logistic_regression_model.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/yiyichanmyae/nlp/blob/master/logistic_regression_model.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_BcxChg5N6tT"
      },
      "source": [
        "# Visualizing tweets and the Logistic Regression model\n",
        "\n",
        "**Objectives:** Visualize and interpret the logistic regression model\n",
        "\n",
        "**Steps:**\n",
        "* Plot tweets in a scatter plot using their positive and negative sums.\n",
        "* Plot the output of the logistic regression model in the same plot as a solid line"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pYxQZDKYN6tV"
      },
      "source": [
        "## Import the required libraries\n",
        "\n",
        "We will be using [*NLTK*](http://www.nltk.org/howto/twitter.html), an opensource NLP library, for collecting, handling, and processing Twitter data. In this lab, we will use the example dataset that comes alongside with NLTK. This dataset has been manually annotated and serves to establish baselines for models quickly. \n",
        "\n",
        "So, to start, let's import the required libraries. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PzkYQrnvN6tW",
        "outputId": "924bf866-7be4-487c-8099-c06c33da7afc"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "[nltk_data] Downloading package twitter_samples to\n",
            "[nltk_data]     /home/jovyan/nltk_data...\n",
            "[nltk_data]   Unzipping corpora/twitter_samples.zip.\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "execution_count": 1,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import nltk                         # NLP toolbox\n",
        "from os import getcwd\n",
        "import pandas as pd                 # Library for Dataframes \n",
        "from nltk.corpus import twitter_samples \n",
        "import matplotlib.pyplot as plt     # Library for visualization\n",
        "import numpy as np                  # Library for math functions\n",
        "\n",
        "from utils import process_tweet, build_freqs # Our functions for NLP\n",
        "\n",
        "nltk.download('twitter_samples')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lzbF-UegN6tY"
      },
      "source": [
        "## Load the NLTK sample dataset\n",
        "\n",
        "To complete this lab, you need the sample dataset of the previous lab. Here, we assume the files are already available, and we only need to load into Python lists."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gTAHQXIqN6tY",
        "outputId": "d0e5b0e5-0c36-4db8-8c9c-62fb6890e5e5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Number of tweets:  8000\n"
          ]
        }
      ],
      "source": [
        "# select the set of positive and negative tweets\n",
        "all_positive_tweets = twitter_samples.strings('positive_tweets.json')\n",
        "all_negative_tweets = twitter_samples.strings('negative_tweets.json')\n",
        "\n",
        "tweets = all_positive_tweets + all_negative_tweets ## Concatenate the lists. \n",
        "labels = np.append(np.ones((len(all_positive_tweets),1)), np.zeros((len(all_negative_tweets),1)), axis = 0)\n",
        "\n",
        "# split the data into two pieces, one for training and one for testing (validation set) \n",
        "train_pos  = all_positive_tweets[:4000]\n",
        "train_neg  = all_negative_tweets[:4000]\n",
        "\n",
        "train_x = train_pos + train_neg \n",
        "\n",
        "print(\"Number of tweets: \", len(train_x))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V2tH0D-mN6tZ"
      },
      "source": [
        "# Load the extracted features\n",
        "\n",
        "Part of this week's assignment is the creation of the numerical features needed for the Logistic regression model. In order not to interfere with it, we have previously calculated and stored these features in a CSV file for the entire training set.\n",
        "\n",
        "So, please load these features created for the tweets sample. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bDREYzoeN6tZ",
        "outputId": "30f8ee2a-eadd-45d0-d859-ab315e8790b5"
      },
      "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>bias</th>\n",
              "      <th>positive</th>\n",
              "      <th>negative</th>\n",
              "      <th>sentiment</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1.0</td>\n",
              "      <td>3020.0</td>\n",
              "      <td>61.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1.0</td>\n",
              "      <td>3573.0</td>\n",
              "      <td>444.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1.0</td>\n",
              "      <td>3005.0</td>\n",
              "      <td>115.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1.0</td>\n",
              "      <td>2862.0</td>\n",
              "      <td>4.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1.0</td>\n",
              "      <td>3119.0</td>\n",
              "      <td>225.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1.0</td>\n",
              "      <td>2955.0</td>\n",
              "      <td>119.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>1.0</td>\n",
              "      <td>3934.0</td>\n",
              "      <td>538.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>1.0</td>\n",
              "      <td>3162.0</td>\n",
              "      <td>276.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>1.0</td>\n",
              "      <td>628.0</td>\n",
              "      <td>189.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>1.0</td>\n",
              "      <td>264.0</td>\n",
              "      <td>112.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   bias  positive  negative  sentiment\n",
              "0   1.0    3020.0      61.0        1.0\n",
              "1   1.0    3573.0     444.0        1.0\n",
              "2   1.0    3005.0     115.0        1.0\n",
              "3   1.0    2862.0       4.0        1.0\n",
              "4   1.0    3119.0     225.0        1.0\n",
              "5   1.0    2955.0     119.0        1.0\n",
              "6   1.0    3934.0     538.0        1.0\n",
              "7   1.0    3162.0     276.0        1.0\n",
              "8   1.0     628.0     189.0        1.0\n",
              "9   1.0     264.0     112.0        1.0"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data = pd.read_csv('./data/logistic_features.csv'); # Load a 3 columns csv file using pandas function\n",
        "data.head(10) # Print the first 10 data entries"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rtVa2LrPN6tZ"
      },
      "source": [
        "Now let us get rid of the data frame to keep only Numpy arrays."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZmYmvu7TN6tZ",
        "outputId": "2a822c0e-2e36-4e80-d573-3fa55e98cf33"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(8000, 3)\n",
            "[[1.000e+00 3.020e+03 6.100e+01]\n",
            " [1.000e+00 3.573e+03 4.440e+02]\n",
            " [1.000e+00 3.005e+03 1.150e+02]\n",
            " ...\n",
            " [1.000e+00 1.440e+02 7.830e+02]\n",
            " [1.000e+00 2.050e+02 3.890e+03]\n",
            " [1.000e+00 1.890e+02 3.974e+03]]\n"
          ]
        }
      ],
      "source": [
        "# Each feature is labeled as bias, positive and negative\n",
        "X = data[['bias', 'positive', 'negative']].values # Get only the numerical values of the dataframe\n",
        "Y = data['sentiment'].values; # Put in Y the corresponding labels or sentiments\n",
        "\n",
        "print(X.shape) # Print the shape of the X part\n",
        "print(X) # Print some rows of X"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nLv9P10UN6ta"
      },
      "source": [
        "## Load a pretrained Logistic Regression model\n",
        "\n",
        "A Logistic regression model must be trained in the other lab. The next cell contains the resulting model from such training. Notice that a list of 3 numeric values represents the whole model, that we have called _theta_ $\\theta$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "64w07dxMN6ta"
      },
      "outputs": [],
      "source": [
        "theta = [6.03518871e-08, 5.38184972e-04, -5.58300168e-04]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "llgkIRk7N6tb"
      },
      "source": [
        "## Plot the samples in a scatter plot\n",
        "\n",
        "The vector theta represents a plane that split our feature space into two parts. Samples located over that plane are considered positive, and samples located under that plane are considered negative. Remember that we have a 3D feature space, i.e., each tweet is represented as a vector comprised of three values: `[bias, positive_sum, negative_sum]`, always having `bias = 1`. \n",
        "\n",
        "If we ignore the bias term, we can plot each tweet in a cartesian plane, using `positive_sum` and `negative_sum`. In the cell below, we do precisely this. Additionally, we color each tweet, depending on its class. Positive tweets will be green and negative tweets will be red."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mEqsTFsFN6tb",
        "outputId": "189ae2cc-06cf-47d9-98df-62127ea5a4ac"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Negative')"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot the samples using columns 1 and 2 of the matrix\n",
        "fig, ax = plt.subplots(figsize = (8, 8))\n",
        "\n",
        "colors = ['red', 'green']\n",
        "\n",
        "# Color based on the sentiment Y\n",
        "ax.scatter(X[:,1], X[:,2], c=[colors[int(k)] for k in Y], s = 0.1)  # Plot a dot for each pair of words\n",
        "plt.xlabel(\"Positive\")\n",
        "plt.ylabel(\"Negative\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "st8MHq2wN6tb"
      },
      "source": [
        "From the plot, it is evident that the features that we have chosen to represent tweets as numerical vectors allow an almost perfect separation between positive and negative tweets. So you can expect a very high accuracy for this model! \n",
        "\n",
        "## Plot the model alongside the data\n",
        "\n",
        "We will draw a gray line to show the cutoff between the positive and negative regions. In other words, the gray line marks the line where $$ z = \\theta * x = 0.$$\n",
        "To draw this line, we have to solve the above equation in terms of one of the independent variables.\n",
        "\n",
        "$$ z = \\theta * x = 0$$\n",
        "$$ x = [1, pos, neg] $$\n",
        "$$ z(\\theta, x) = \\theta_0+ \\theta_1 * pos + \\theta_2 * neg = 0 $$\n",
        "$$ neg = (-\\theta_0 - \\theta_1 * pos) / \\theta_2 $$\n",
        "\n",
        "The red and green lines that point in the direction of the corresponding sentiment are calculated using a perpendicular line to the separation line calculated in the previous equations (neg function). It must point in the same direction as the derivative of the Logit function, but the magnitude may differ. It is only for a visual representation of the model. \n",
        "\n",
        "$$direction = pos * \\theta_2 / \\theta_1$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "B8U0raygN6tb"
      },
      "outputs": [],
      "source": [
        "# Equation for the separation plane\n",
        "# It give a value in the negative axe as a function of a positive value\n",
        "# f(pos, neg, W) = w0 + w1 * pos + w2 * neg = 0\n",
        "# s(pos, W) = (-w0 - w1 * pos) / w2\n",
        "def neg(theta, pos):\n",
        "    return (-theta[0] - pos * theta[1]) / theta[2]\n",
        "\n",
        "# Equation for the direction of the sentiments change\n",
        "# We don't care about the magnitude of the change. We are only interested \n",
        "# in the direction. So this direction is just a perpendicular function to the \n",
        "# separation plane\n",
        "# df(pos, W) = pos * w2 / w1\n",
        "def direction(theta, pos):\n",
        "    return    pos * theta[2] / theta[1]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FvJxy7USN6tc"
      },
      "source": [
        "The green line in the chart points in the direction where z > 0 and the red line points in the direction where z < 0. The direction of these lines are given by the weights $\\theta_1$ and $\\theta_2$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "z6lpdtNbN6tc",
        "outputId": "a97ba459-f7d7-4ae4-c63f-cad528b77c4c"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot the samples using columns 1 and 2 of the matrix\n",
        "fig, ax = plt.subplots(figsize = (8, 8))\n",
        "\n",
        "colors = ['red', 'green']\n",
        "\n",
        "# Color base on the sentiment Y\n",
        "ax.scatter(X[:,1], X[:,2], c=[colors[int(k)] for k in Y], s = 0.1)  # Plot a dot for each pair of words\n",
        "plt.xlabel(\"Positive\")\n",
        "plt.ylabel(\"Negative\")\n",
        "\n",
        "# Now lets represent the logistic regression model in this chart. \n",
        "maxpos = np.max(X[:,1])\n",
        "\n",
        "offset = 5000 # The pos value for the direction vectors origin\n",
        "\n",
        "# Plot a gray line that divides the 2 areas.\n",
        "ax.plot([0,  maxpos], [neg(theta, 0),   neg(theta, maxpos)], color = 'gray') \n",
        "\n",
        "# Plot a green line pointing to the positive direction\n",
        "ax.arrow(offset, neg(theta, offset), offset, direction(theta, offset), head_width=500, head_length=500, fc='g', ec='g')\n",
        "# Plot a red line pointing to the negative direction\n",
        "ax.arrow(offset, neg(theta, offset), -offset, -direction(theta, offset), head_width=500, head_length=500, fc='r', ec='r')\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D96GdeBkN6tc"
      },
      "source": [
        "**Note that more critical than the Logistic regression itself, are the features extracted from tweets that allow getting the right results in this exercise.**\n",
        "\n",
        "That is all, folks. Hopefully, now you understand better what the Logistic regression model represents, and why it works that well for this specific problem. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zrMZiBu_N6tc"
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.6"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}