Assignment-1-17110021-Anubhav_Jain.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 1 (No. of Tokens,Types and TTR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No. of tokens  305672\n",
      "No. of Types 43853\n",
      "TTR 0.14346423617472323\n"
     ]
    }
   ],
   "source": [
    "from nltk.tokenize import TweetTokenizer\n",
    "import nltk\n",
    "import string\n",
    "import sys\n",
    "import numpy as np\n",
    "import re\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit\n",
    "from nltk.corpus import wordnet\n",
    "import math\n",
    "import random\n",
    "\n",
    "\n",
    "punc1 = string.punctuation\n",
    "punc = []\n",
    "for i in punc1:\n",
    "    punc.append(i)\n",
    "\n",
    "#print(punc, len(punc))\n",
    "#print(\"Default encoding is .. \",sys.getdefaultencoding())\n",
    "\n",
    "file = open('/Users/anubhavjain/Desktop/Anubhav_MacBook_Pro/Natural Language Processing/NLP_2/tweets-dataset.csv', \"r\", encoding=\"utf-8\")\n",
    "\n",
    "tknr = TweetTokenizer(strip_handles=True)\n",
    "sum = 0\n",
    "count_punc = 0\n",
    "arr = []\n",
    "\n",
    "heap_tok = []\n",
    "heap_voc = []\n",
    "c_tok = 0\n",
    "c_voc = 0\n",
    "s_voc = set()\n",
    "\n",
    "for i in file:\n",
    "    a = tknr.tokenize(i)\n",
    "    b = []\n",
    "    for j in a:\n",
    "        if(re.match(r\"\\.[\\s.]*\\.\",j)):\n",
    "            count_punc+=1\n",
    "        elif(j in punc):\n",
    "            count_punc+=1\n",
    "        elif(re.match(r\"https:\\/\\/\\S*|pic.twitter\\S*\",j)):\n",
    "            count_punc+=1\n",
    "        else:\n",
    "            arr.append(j)\n",
    "            b.append(j)\n",
    "            s_voc.add(j)\n",
    "\n",
    "    c_tok+=len(b)\n",
    "    c_voc= len(s_voc)\n",
    "    heap_tok.append(c_tok)\n",
    "    heap_voc.append(c_voc)\n",
    "    sum+=len(a)\n",
    "\n",
    "no_tokens = len(arr)\n",
    "print(\"No. of tokens \", no_tokens)\n",
    "\n",
    "type_arr = np.unique(arr)\n",
    "no_type = len(type_arr)\n",
    "\n",
    "print(\"No. of Types\", no_type)\n",
    "print(\"TTR\",no_type/no_tokens)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 2 (Zipf's Law for Length and Frequency Graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length = 9.132130272878975 * 1 / Frequency\n"
     ]
    },
    {
     "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": [
    "def test_zipf1(n,k):\n",
    "    return k*(1/n)\n",
    "\n",
    "frequency_dist = nltk.FreqDist(arr)\n",
    "result = dict()\n",
    "\n",
    "length_arr = []\n",
    "freq_arr = []\n",
    "\n",
    "for word, frequency in frequency_dist.most_common(50000):\n",
    "            result[word] = frequency\n",
    "            length_arr.append(len(word))\n",
    "            freq_arr.append(frequency)\n",
    "\n",
    "param1, param_cov1 = curve_fit(test_zipf1, freq_arr, length_arr)\n",
    "print(\"Length = \"+ str(param1[0]) + \" * 1 / Frequency\")\n",
    "ans = param1[0]/freq_arr\n",
    "\n",
    "plt.scatter(freq_arr,length_arr,s=1, color ='green')\n",
    "plt.plot(freq_arr,ans, '-', color='red')\n",
    "plt.xlabel(\"Frequency of words\")\n",
    "plt.ylabel(\"Length of Words\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 2 (Zipf's Law for Meaning and Frequency Graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Meaning = 0.8927070978386349 * Sqrt(Frequency)\n"
     ]
    },
    {
     "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": [
    "def test_zipf2(n,k):\n",
    "    return k*np.sqrt(n)\n",
    "\n",
    "random_words = [type_arr[random.randrange(no_type)]for i in range(5000)]\n",
    "#print(random_words)\n",
    "\n",
    "#rand_words = [\"India\"]\n",
    "words_mean = []\n",
    "freq_words = []\n",
    "\n",
    "for i in random_words:\n",
    "    synonyms = []\n",
    "    for syn in wordnet.synsets(i):\n",
    "        for l in syn.lemmas():\n",
    "            synonyms.append(l.name())\n",
    "    l = len(set(synonyms))\n",
    "    words_mean.append(l)\n",
    "    freq_words.append(result[i])\n",
    "\n",
    "param2, param_cov2 = curve_fit(test_zipf2, freq_words, words_mean)\n",
    "print(\"Meaning = \"+ str(param2[0]) + \" * Sqrt(Frequency)\")\n",
    "ans1 = param2[0]*np.sqrt(freq_words)\n",
    "\n",
    "plt.scatter(freq_words,words_mean,s=1, color ='red')\n",
    "#plt.plot(freq_words,ans1,color=\"green\")\n",
    "plt.xlabel(\"Frequency of words\")\n",
    "plt.ylabel(\"Meaning of words\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 3 (Heap's Law)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "V = 10.887305419830385*(N^0.657968907783682)\n",
      "10.887305419830385 0.657968907783682\n"
     ]
    },
    {
     "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": [
    "def test(n, k, beta):\n",
    "    return k * np.power(n, beta)\n",
    "\n",
    "param, param_cov = curve_fit(test, heap_tok, heap_voc)\n",
    "\n",
    "K = param[0]\n",
    "beta = param[1]\n",
    "print(\"V = \" +str(K)+\"*(N^\"+str(beta)+\")\")\n",
    "print(K,beta)\n",
    "\n",
    "plt.scatter(heap_tok,heap_voc,s=0.001,color ='red')\n",
    "plt.plot(heap_tok,K*np.power(heap_tok,beta), color='green')\n",
    "plt.xlabel(\"No. of Tokens\")\n",
    "plt.ylabel(\"Vocabulary Count\")\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}