mnist_cnn.ipynb

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    "colab": {
      "name": "Untitled8.ipynb",
      "version": "0.3.2",
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    {
      "cell_type": "code",
      "metadata": {
        "id": "JdxU1mDFL774",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Description: This program uses Convolutional Neural Networks (CNN) \n",
        "#              to classify handwritten digits as numbers 0 - 9"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lwMm2jdjMGox",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#import the libraries\n",
        "from keras.models import Sequential\n",
        "from keras.layers import Dense, Conv2D, Flatten\n",
        "from keras.datasets import mnist\n",
        "from keras.utils import to_categorical\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k2cVbRu3MceW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Load the data and split it into train and test sets\n",
        "(X_train,y_train), (X_test, y_test) = mnist.load_data()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fQj6JKgxMs4-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "5ae9b494-e1f5-4437-abf8-4c7c4945066d"
      },
      "source": [
        "#Get the image shape\n",
        "print(X_train.shape)#60000 rows of 28x28 pixel images with a depth=1 which signifies the images are gray scale (8 bit integers giving 256 possible shades of gray from black to white)\n",
        "print(X_test.shape)#10000 rows of 28x28 pixel images with a depth=1 which signifies the images are gray scale (8 bit integers giving 256 possible shades of gray from black to white)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(60000, 28, 28)\n",
            "(10000, 28, 28)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oqKxI7ffM6OT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "cd7d83df-11fc-426c-c1b4-9226000568af"
      },
      "source": [
        "#Take a look at the first image (at index=0) in the training data set as a numpy array, This shows the image as a series of pixel values\n",
        "X_train[0]"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3IJJFs1INMbg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "1ef37709-1a34-44b4-d197-0ed499407cb5"
      },
      "source": [
        "#Print the image label\n",
        "y_train[0]"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2RLcIND2NRq8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "outputId": "ff4a1276-7901-4d23-f724-2ea9c300732e"
      },
      "source": [
        "#Show the image as a picture\n",
        "plt.imshow(X_train[0])"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f906e73d5f8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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C+/mdZpq5ebyZpdUEx66ZZrwuIvyPSFpkZgvMbLqkT0vaUUAf72Bms7I3YmRmsyQtV/PN\nPrxD0prs9hpJ9xbYy+9plpmby80srYKPXdPNeO3uDf+RdIlG3/F/QdLfFtFDmb4+JOmx7OfJonuT\ndLtGnwYOa/S9kaskvU9St6TnJP23pPYm6u27kh6XtFujQessqLdlGn1Kv1vSruznkqKPXaKvQo4b\nn/ADguINPyAowg8ERfiBoAg/EBThB4Ii/EBQhB8IivADQf0/sEWOix6VKakAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Duw_KBUNNbcO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Reshape the data to fit the model\n",
        "X_train = X_train.reshape(60000, 28,28,1)\n",
        "X_test = X_test.reshape(10000, 28, 28, 1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lWgkkP9BNwWZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "db1b5f49-2f54-4a9e-9ce0-0e480d708084"
      },
      "source": [
        "#One-Hot Encode target column (Y-Data sets) : Convert the labels into a set of 10 numbers to input into the neural network\n",
        "y_train_one_hot = to_categorical(y_train)\n",
        "y_test_one_hot = to_categorical(y_test)\n",
        "\n",
        "#Print the new label\n",
        "print(y_train_one_hot[0])"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eyso3JIlOR5-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Build the CNN model\n",
        "model = Sequential()\n",
        "# add model layers\n",
        "model.add(Conv2D(64, kernel_size=3, activation='relu', input_shape=(28,28,1)))#Convolution layer to extract features from the input image, and create 64 channels of ReLu 3x3 convolved features (NOTE: Rectifier Linear Unit aka (ReLu))\n",
        "model.add(Conv2D(32, kernel_size=3, activation='relu'))#Convolution layer to extract features from the input image, and create 32 channels of ReLu 3x3 convolved features\n",
        "model.add(Flatten())#Flattening  layer makes the image a linear array or 1D Array or 1D Vector to feed into and connect with the neural network\n",
        "model.add(Dense(10, activation='softmax'))# The neural network last layer with 10 neurons and activation function softmax, 10 neurons used because we have 10 labels"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fhRjMnImO43w",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 107
        },
        "outputId": "5771522d-ec91-47a8-9bad-ae40c40ae2c2"
      },
      "source": [
        "#Compile the model\n",
        "model.compile(optimizer='adam', loss='categorical_crossentropy', metrics=['accuracy'])"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "W0712 17:30:11.366239 140259247986560 deprecation_wrapper.py:119] From /usr/local/lib/python3.6/dist-packages/keras/optimizers.py:790: The name tf.train.Optimizer is deprecated. Please use tf.compat.v1.train.Optimizer instead.\n",
            "\n",
            "W0712 17:30:11.403307 140259247986560 deprecation_wrapper.py:119] From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:3295: The name tf.log is deprecated. Please use tf.math.log instead.\n",
            "\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "clc7qn8CPEwm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 245
        },
        "outputId": "aa414e52-5a5c-44ae-e13b-041fbb412374"
      },
      "source": [
        "#Train the model\n",
        "#Batch: Total number of training examples present in a single batch (None = default 32)\n",
        "#Epoch:The number of iterations when an ENTIRE dataset is passed forward and backward through the neural network only ONCE.\n",
        "#Fit: Another word for train\n",
        "hist = model.fit(X_train, y_train_one_hot, validation_data=(X_test, y_test_one_hot), epochs=3)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "W0712 17:31:56.019908 140259247986560 deprecation.py:323] From /usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/math_grad.py:1250: add_dispatch_support.<locals>.wrapper (from tensorflow.python.ops.array_ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Use tf.where in 2.0, which has the same broadcast rule as np.where\n",
            "W0712 17:31:56.088547 140259247986560 deprecation_wrapper.py:119] From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:986: The name tf.assign_add is deprecated. Please use tf.compat.v1.assign_add instead.\n",
            "\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/3\n",
            "60000/60000 [==============================] - 200s 3ms/step - loss: 1.4287 - acc: 0.8797 - val_loss: 0.0900 - val_acc: 0.9715\n",
            "Epoch 2/3\n",
            "60000/60000 [==============================] - 200s 3ms/step - loss: 0.0659 - acc: 0.9799 - val_loss: 0.0762 - val_acc: 0.9758\n",
            "Epoch 3/3\n",
            "60000/60000 [==============================] - 201s 3ms/step - loss: 0.0431 - acc: 0.9859 - val_loss: 0.0783 - val_acc: 0.9768\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8jXr3pZ2R9nC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "6b2e9737-4e25-471b-b39f-23dee79863c1"
      },
      "source": [
        "#Visualize the models accuracy\n",
        "plt.plot(hist.history['acc'])\n",
        "plt.plot(hist.history['val_acc'])\n",
        "plt.title('Model Accuracy')\n",
        "plt.ylabel('Accuracy')\n",
        "plt.xlabel('Epoch')\n",
        "plt.legend(['Train', 'Val'], loc='upper left')\n",
        "plt.show()"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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yTAp7tudXpx+qZ1OItBKxjFm8SOTqJ4gklwHAk/EMSlqmsk07GFtUTIfsDP46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\nSUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TiVplNxISkR6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 225
        },
        "outputId": "c5b739a2-6e11-44f7-84c4-ac0a82bcde79"
      },
      "source": [
        "#Show predictions as probabilites for the first 4 images in the test set\n",
        "predictions = model.predict(X_test[:4])\n",
        "predictions"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.34177355e-07, 2.48542209e-09, 8.91900864e-09, 9.77532750e-07,\n",
              "        6.71991271e-13, 5.89210902e-11, 6.14161825e-13, 9.99998927e-01,\n",
              "        3.00458569e-09, 4.02709599e-09],\n",
              "       [6.14337750e-06, 1.04692994e-07, 9.99898434e-01, 5.43854867e-06,\n",
              "        4.74248252e-10, 7.02491190e-11, 8.21188223e-05, 1.48188725e-10,\n",
              "        7.57780845e-06, 1.40203557e-10],\n",
              "       [2.35221000e-06, 9.98755455e-01, 5.15569263e-06, 1.32248923e-09,\n",
              "        8.23073151e-06, 4.68670260e-06, 1.06355637e-05, 5.41945262e-08,\n",
              "        1.21341727e-03, 6.27768459e-09],\n",
              "       [9.99935389e-01, 4.53953021e-11, 1.37671577e-07, 1.21291833e-12,\n",
              "        2.59405852e-09, 1.30445734e-08, 6.43264575e-05, 4.99175978e-11,\n",
              "        6.86783475e-09, 1.68532097e-07]], dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6K1QJ_zITMI_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "20c2c2c2-e5b5-4a1a-ab90-fc975f69ce95"
      },
      "source": [
        "#Print our predicitons as number labels for the first 4 images\n",
        "print( np.argmax(predictions, axis=1))\n",
        "#Print the actual labels\n",
        "print(y_test[:4])"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[7 2 1 0]\n",
            "[7 2 1 0]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bJwj9AmdTloe",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "360dc444-fce7-4101-ad2d-7144f6c57be4"
      },
      "source": [
        "#Show the first 4 images as pictures\n",
        "for i in range(0,4):\n",
        "  image = X_test[i]\n",
        "  image = np.array(image, dtype='float')\n",
        "  pixels = image.reshape((28,28))\n",
        "  plt.imshow(pixels, cmap='gray')\n",
        "  plt.show()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWv8QfFP9AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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FAfaK+yOWZZUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}