{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Working With Image Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'target_names', 'images', 'DESCR'])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits_data.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels = pd.Series(digits_data['target'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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",
       "      <td>0</td>\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",
       "      <td>0.0</td>\n",
       "      <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": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame(digits_data['data'])\n",
    "data.head(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7ffb8fa43250>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7ffb8ea4d690>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9677233358079684"
      ]
     },
     "execution_count": 7,
     "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": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7ffb8eb2b250>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn.neural_network import MLPClassifier\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": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: 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 0x7ffb8c136190>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7ffb8deee050>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.9398861667903984, 0.9571492204899779, 0.9515837663944569]"
      ]
     },
     "execution_count": 14,
     "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": 15,
   "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": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (200) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/home/yunoac/anaconda3/lib/python3.7/site-packages/sklearn/neural_network/multilayer_perceptron.py:566: 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 0x7ffb8c4f7550>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.9154124860646601, 0.950479375696767, 0.9582552954292085]"
      ]
     },
     "execution_count": 17,
     "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}