaRCoKhXkZctegDhw4nMfD7y8Pu5Qy7e1FGzjroY956/P13HRGGyb//DROalEn7LLKhGZ1qjLxht4M6NKIe9/O5DZN1CJSISjMy5DW9avz01Oa8+KcNazYtDvscsqczbsP8LNn53HD8/NpWKMyk27qw+3nti/VaUrjQdWUJMYM687t57TjjQXr+MkTn7Fh5/6wyxKRY0hhXsb84qx2VKuUxF/ezgy7lDLD3XltXjZnPzSdj5Zt5lcD2vPmjX3ofFzNsEsrs8yMm/q3ZdwV6azK2cuPHv2EeV9rLAOR8kphXsbUqZbCzf3bMHVZDjNW6CGm7O37uPLpudz+6kLaNqjO2z8/jRtOb0Nyov7pxuLsTg1544beVK+UyKVjZ/HSHE3UIlIe6SdiGXRl7zSa1anCvZMzyaugA4Hk5zsTPlvNuQ9PJ2P1Nv74o068MqoXbRpUD7u0uNO2YSpv3XgqPVvV5c6Ji/i9JmoRKXcU5mVQpaREfj2gA19u3M1r89aGXU6pW5mzh6FjP+P3by2he4vavHtLX0b0aRlXE6OUNTWrJvP0iJMZ2bcVE4KJWrbqUxMi5YbCvIw6r2tjujevxQPvLWfvwdywyykV2/ceYszULAb+YwbLNu7m/ou7MeHqHjSrUzXs0sqFpMQE7h7UkYeHHs/8NTsYPPoTlq7fFXZZIlICFOZllJnxm/M6kbP7IE9MXxV2OcdMzu6DPD87cqWYfu8H3P/uMs5oX58PbuvHJenNysXEKGXNhSc25bWf9SIvPzJRy+QvNFGLSLyruCNsxIGTWtTm/G6NGTt9JcN6NKdRzcphl1QiNu06wDuLN/L2og3MXb2NfIe0ulUZ2bcVg7o0pkuTGgrxY6xb08hELdc/N58bX5hP5oY23HZ2O93KEIlTms+8jFu7bR9nPvgxPzr+OB78yfFhl1Ns2dv38c7ijUxZvJF5X28HoG2D6gzs2piBXRrRoVGqAjwEB3Pz+P2bS3g5Yy1ndWzAw0NPILVy+R/TXiRexDqfua7My7hmdapyVZ80xs5YxVV90ujSJH4+W716y16mLN7IO4s3sDB7JwCdGtfgl2e3Y2DXRrRpkBpyhVIwUUvnJjX407+XcuFjnzLuinRa1qsWdmki8gPoyjwO7Nx/mNPvn0qHRjV44bpTyvQVbNbm3UxZtJG3F28kc0Pk4arjm9ZkYNfGDOjciDSFRJn12cqt3PD8PPLynUeHdadfu/phlyRS4cV6Za4wjxPPfLqaP0xawvgr0jmrU8Owy/mGu/Plxt1MWbSBKYs3smLzHiByv39gl0YM6NKIprX1NHq8WLttH9dNyGD5pt3cObAD153Wqkz/8ihS3inMy5nDefmc+/fpALx7S99QR0Bzdxat28mUxRuZsmgDq7fuI8GgR8s6DOzSmHM7Nyo3D+tVRPsO5XLHq18wedEGfnzCcdw3pJvGvxcJie6ZlzPJiQncPbAj107I4MU5a7iiV1qpHj8/31mwdgfvLN7A24s2sm7HfhITjN6t6zKyb2vO6dyQetUrlWpNcmxUTUli9LAT6TStBg+8t4yVOXt5YvhJHFerStilich3iOnK3MwGAP8AEoHx7n5fofYWwFNAfWAbcLm7ZwdtzYHxQDPAgUHuvtrMngfSgcPAHGCUux/+vjoq8pU5RK6Ih42bzZcbdzHtjjOoWeXYPnWcl+9krN4WPMS2kY27DpCcaJzWtj4DujTi7I4NqV0t5ZjWIOH6YOkmbnn5c6pXSuLFkT31YJxIKSuxbnYzSwSWA2cD2cBc4DJ3Xxq1zqvAf9z9GTPrD1zl7sODtmnAve7+vplVB/LdfZ+ZDQKmBLt4AZju7o9/Xy0VPcwBFq/byY9Gz2Tkaa24a1DHEt9/bl4+s1ZtY8riDby7ZCNb9hyiUlIC/drVZ1DXxvTv2IAa+uhShZK5YReXj59NYoLxwnWn6FMIIqWoJLvZewBZ7r4q2PFLwAXA0qh1OgG3Bq+nAm8G63YCktz9fQB331Owgbu/HVXsHKBpDLVUeF2a1OSiE5vy9CerubxnixIZ6vRQbj6frNzClEUbeH/pJrbvO0yV5ET6d2jAwK6NOKN9A6pV0h2Ziqpj4xq8NLInw8bP5tKxs3j+2p60b6RAFylLYvkJ3QSInu0jGzil0DoLgSFEuuIvBFLNrC7QDthhZhOBlsAHwJ3unlewoZklA8OBXxR1cDMbCYwEaN68eQzlln93nNueyYvW87d3vmT0sO7F2seBw3nMWBEEeOYmdh/IpXqlJM7q2IABXRrTr119qqTooSeJaNswlZdH9mTYuNlcOvYznrv2FM0nL1KGxBLmRX0upXDf/O3AaDMbAUwH1gG5wf5PA04E1gAvAyOAJ6O2fYxIF/uMog7u7mOBsRDpZo+h3nKvUc3KjOzbmkc+XMHVp26ne/PaMW2371Au05blMGXxRj7K3MTeQ3nUrJLMuZ0bMahrI/q0qUelJAW4FK1V/eq8PCoS6MPGzebZa3rQrWmtsMsSEWIL82wiD68VaAqsj17B3dcDFwEE98WHuPtOM8sGFkR10b8J9CQIczP7A5GH5kYd5XlUOKP6tuLFOWv483+W8vr1vb/zs8C7Dxzmoy83M2XRRqYt38yBw/nUrZbC4BOOY2CXxvRqXTfUj7lJfGlRt1rQ5T6Ln46bzb+u7sFJLWL7ZVJEjp1Ywnwu0NbMWhK54r4UGBa9gpnVA7a5ez5wF5En2wu2rW1m9d09B+gPZATbXAucC5wZbCc/QLVKSdx+Tjt+/foiJi/awPndjvumbee+w3yQuYkpizcwffkWDuXl0yC1Ej9Jb8aALo3okVaHJAW4FFOzOlV5eWQvfjp+Nlc8OZunr+pBj5Z1wi5LpEKL9aNpg4C/E/lo2lPufq+Z3QNkuPskM7sY+CuR7vfpwI3ufjDY9mzgQSLd9fOAke5+yMxyga+B3cFhJrr7Pd9Xh55m/7a8fOe8R2aw91Aur47qzbRlm5myeCOfZG0hN985rmZlBnRpzKCujejevLZmxJIStWnXAYaNm8X6HQd4ckQ6vVvXC7skkXJHI8BVEDNW5DD8yTnfvG9epyoDuzZiYJfGHN+0pobilGMqZ/dBLh8/m9Vb9zLuinT6ajx3kRKlMK9AHvlwBYdy8xnYtRGdGmsucCld2/Ye4vLxs8navId/Du9O/w5lZ+4AkXinMBeRUrNj3yGueGoOmRt2MXpYd87t3CjskkTKhVjDXE9BichRq1U1heeuPYUuTWpy4/PzmfzFhrBLEqlQFOYiUiJqVE7m2WtO4cTmtbj5xflqWSI7AAAYJElEQVS89fm6sEsSqTAU5iJSYqpXSuKZq3twSsu63PLy57w2LzvskkQqBIW5iJSoqilJPDXiZE5tU487XlvIi3PWhF2SSLmnMBeRElclJZFxV6Rzerv63DVxERM+Wx12SSLlmsJcRI6JysmJ/HP4SZzdqSG/f2sJ42esCrskkXJLYS4ix0ylpEQe+2l3zuvamD9PzuTxaSvDLkmkXNIk1SJyTCUnJvCPS08gKdH42ztfcjgvn5+f2TbsskTKFYW5iBxzSYkJPPSTE0hKSOCh95dzOC+f285up9EKRUqIwlxESkVignH/xd1ISTIe/SiLQ3n53DmggwJdpAQozEWk1CQkGPf+uCvJiQk88fEqDuXm8/vzOynQRY6SwlxESlVCgvGnwZ1JTkzgyZlfcTgvn3sGd9EUvSJHQWEuIqXOzPjteR1JTkzgnx+vJDfP+cuFXRXoIsWkMBeRUJgZvx7QnpRE45HgHvr9Fx9PogJd5AdTmItIaMyM285pT3JiAg++v5zcPOehnxxPUqKGwBD5IRTmIhK6m89sS3JSAvdNiXwO/ZHLTiRZgS4SM/1vEZEy4Wf9WvO78zsxZfFGrn9uPgdz88IuSSRuKMxFpMy45tSW/N8FnfkgcxOjnp3HgcMKdJFYKMxFpEwZ3iuN+y7qysfLc7j2mQz2H1KgixxJTGFuZgPMbJmZZZnZnUW0tzCzD83sCzObZmZNo9qam9l7ZpZpZkvNLC1Y3tLMZpvZCjN72cxSSuqkRCS+XdqjOQ9cfDyfrtzCVf+aw96DuWGXJFKmHTHMzSwRGAMMBDoBl5lZp0KrPQBMcPduwD3AX6PaJgD3u3tHoAewOVj+N+Bhd28LbAeuOZoTEZHyZchJTXl46AnMXb2dK5+aw+4Dh8MuSaTMiuXKvAeQ5e6r3P0Q8BJwQaF1OgEfBq+nFrQHoZ/k7u8DuPsed99nkbEb+wOvBds8A/z4qM5ERMqdC05owqOXncjna3cw/Mk57NyvQBcpSixh3gRYG/U+O1gWbSEwJHh9IZBqZnWBdsAOM5toZgvM7P7gSr8usMPdc79nnwCY2UgzyzCzjJycnNjOSkTKjUFdG/PYT7uzZP1OLh8/mx37DoVdkkiZE0uYFzUckxd6fzvQz8wWAP2AdUAukc+xnxa0nwy0AkbEuM/IQvex7p7u7un169ePoVwRKW/O6dyIscPTWbZpN5eNm83WPQfDLkmkTIklzLOBZlHvmwLro1dw9/XufpG7nwj8Jli2M9h2QdBFnwu8CXQHtgC1zCzpu/YpIhLtjA4NePLKdL7asofLxs1i8+4DYZckUmbEEuZzgbbB0+cpwKXApOgVzKyemRXs6y7gqahta5tZwSV1f2CpuzuRe+sXB8uvBN4q/mmISEVwWtv6PD2iB9nb93Pp2Fls2qVAF4EYwjy4or4JeBfIBF5x9yVmdo+ZDQ5WOx1YZmbLgYbAvcG2eUS62D80s0VEutfHBdv8GrjNzLKI3EN/ssTOSkTKrV6t6/LM1T3YvOsgQ5/4jPU79oddkkjoLHKRHB/S09M9IyMj7DJEpAyYvybykbWaVZJ58bqeNKtTNeySREqcmc1z9/QjracR4EQkLnVvXpsXru3J7gO5DH3iM77eujfskkRCozAXkbjVtWlNXryuJwdy8/nJE5+xMmdP2CWJhEJhLiJxrdNxNXjxup7k5cPQJ2axYtPusEsSKXUKcxGJe+0bpfLSyJ4kGFw6dhaZG3aFXZJIqVKYi0i50KZBdV4e1YuUpAQuGzeLxet2hl2SSKlRmItIudGyXjVeGdWLailJDBs3i8/X7gi7JJFSoTAXkXKlWZ2qvPKzXtSulsLl42eTsXpb2CWJHHMKcxEpd5rUqsLLI3vRILUSVzw1h1mrtoZdksgxpTAXkXKpUc3KvDSqJ01qVWHE03P4JGtL2CWJHDMKcxEptxqkVualkT1Jq1uNq/81l2nLNoddksgxoTAXkXKtbvVKvHhdT9o2rM7ICfMYP2MV+w/lhV2WSIlSmItIuVe7WgrPX9uTU1rV4c+TMznt/33EEx+vZO/B3LBLEykRmmhFRCqUOV9t49GPVjBjxRZqVU3mmj4tubJPGjUqJ4ddmsj/iHWiFYW5iFRIn6/dweiPVvBB5mZSKycxoncaV/dpSe1qKWGXJvINhbmISAyWrN/J6I+ymLJ4I9VSErm8VwuuO60V9apXCrs0EYW5iMgPsXzTbsZMzeLfC9dHhoTt0ZxRfVvTqGblsEuTCkxhLiJSDKty9vD4tJW8sWAdCWZckt6U609vTdPaVcMuTSoghbmIyFFYu20fj3+8ktcyssl356LuTbjh9Dak1asWdmlSgSjMRURKwIad+3ni41W8OGcNh/PyGXz8cdzUvw1tGqSGXZpUAApzEZEStHn3AcbP+IrnZn3N/sN5DOrSmBvPaEOn42qEXZqUY7GGeUyDxpjZADNbZmZZZnZnEe0tzOxDM/vCzKaZWdOotjwz+zz4mhS1/Ewzmx8sn2lmbWI9ORGR0tYgtTJ3D+rIzF/358bT2zB9eQ6DHpnBtc9ksFBTrUrIjnhlbmaJwHLgbCAbmAtc5u5Lo9Z5FfiPuz9jZv2Bq9x9eNC2x92rF7Hf5cAF7p5pZjcAPdx9xPfVoitzESkrdu4/zDOfrubJmV+xc/9h+rarz8/7tyE9rU7YpUk5UpJX5j2ALHdf5e6HgJeACwqt0wn4MHg9tYj2ojhQ0D9VE1gfwzYiImVCzSrJ/PzMtnxyZ39+PaADS9bt5OJ/fsZlY2fxadYW4ukWpsS/WMK8CbA26n12sCzaQmBI8PpCINXM6gbvK5tZhpnNMrMfR21zLfC2mWUDw4H7ijq4mY0Mts/IycmJoVwRkdJTvVIS15/emhm/PoPfnd+JlTl7GDZ+Nhf/8zOmLdusUJdSEUuYWxHLCv/rvB3oZ2YLgH7AOqBgBoPmQRfBMODvZtY6WH4rMMjdmwJPAw8VdXB3H+vu6e6eXr9+/RjKFREpfVVTkrjm1JZM/9UZ/N8FndmwYz8jnp7LBWM+4b0lGxXqckwlxbBONtAs6n1TCnWJu/t64CIAM6sODHH3nVFtuPsqM5sGnGhmu4Dj3X12sIuXgXeO4jxERMqEysmJDO+VxtCTm/PGgmzGTF3JyGfn0aFRKjf3b8uALo1ITCjqGkmk+GK5Mp8LtDWzlmaWAlwKTIpewczqmVnBvu4CngqW1zazSgXrAH2ApcB2oKaZtQu2ORvIPNqTEREpK1KSEhh6cnM++mU/HvrJ8RzKy+fGF+ZzzsMf88aCbHLz8sMuUcqRI4a5u+cCNwHvEgncV9x9iZndY2aDg9VOB5YFT6g3BO4NlncEMsxsIZEH4+5z96XBPq8DXg/ahgN3lOB5iYiUCUmJCVzUvSnv39qP0cNOJDkxgVtfXsiZD33My3PXcChXoS5HT4PGiIiUovx854PMTTz6URaL1u2kSa0q/Oz01lxyUlMqJyeGXZ6UMRoBTkSkDHN3pi3P4dEPVzB/zQ4a1qjEyL6tGdajOVVSFOoSoTAXEYkD7s5nK7fyyEcrmLVqG3WrpXDtaa0Y3qsF1SvF8oyylGcKcxGRODN39TYe/SiL6ctzqFU1mav7tOTK3mnUrJIcdmkSEoW5iEic+nztDkZ/tIIPMjeTWimJK3uncfWpLalTLSXs0qSUKcxFROLckvU7GTM1iymLN1IlOZHLe7bg2tNa0iC1ctilSSlRmIuIlBMrNu1m9NQs/r1wPcmJCVzWozmj+rWiUY3YQt1Mg9TEK4W5iEg589WWvTw2NYs3FqwjNz+8n90/5HeDWFZtUbcaj152Il2a1Cx2TeWVwlxEpJxau20f//5ifUwDzsT6Iz7mJIhxh7Huzx1en5/N9n2H+H8XH8/g44+LtZIKQWEuIiJxIWf3QW54fh5zV2/n+tNbc/s57TV+faAk5zMXERE5ZuqnVuL5a3sy7JTmPD5tJdc8M5ed+w+HXVZcUZiLiEjoUpIS+MuFXfnzj7swc8UWLhzzCVmb94RdVtxQmIuISJlxec8WvHBdT3buP8yFYz7hoy83hV1SXFCYi4hImdKjZR0m3XwqLepV5ZpnMhgzNYt4er4rDApzEREpc5rUqsKro3rzo27Hcf+7y7jpxQXsO5QbdllllsJcRETKpCopifzj0hO4a2AH3l60gSGPf8babfvCLqtMUpiLiEiZZWaM6teap0acTPb2fVww5hNmrdoadllljsJcRETKvDPaN+CtG/tQu2oyl4+fzYTPVus+ehSFuYiIxIVW9avzxo196NeuPr9/awl3vr6Ig7l5YZdVJijMRUQkbtSonMy4K9K56Yw2vJyxlsvGzmLz7gNhlxU6hbmIiMSVhATj9nPbM2ZYdzI37Gbwo5+wcO2OsMsKlcJcRETi0nndGvP69b1JTDAueeIzJs7PDruk0MQU5mY2wMyWmVmWmd1ZRHsLM/vQzL4ws2lm1jSqLc/MPg++JkUtNzO718yWm1mmmf28ZE5JREQqik7H1eDfN59K9+a1uO2Vhfz5P0vJzTvybHLlzRHD3MwSgTHAQKATcJmZdSq02gPABHfvBtwD/DWqbb+7nxB8DY5aPgJoBnRw947AS8U/DRERqajqVEvh2WtOYUTvNMbP/Iqr/jWXHfsOhV1WqYrlyrwHkOXuq9z9EJHQvaDQOp2AD4PXU4toL8r1wD3ung/g7ptjK1lEROTbkhMT+OPgzvxtSFdmrdrK4NGfsHzT7rDLKjWxhHkTYG3U++xgWbSFwJDg9YVAqpnVDd5XNrMMM5tlZj+O2qY1MDRom2JmbYs6uJmNDNbJyMnJiaFcERGpqIae3JyXRvZi/+E8LhzzCe8u2Rh2SaUiljAvaob4wp/Uvx3oZ2YLgH7AOqBgEN3mwcTqw4C/m1nrYHkl4EDQNg54qqiDu/tYd0939/T69evHUK6IiFRkJ7Wozb9vOpU2Daoz6tl5/OODFeTnl+8BZmIJ82wi97YLNAXWR6/g7uvd/SJ3PxH4TbBsZ0Fb8OcqYBpwYtR+Xw9evwF0K94piIiIfFujmpV5eVQvLurehIc/WM71z89jz8HyO1FLLGE+F2hrZi3NLAW4FJgUvYKZ1TOzgn3dRXCVbWa1zaxSwTpAH2BpsN6bQP/gdT9g+dGciIiISLTKyYk8eMnx/O78Try/dBNDHvuUNVvL50QtRwxzd88FbgLeBTKBV9x9iZndY2YFT6efDiwzs+VAQ+DeYHlHIMPMFhJ5MO4+dy8I8/uAIWa2iMjT79eW0DmJiIgAkYlarjm1Jc9c3YONuw4weMxMZq7YEnZZJc7iaaD69PR0z8jICLsMERGJQ19v3ct1EzLI2ryHuwd15JpTW2JW1GNhZYeZzQueLfteGgFOREQqhBZ1qzHxhj6c3akhf56cyS9fXciBw+VjohaFuYiIVBjVKyXx+E9P4paz2jJx/jqGjp3Fxp3xP1GLwlxERCqUhATjlrPa8cTwk8jatJsfjZ7JvK+3h13WUVGYi4hIhXRu50ZMvKEPVZITuWzsLF6Zu/bIG5VRCnMREamw2jdKZdJNfejRsg6/ev0L/vDWYg7H4UQtCnMREanQalVN4V9XnRz5CNtnXzP8ydls2xtfE7UozEVEpMJLSkzgd+d34sFLjmf+mh0MHj2Tpet3hV1WzBTmIiIigSEnNeWVUb04nJfPkMc/ZfIXG8IuKSYKcxERkSgnNKvFv286lY6NU7nxhfk88O6yMj9Ri8JcRESkkAY1KvPiyJ4MTW/G6KlZjHw2g90HDodd1ndSmIuIiBShUlIi9w3pyp8Gd2bqshwufOxTVuXsCbusIinMRUREvoOZcWXvNJ675hS27jnIBWM+YdqyzWGX9T8U5iIiIkfQq3VdJt10Kk1qVeGqf83lnx+vpCxNVKYwFxERiUGzOlWZeENvBnVpzH1TvuQXL33O/kNlY6IWhbmIiEiMqqYkMXrYidxxbnv+/cV6LnniU9bt2B92WQpzERGRH8LMuPGMNoy/Ip3VW/ZxweiZzPlqW6g1KcxFRESK4cyODXnzxt6kVk5m2LhZPDfr69BqUZiLiIgUU5sGqbx5Yx/6tKnHb99czO/fWhxKHQpzERGRo1CzSjJPjTiZn/VrTat61UKpISmUo4qIiJQjiQnGnQM7hHb8mK7MzWyAmS0zsywzu7OI9hZm9qGZfWFm08ysaVRbnpl9HnxNKmLbR82sbA6pIyIiEgeOeGVuZonAGOBsIBuYa2aT3H1p1GoPABPc/Rkz6w/8FRgetO139xO+Y9/pQK2jOQEREZGKLpYr8x5AlruvcvdDwEvABYXW6QR8GLyeWkT7/wh+Sbgf+FXs5YqIiEhhsYR5E2Bt1PvsYFm0hcCQ4PWFQKqZ1Q3eVzazDDObZWY/jtrmJmCSu8fHZLEiIiJlVCwPwFkRywoPSHs7MNrMRgDTgXVAbtDW3N3Xm1kr4CMzWwTsBy4BTj/iwc1GAiMBmjdvHkO5IiIiFUssYZ4NNIt63xRYH72Cu68HLgIws+rAEHffGdWGu68ys2nAiUTCvA2QZWYAVc0sy93bFD64u48FxgKkp6eXnVHtRUREyohYutnnAm3NrKWZpQCXAt96Kt3M6plZwb7uAp4Kltc2s0oF6wB9gKXuPtndG7l7mrunAfuKCnIRERE5siOGubvnErm//S6QCbzi7kvM7B4zGxysdjqwzMyWAw2Be4PlHYEMM1tI5MG4+wo9BS8iIiJHycrSfKxHYmY5QEkOflsP2FKC+wuTzqXsKS/nATqXsqi8nAfoXL5PC3evf6SV4irMS5qZZbh7eth1lASdS9lTXs4DdC5lUXk5D9C5lASNzS4iIhLnFOYiIiJxrqKH+diwCyhBOpeyp7ycB+hcyqLych6gczlqFfqeuYiISHlQ0a/MRURE4p7CXEREJM5VyDA3s6fMbLOZLQ67lqNhZs3MbKqZZZrZEjP7Rdg1FZeZVTazOWa2MDiXP4Vd09Eys0QzW2Bm/wm7lqNhZqvNbJGZfW5mGWHXU1xmVsvMXjOzL4P/M73Crqk4zKx98HdR8LXLzG4Ju67iMrNbg//zi83sRTOrHHZNxWFmvwjOYUkYfx8V8p65mfUF9hCZg71L2PUUl5k1Bhq7+3wzSwXmAT+Ox1H2LDJIfzV332NmycBM4BfuPivk0orNzG4D0oEa7n5+2PUUl5mtBtLdPa4H9TCzZ4AZ7j4+GJq6qrvvCLuuoxFMJb0OOMXdS3JArVJhZk2I/F/v5O77zewV4G13/1e4lf0wZtaFyPTgPYBDwDvA9e6+orRqqJBX5u4+HdgWdh1Hy903uPv84PVuIsPtFp6eNi54xJ7gbXLwFbe/aZpZU+A8YHzYtQiYWQ2gL/AkgLsfivcgD5wJrIzHII+SBFQxsySgKoUm8ooTHYFZ7r4vGAL9YyLTgZeaChnm5ZGZpRGZkW52uJUUX9At/TmwGXjf3eP2XIC/A78C8sMupAQ48J6ZzQumJI5HrYAc4Ong1sd4M6sWdlEl4FLgxbCLKC53Xwc8AKwBNgA73f29cKsqlsVAXzOra2ZVgUF8e7bRY05hXg4E086+Dtzi7rvCrqe43D3P3U8gMs1uj6DrKu6Y2fnAZnefF3YtJaSPu3cHBgI3Brep4k0S0B143N1PBPYCd4Zb0tEJbhUMBl4Nu5biMrPawAVAS+A4oJqZXR5uVT+cu2cCfwPeJ9LFvhDILc0aFOZxLri//DrwvLtPDLuekhB0f04DBoRcSnH1AQYH95pfAvqb2XPhllR87r4++HMz8AaR+4LxJhvIjurteY1IuMezgcB8d98UdiFH4SzgK3fPcffDwESgd8g1FYu7P+nu3d29L5HbuKV2vxwU5nEteGjsSSDT3R8Ku56jYWb1zaxW8LoKkf/kX4ZbVfG4+13u3tTd04h0g37k7nF3tQFgZtWChysJuqXPIdKlGFfcfSOw1szaB4vOBOLuQdFCLiOOu9gDa4CeZlY1+Hl2JpFnf+KOmTUI/mwOXEQp/90klebBygoze5HIHOz1zCwb+IO7PxluVcXSBxgOLAruNQPc7e5vh1hTcTUGngmezk0AXnH3uP5IVznREHgj8nOWJOAFd38n3JKK7Wbg+aB7ehVwVcj1FFtwX/ZsYFTYtRwNd59tZq8B84l0Sy8gfod2fd3M6gKHgRvdfXtpHrxCfjRNRESkPFE3u4iISJxTmIuIiMQ5hbmIiEicU5iLiIjEOYW5iIhInFOYi4iIxDmFuYiISJz7/5P4fwi/gWKcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k_values = list(range(1,10))\n",
    "k_overall_accuracies = []\n",
    "\n",
    "for k in k_values:\n",
    "    k_accuracies = cross_validate(k)\n",
    "    k_mean_accuracy = np.mean(k_accuracies)\n",
    "    k_overall_accuracies.append(k_mean_accuracy)\n",
    "    \n",
    "plt.figure(figsize=(8,4))\n",
    "plt.title(\"Mean Accuracy vs. k\")\n",
    "plt.plot(k_values, k_overall_accuracies)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Network With One Hidden Layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.model_selection import KFold\n",
    "\n",
    "# 50% Train / test validation\n",
    "def train_nn(neuron_arch, train_features, train_labels):\n",
    "    mlp = MLPClassifier(hidden_layer_sizes=neuron_arch)\n",
    "    mlp.fit(train_features, train_labels)\n",
    "    return mlp\n",
    "\n",
    "def test(model, test_features, test_labels):\n",
    "    predictions = model.predict(test_features)\n",
    "    train_test_df = pd.DataFrame()\n",
    "    train_test_df['correct_label'] = test_labels\n",
    "    train_test_df['predicted_label'] = predictions\n",
    "    overall_accuracy = sum(train_test_df[\"predicted_label\"] == train_test_df[\"correct_label\"])/len(train_test_df)    \n",
    "    return overall_accuracy\n",
    "\n",
    "def cross_validate(neuron_arch):\n",
    "    fold_accuracies = []\n",
    "    kf = KFold(n_splits = 4, random_state=2)\n",
    "    for train_index, test_index in kf.split(data):\n",
    "        train_features, test_features = data.loc[train_index], data.loc[test_index]\n",
    "        train_labels, test_labels = labels.loc[train_index], labels.loc[test_index]\n",
    "       \n",
    "        model = train_nn(neuron_arch, train_features, train_labels)\n",
    "        overall_accuracy = test(model, test_features, test_labels)\n",
    "        fold_accuracies.append(overall_accuracy)\n",
    "    return fold_accuracies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/srinify/anaconda/envs/dq/lib/python3.6/site-packages/sklearn/neural_network/multilayer_perceptron.py:564: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a16fd7dd8>]"
      ]
     },
     "execution_count": 339,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nn_one_neurons = [\n",
    "    (8,),\n",
    "    (16,),\n",
    "    (32,),\n",
    "    (64,),\n",
    "    (128,),\n",
    "    (256,)\n",
    "]\n",
    "nn_one_accuracies = []\n",
    "\n",
    "for n in nn_one_neurons:\n",
    "    nn_accuracies = cross_validate(n)\n",
    "    nn_mean_accuracy = np.mean(nn_accuracies)\n",
    "    nn_one_accuracies.append(nn_mean_accuracy)\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.title(\"Mean Accuracy vs. Neurons In Single Hidden Layer\")\n",
    "\n",
    "x = [i[0] for i in nn_one_neurons]\n",
    "plt.plot(x, nn_one_accuracies)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary:\n",
    "\n",
    "It looks like adding more neurons to the single hidden layer helped massively improved simple accuracy from approximately `86%` to approximately `94%`. Simple accuracy computes the number of correct classifications the model made, but doesn't tell us anything about false or true positives or false or true negatives.\n",
    "\n",
    "Given that k-nearest neighbors achieved approximately `96%` accuracy, there doesn't seem to be any advantages to using a single hidden layer neural network for this problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Network With Two Hidden Layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a1772b6a0>]"
      ]
     },
     "execution_count": 340,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nn_two_neurons = [\n",
    "    (64,64),\n",
    "    (128, 128),\n",
    "    (256, 256)\n",
    "]\n",
    "nn_two_accuracies = []\n",
    "\n",
    "for n in nn_two_neurons:\n",
    "    nn_accuracies = cross_validate(n)\n",
    "    nn_mean_accuracy = np.mean(nn_accuracies)\n",
    "    nn_two_accuracies.append(nn_mean_accuracy)\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.title(\"Mean Accuracy vs. Neurons In Two Hidden Layers\")\n",
    "\n",
    "x = [i[0] for i in nn_two_neurons]\n",
    "plt.plot(x, nn_two_accuracies)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.9382318732986884, 0.9510257362039098, 0.9532467211086364]"
      ]
     },
     "execution_count": 341,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nn_two_accuracies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary\n",
    "\n",
    "Using 2 hidden layers improved our simple accuracy to `95%`. While I'd traditionally be worried about overfitting, using 4-fold cross validation also gives me a bit more assurance that the model is generalizing to achieve the extra `1%` in simple accuracy over the single hidden layer networks we tried earlier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Network With Three Hidden Layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.model_selection import KFold\n",
    "\n",
    "# 50% Train / test validation\n",
    "def train_nn(neuron_arch, train_features, train_labels):\n",
    "    mlp = MLPClassifier(hidden_layer_sizes=neuron_arch)\n",
    "    mlp.fit(train_features, train_labels)\n",
    "    return mlp\n",
    "\n",
    "def test(model, test_features, test_labels):\n",
    "    predictions = model.predict(test_features)\n",
    "    train_test_df = pd.DataFrame()\n",
    "    train_test_df['correct_label'] = test_labels\n",
    "    train_test_df['predicted_label'] = predictions\n",
    "    overall_accuracy = sum(train_test_df[\"predicted_label\"] == train_test_df[\"correct_label\"])/len(train_test_df)    \n",
    "    return overall_accuracy\n",
    "\n",
    "def cross_validate_six(neuron_arch):\n",
    "    fold_accuracies = []\n",
    "    kf = KFold(n_splits = 6, random_state=2)\n",
    "    for train_index, test_index in kf.split(data):\n",
    "        train_features, test_features = data.loc[train_index], data.loc[test_index]\n",
    "        train_labels, test_labels = labels.loc[train_index], labels.loc[test_index]\n",
    "       \n",
    "        model = train_nn(neuron_arch, train_features, train_labels)\n",
    "        overall_accuracy = test(model, test_features, test_labels)\n",
    "        fold_accuracies.append(overall_accuracy)\n",
    "    return fold_accuracies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/srinify/anaconda/envs/dq/lib/python3.6/site-packages/sklearn/neural_network/multilayer_perceptron.py:564: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a16f03a58>]"
      ]
     },
     "execution_count": 343,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nn_three_neurons = [\n",
    "    (10, 10, 10),\n",
    "    (64, 64, 64),\n",
    "    (128, 128, 128)\n",
    "]\n",
    "\n",
    "nn_three_accuracies = []\n",
    "\n",
    "for n in nn_three_neurons:\n",
    "    nn_accuracies = cross_validate_six(n)\n",
    "    nn_mean_accuracy = np.mean(nn_accuracies)\n",
    "    nn_three_accuracies.append(nn_mean_accuracy)\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.title(\"Mean Accuracy vs. Neurons In Three Hidden Layers\")\n",
    "\n",
    "x = [i[0] for i in nn_three_neurons]\n",
    "plt.plot(x, nn_three_accuracies)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.8870401337792643, 0.947699739873653, 0.960479375696767]"
      ]
     },
     "execution_count": 324,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nn_three_accuracies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary\n",
    "\n",
    "Using 3 hidden layers improved our simple accuracy to `96%`, even with 6-fold cross validation. This seems to be in line with the research literature out there about deep neural networks for computer vision. Having more layers and more neurons tends to improve the network's performance."
   ]
  }
 ],
 "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}