machine-learning/classification/logistic-regression-implementation-using-tensorflow-and-keras.ipynb

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  "metadata": {
    "colab": {
      "name": "Logistic Regression Implementation Using TensorFlow and Keras",
      "provenance": [],
      "authorship_tag": "ABX9TyNDCbHgOIFkNb5/oa79vRfE"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oRTwweeen8Mu"
      },
      "source": [
        "# **Logistic Regression Implementation Using TensorFlow and Keras**\n",
        "*By Carlos Santiago Bañón*\n",
        "\n",
        "* **Year:** 2020\n",
        "* **Technologies:** Python, NumPy, Matplotlib, TensorFlow, Keras, Scikit-Learn\n",
        "* **Areas:** Machine Learning, Classification\n",
        "* **Keywords:** `binary-classification`, `classification`, `deep-learning`, `logistic-regression`, `machine-learning`\n",
        "* **Description:** This notebook presents an implementation of logistic regression using TensorFlow and Keras."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bfTSzJdhoU0Z"
      },
      "source": [
        "## 1. Import Statements\n",
        "---"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6jxE_o4gogyV"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.model_selection import train_test_split"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rXvoyoOHonoQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8ee77363-6b65-44c9-a441-1232df3ea474"
      },
      "source": [
        "%tensorflow_version 2.x\n",
        "import tensorflow as tf\n",
        "print(tf.__version__)"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "2.4.1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2RYKumP1o4QS"
      },
      "source": [
        "## 2. Random Data Generation\n",
        "---\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wcj_NYGFo8Ec"
      },
      "source": [
        "To generate random data for our model, we must first specify the parameters used in our function."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n6mDR_zzpKU2"
      },
      "source": [
        "# Define the parameters.\n",
        "weight = 20\n",
        "bias = 10\n",
        "mu = 20\n",
        "sigma = 6\n",
        "m = 1000"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M5xKXxOzpVtG"
      },
      "source": [
        "The data for implementing logistic regression is then generated randomly with two features, $x_1$ and $x_2$. This function returns a `data` array of shape $(m, 2)$ and a `labels` array of shape $(m, 1)$.\n",
        "\n",
        "The data is generated as follows:\n",
        "\n",
        "*   Feature $x_1$: Chosen uniformly at random in the interval $[0, 1)$.\n",
        "*   Feature $x_2$: Chosen with the formula $x_2 = w * x_1 + b - 1^c * n$, where the \"noise\" `n` is chosen according to the normal distribution with mean $\\mu$ and standard deviation $\\sigma$.\n",
        "*   Class Labels: Choose $c = 0$ with probability $\\frac{1}{2}$ or $c = 1$ with probability $\\frac{1}{2}$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A_mYSW2wp4Eo"
      },
      "source": [
        "def get_random_data(w, b, mu, sigma, m):\n",
        "  \"\"\"\n",
        "  Generate random data.\n",
        "\n",
        "  :w: the weigths.\n",
        "  :b: the bias.\n",
        "  :mu: the mean.\n",
        "  :sigma: the standard deviation.\n",
        "  :m: the number of data points.\n",
        "  \"\"\"\n",
        "\n",
        "  data = np.empty([m, 2])\n",
        "  labels = np.empty([m, 1], dtype=int)\n",
        "\n",
        "  for i in range(m):\n",
        "\n",
        "    # Choose either 0 or 1 for the label.\n",
        "    labels[i] = np.random.choice([0, 1], p=[0.5, 0.5])\n",
        "\n",
        "    # Set the first feature.\n",
        "    data[i, 0] = np.random.default_rng().uniform(0, 1)\n",
        "\n",
        "    # Set the second feature.\n",
        "    n = np.random.default_rng().normal(mu, sigma)\n",
        "    data[i, 1] = w * data[i, 0] + b + (-1) ** labels[i] * n\n",
        "\n",
        "  return data, labels"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4_O-0wOyqBBS"
      },
      "source": [
        "data, labels = get_random_data(weight, bias, mu, sigma, m)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gt-_D5u7qFKp"
      },
      "source": [
        "Then, we can use Matplotlib to display the data generated by our function."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "71MWQx1pqHmo"
      },
      "source": [
        "def display_random_data(data, labels):\n",
        "  \"\"\"\n",
        "  Display the data on a 2-D plot.\n",
        "\n",
        "  :data: the data to be visualized.\n",
        "  :labels: the labels used for coloring.\n",
        "  \"\"\"\n",
        "\n",
        "  # Define the classes and colors.\n",
        "  classes = ['1', '0']\n",
        "  colors = ['red', 'blue']\n",
        "\n",
        "  # Generate the scatter plot.\n",
        "  scatter = plt.scatter(data[:, 0], data[:, 1], c=labels, cmap=matplotlib.colors.ListedColormap(colors))\n",
        "  \n",
        "  # Format the title and axis labels.\n",
        "  plt.title('Random Data for Logistic Regression', fontsize=14)\n",
        "  plt.xlabel(r'$ x_1 $', fontsize=14)\n",
        "  plt.ylabel(r'$ x_2 $', fontsize=14)\n",
        "\n",
        "  # Include a legend.\n",
        "  plt.legend(handles=scatter.legend_elements()[0], labels=classes, fontsize=8)\n",
        "\n",
        "  plt.show()"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VilSZSVRqda5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "outputId": "2a27f9ff-f803-4485-acc1-126b11694def"
      },
      "source": [
        "display_random_data(data, labels)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KcDqE1OvqjMp"
      },
      "source": [
        "## 3. Split the Data into Training and Test Sets\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X_CSy4qBqn_n"
      },
      "source": [
        "Once we have our data generated, we need to split it into training and test sets. Here, we use 80% of our data for training, and the remaining 20% for testing."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h3xWq5dxqvBv"
      },
      "source": [
        "# Split the data into training and test sets.\n",
        "data_train, data_test, labels_train, labels_test = train_test_split(data, labels, train_size=0.8)"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SedRzdFcq0uK"
      },
      "source": [
        "## 4. Logistic Regression\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "si4PZrN3q8aY"
      },
      "source": [
        "Now we're ready to implement logistic regression using TensorFlow and Keras. A prediction model is built and trained, and is then displayed with the original data. The loss function used is binary cross-entropy loss."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9XNZyrHyrRJa"
      },
      "source": [
        "We first have to build our model using *Keras*. Here, we use a dense layer with sigmoid activation for our model."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "45856bYGrY0J"
      },
      "source": [
        "def build_model():\n",
        "  \"\"\"\n",
        "  Build the logistic regression model.\n",
        "  \"\"\"\n",
        "\n",
        "  # Build the model.\n",
        "  model = tf.keras.Sequential()\n",
        "\n",
        "  # Add a dense layer with sigmoid activation.\n",
        "  model.add(tf.keras.layers.Dense(1, activation='sigmoid', input_shape=(2,)))\n",
        "\n",
        "  return model"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "op5GW6K1rZQ4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "46e0d32b-4245-4db0-fb75-afb2eecd768e"
      },
      "source": [
        "model = build_model()\n",
        "model.summary()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"sequential\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "dense (Dense)                (None, 1)                 3         \n",
            "=================================================================\n",
            "Total params: 3\n",
            "Trainable params: 3\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O9YTUB41rhpU"
      },
      "source": [
        "Then, we can compile our model using binary cross-entropy loss as our loss function."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fbsrSauJrojd"
      },
      "source": [
        "def compile_model(model):\n",
        "  \"\"\"\n",
        "  Compile the logistic regression model.\n",
        "  \"\"\"\n",
        "\n",
        "  model.compile(optimizer='rmsprop',\n",
        "                loss='binary_crossentropy',\n",
        "                metrics=['accuracy'])"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "359NysWirsMr"
      },
      "source": [
        "compile_model(model)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G-lInj8drsz7"
      },
      "source": [
        "After compiling the model, we are ready to train it using our data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2aWdsXRVrzgx",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eef58109-838a-4b86-8a16-b29012e0e4b7"
      },
      "source": [
        "history = model.fit(data_train, labels_train, epochs=100)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 1.2317 - accuracy: 0.7278\n",
            "Epoch 2/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 1.1288 - accuracy: 0.7393\n",
            "Epoch 3/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 1.0931 - accuracy: 0.7401\n",
            "Epoch 4/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 1.0195 - accuracy: 0.7366\n",
            "Epoch 5/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.9464 - accuracy: 0.7489\n",
            "Epoch 6/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 1.0493 - accuracy: 0.7285\n",
            "Epoch 7/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.8230 - accuracy: 0.7570\n",
            "Epoch 8/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.8592 - accuracy: 0.7374\n",
            "Epoch 9/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.7867 - accuracy: 0.7540\n",
            "Epoch 10/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.7712 - accuracy: 0.7485\n",
            "Epoch 11/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.7718 - accuracy: 0.7338\n",
            "Epoch 12/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.6144 - accuracy: 0.7818\n",
            "Epoch 13/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.5518 - accuracy: 0.7888\n",
            "Epoch 14/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.5923 - accuracy: 0.7726\n",
            "Epoch 15/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.5177 - accuracy: 0.7713\n",
            "Epoch 16/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.4728 - accuracy: 0.7649\n",
            "Epoch 17/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.4370 - accuracy: 0.7854\n",
            "Epoch 18/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.4129 - accuracy: 0.7951\n",
            "Epoch 19/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.3996 - accuracy: 0.8051\n",
            "Epoch 20/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.3296 - accuracy: 0.8181\n",
            "Epoch 21/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.3148 - accuracy: 0.8364\n",
            "Epoch 22/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2996 - accuracy: 0.8455\n",
            "Epoch 23/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2752 - accuracy: 0.8528\n",
            "Epoch 24/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2678 - accuracy: 0.8833\n",
            "Epoch 25/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.2790 - accuracy: 0.8788\n",
            "Epoch 26/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2466 - accuracy: 0.8953\n",
            "Epoch 27/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2629 - accuracy: 0.8977\n",
            "Epoch 28/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2292 - accuracy: 0.9221\n",
            "Epoch 29/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2295 - accuracy: 0.9252\n",
            "Epoch 30/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2268 - accuracy: 0.9268\n",
            "Epoch 31/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2273 - accuracy: 0.9209\n",
            "Epoch 32/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2172 - accuracy: 0.9312\n",
            "Epoch 33/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2355 - accuracy: 0.9233\n",
            "Epoch 34/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.2381 - accuracy: 0.9237\n",
            "Epoch 35/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1872 - accuracy: 0.9521\n",
            "Epoch 36/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.2230 - accuracy: 0.9263\n",
            "Epoch 37/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1856 - accuracy: 0.9531\n",
            "Epoch 38/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1942 - accuracy: 0.9588\n",
            "Epoch 39/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1973 - accuracy: 0.9503\n",
            "Epoch 40/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1754 - accuracy: 0.9671\n",
            "Epoch 41/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1672 - accuracy: 0.9721\n",
            "Epoch 42/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1688 - accuracy: 0.9755\n",
            "Epoch 43/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1717 - accuracy: 0.9711\n",
            "Epoch 44/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1617 - accuracy: 0.9792\n",
            "Epoch 45/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1628 - accuracy: 0.9734\n",
            "Epoch 46/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1622 - accuracy: 0.9798\n",
            "Epoch 47/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.1625 - accuracy: 0.9736\n",
            "Epoch 48/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1637 - accuracy: 0.9687\n",
            "Epoch 49/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1510 - accuracy: 0.9737\n",
            "Epoch 50/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1413 - accuracy: 0.9755\n",
            "Epoch 51/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1500 - accuracy: 0.9762\n",
            "Epoch 52/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1334 - accuracy: 0.9816\n",
            "Epoch 53/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1243 - accuracy: 0.9814\n",
            "Epoch 54/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1289 - accuracy: 0.9754\n",
            "Epoch 55/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1369 - accuracy: 0.9795\n",
            "Epoch 56/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1235 - accuracy: 0.9872\n",
            "Epoch 57/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1199 - accuracy: 0.9859\n",
            "Epoch 58/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1324 - accuracy: 0.9887\n",
            "Epoch 59/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1284 - accuracy: 0.9829\n",
            "Epoch 60/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1182 - accuracy: 0.9893\n",
            "Epoch 61/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1102 - accuracy: 0.9911\n",
            "Epoch 62/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1142 - accuracy: 0.9894\n",
            "Epoch 63/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1065 - accuracy: 0.9897\n",
            "Epoch 64/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1103 - accuracy: 0.9932\n",
            "Epoch 65/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1059 - accuracy: 0.9897\n",
            "Epoch 66/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0944 - accuracy: 0.9938\n",
            "Epoch 67/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.1059 - accuracy: 0.9894\n",
            "Epoch 68/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0968 - accuracy: 0.9904\n",
            "Epoch 69/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0879 - accuracy: 0.9952\n",
            "Epoch 70/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0853 - accuracy: 0.9952\n",
            "Epoch 71/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0903 - accuracy: 0.9921\n",
            "Epoch 72/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0851 - accuracy: 0.9926\n",
            "Epoch 73/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0882 - accuracy: 0.9923\n",
            "Epoch 74/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0755 - accuracy: 0.9966\n",
            "Epoch 75/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0763 - accuracy: 0.9956\n",
            "Epoch 76/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0753 - accuracy: 0.9914\n",
            "Epoch 77/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0813 - accuracy: 0.9931\n",
            "Epoch 78/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0727 - accuracy: 0.9977\n",
            "Epoch 79/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0730 - accuracy: 0.9949\n",
            "Epoch 80/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0709 - accuracy: 0.9966\n",
            "Epoch 81/100\n",
            "25/25 [==============================] - 0s 2ms/step - loss: 0.0765 - accuracy: 0.9953\n",
            "Epoch 82/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0725 - accuracy: 0.9915\n",
            "Epoch 83/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0675 - accuracy: 0.9909\n",
            "Epoch 84/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0664 - accuracy: 0.9963\n",
            "Epoch 85/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0625 - accuracy: 0.9941\n",
            "Epoch 86/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0621 - accuracy: 0.9956\n",
            "Epoch 87/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0633 - accuracy: 0.9966\n",
            "Epoch 88/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0582 - accuracy: 0.9971\n",
            "Epoch 89/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0591 - accuracy: 0.9962\n",
            "Epoch 90/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0603 - accuracy: 0.9929\n",
            "Epoch 91/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0591 - accuracy: 0.9912\n",
            "Epoch 92/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0556 - accuracy: 0.9958\n",
            "Epoch 93/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0536 - accuracy: 0.9966\n",
            "Epoch 94/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0495 - accuracy: 0.9984\n",
            "Epoch 95/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0574 - accuracy: 0.9928\n",
            "Epoch 96/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0515 - accuracy: 0.9975\n",
            "Epoch 97/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0527 - accuracy: 0.9964\n",
            "Epoch 98/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0481 - accuracy: 0.9973\n",
            "Epoch 99/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0471 - accuracy: 0.9957\n",
            "Epoch 100/100\n",
            "25/25 [==============================] - 0s 1ms/step - loss: 0.0535 - accuracy: 0.9895\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DldqbXjgr8Hw"
      },
      "source": [
        "We then need to extract the weight, or $\\theta$, values produced by our model. Here, `get_weights()` is used to get the weights and bias into an array."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u3aF_G4lsHT6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9c648981-6944-4a86-cfe9-516bd6361838"
      },
      "source": [
        "weights = model.get_weights()\n",
        "\n",
        "w1 = weights[0][0][0]\n",
        "w2 = weights[0][1][0]\n",
        "b = weights[1][0]\n",
        "\n",
        "print(w1, w2, b)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1.9290528 -0.19694744 2.3408415\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "80Q8n8J6sUeI"
      },
      "source": [
        "Using the testing data and labels, the model can then be analyzed to measure the total loss and accuracy."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tuI1RWvZsbEZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b197187c-d2cd-4566-f837-dc0c6a7a112d"
      },
      "source": [
        "results = model.evaluate(data_test, labels_test)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "7/7 [==============================] - 0s 2ms/step - loss: 0.0529 - accuracy: 0.9900\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S0SoC7HkshAm"
      },
      "source": [
        "Once our model is trained, we can visualize it with the original data. We can use the model to get a new separating line. To it, we use the function `get_separating_line()`, which sets $w_1x_1 + w_2x_2 + b = 0$. From there, it simply solves for $x_2$ to get the sepatating line when the sigmoid function is $1/2$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oC54q8W8sv9F"
      },
      "source": [
        "def get_separating_line(w1, w2, b):\n",
        "  \"\"\"\n",
        "  Generate a separating line based on the weights.\n",
        "\n",
        "  :w1: the first weight.\n",
        "  :w2: the second weight.\n",
        "  :b: the bias.\n",
        "  \"\"\"\n",
        "\n",
        "  return -(w1 * 0.5 + b) / w2"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u4R0JRHAs056"
      },
      "source": [
        "def display_model_data(data, labels):\n",
        "  \"\"\"\n",
        "  Display the data on a 2-D plot.\n",
        "\n",
        "  :data: the data to be visualized.\n",
        "  :labels: the labels used for coloring.\n",
        "  \"\"\"\n",
        "\n",
        "  # Define the classes and colors.\n",
        "  classes = ['0', '1']\n",
        "  colors = ['red', 'blue']\n",
        "\n",
        "  # Generate the scatter plot.\n",
        "  scatter = plt.scatter(data[:, 0], data[:, 1], c=labels, cmap=matplotlib.colors.ListedColormap(colors))\n",
        "  \n",
        "  # Format the title and axis labels\n",
        "  plt.title('Trained Model', fontsize=14)\n",
        "  plt.xlabel('$ x_1 $', fontsize=14)\n",
        "  plt.ylabel('$ x_2 $', fontsize=14)\n",
        "\n",
        "  # Inlcude a legend.\n",
        "  plt.legend(handles=scatter.legend_elements()[0], labels=classes, fontsize=8)\n",
        "\n",
        "  # Plot the true line used to generate the data.\n",
        "  x = np.linspace(0,1,100)\n",
        "  y = weight * x + bias\n",
        "  plt.plot(x, y)\n",
        "\n",
        "  # Plot the separating line of the trained model.\n",
        "  separating_line = get_separating_line(w1, w2, b)\n",
        "  print(separating_line)\n",
        "  y = separating_line * x + b\n",
        "  plt.plot(x, y)\n",
        "\n",
        "  plt.show()"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-GiAL8Abs7z2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 318
        },
        "outputId": "0c87bea2-c06f-41fc-fc3d-2210289fc29c"
      },
      "source": [
        "display_model_data(data, labels)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "16.782995189726137\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a3oNpvwktEvX"
      },
      "source": [
        "Finally, we can visualize the model with a heatmap, using the original weights and bias and the sigmoid function.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HAh88WFUtKLg"
      },
      "source": [
        "def sigmoid(x):\n",
        "  \"\"\"\n",
        "  Compute the sigmoid.\n",
        "\n",
        "  :x: the original value.\n",
        "  \"\"\"\n",
        "  \n",
        "  return 1 / (1 + np.exp(-x))"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i-WxVM2etMMp"
      },
      "source": [
        "def display_heatmap(w1, w2, b):\n",
        "  \"\"\"\n",
        "  Display the data on a 2-D heatmap.\n",
        "\n",
        "  :w1: the first weight.\n",
        "  :w2: the second weight.\n",
        "  :b: the bias.\n",
        "  \"\"\"\n",
        "\n",
        "  # Get the data for the heatmap.\n",
        "  x1, x2 = np.meshgrid(np.linspace(0, 1, 200), np.linspace(-20, 60, 200))\n",
        "  z = sigmoid(w1 * x1 + w2 * x2 + b)\n",
        "\n",
        "  # Set the bounds for z.\n",
        "  z = z[:-1, :-1]\n",
        "  z_min, z_max = -np.abs(z).max(), np.abs(z).max()\n",
        "\n",
        "  # Generate the heatmap.\n",
        "  fig, ax = plt.subplots()\n",
        "  c = ax.pcolormesh(x1, x2, z, cmap='RdBu', vmin=0, vmax=1)\n",
        "  ax.set_title('Trained Model (Heatmap)', fontsize=14)\n",
        "  fig.colorbar(c, ax=ax)\n",
        "  plt.xlabel(r'$ x_1 $', fontsize=14)\n",
        "  plt.ylabel(r'$ x_2 $', fontsize=14)\n",
        "  \n",
        "  # Set the limits of the plot.\n",
        "  ax.axis([x1.min(), x1.max(), x2.min(), x2.max()])\n",
        "\n",
        "  plt.show()"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lQNx6GQrtQ7H",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "outputId": "27ff8694-9f4b-4413-94c5-41ce618c886e"
      },
      "source": [
        "display_heatmap(w1, w2, b)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}