Lab3_vamsi.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[nltk_data] Downloading package twitter_samples to\n",
      "[nltk_data]     /Users/vamsioruganti/nltk_data...\n",
      "[nltk_data]   Package twitter_samples is already up-to-date!\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": {},
   "source": [
    "## Load the NLTK sample dataset\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "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": {},
   "source": [
    "# Load the extracted features\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>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": {},
   "source": [
    "Now let us get rid of the data frame to keep only Numpy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "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": {},
   "source": [
    "## Load a pretrained Logistic Regression model\n",
    "\n",
    "In the same way, as part of this week's assignment, a Logistic regression model must be trained. 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": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = [6.03518871e-08, 5.38184972e-04, -5.58300168e-04]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Negative')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": {},
   "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": 7,
   "metadata": {},
   "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": {},
   "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": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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