0-nlp_preprocessing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What is NLP (Natural Language Processing)?\n",
    "NLP is a very board field, anything that processes natural language is a part of it.\n",
    "\n",
    "Here are some examples:\n",
    "1. Translation between languages: https://translate.google.com/\n",
    "2. Answering questions about an image: http://vqa.cloudcv.org/\n",
    "3. Checking Grammar of a given passage: https://www.grammarly.com/grammar-check"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rule-based NLP\n",
    "In the early days of NLP, the processing was done by a set of predefined rules. \n",
    "\n",
    "For example, a rule-based grammar checker may have a rule that states \"is\" which follows a \"you\" is wrong and should be changed to \"are\".  \n",
    "\n",
    "\"You is a student.\" $\\to$ \"You are a student\"\n",
    "\n",
    "For these systems, thousands or more rules have to be manually defined."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistical NLP\n",
    "As the name implies statistical NLP uses statistics to process natural language. \n",
    "\n",
    "One of the most well-known successes of statistical NLP is the statistical machine translation with the IBM alignment models. The phrase-based version of these models are what Google Translation was based on before moving on to neural methods.\n",
    "\n",
    "For the next lesson, we will focus on the n-gram language model of statistical NLP. As the common Neural NLP uses a similar probability approach as the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Machine learning\n",
    "\n",
    "In machine learning, rather than manually design a model, we create a model that can learn from a set of data.\n",
    "\n",
    "For example, if we want of computer to identify handwriting, we will need a large number of images of handwriting. These images are used to train a model. After training, we will have a model that takes in an image of handwriting and outputs what it identifies. \n",
    "\n",
    "Statistical NLP is a form of machine learning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: regression\n",
    "\n",
    "Say we have a set of data points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note: You don't need to understand the code in this section. This is for demonstration only.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate data points\n",
    "X = np.linspace(-10, 10, 10)\n",
    "X = np.random.normal(X, 0.2)  # Add noise to data\n",
    "Y = X ** 2\n",
    "Y = np.random.normal(Y, 10)  # Add noise to data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.scatter(X, Y, s=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we want to find a function that models the underlying relationship between input and output.\n",
    "\n",
    "Say the underlying relationship is the following red line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "x = np.linspace(-10, 10, 100)\n",
    "\n",
    "y = x ** 2\n",
    "\n",
    "plt.scatter(X, Y, s=10)\n",
    "plt.plot(x, y, 'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Real-life data often have noises which is why the data points are not necessary on the red line."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One class of machine learning algorithm called regression or curve fitting can produce a function given a set of data.\n",
    "\n",
    "We can use it to find the underlying relationship."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "X_2 = PolynomialFeatures(degree=2).fit_transform(X.reshape(-1, 1))\n",
    "x_2 = PolynomialFeatures(degree=2).fit_transform(x.reshape(-1, 1))\n",
    "\n",
    "reg_2 = LinearRegression().fit(X_2, Y.reshape(-1, 1))\n",
    "y_2 = reg_2.predict(x_2)\n",
    "\n",
    "plt.scatter(X, Y, s=10)\n",
    "plt.plot(x, y, 'r', label='Underlying relationship')\n",
    "plt.plot(x, y_2, 'g', label='Our model')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the model actual matches the real underlying relationship pretty well in this case.\n",
    "\n",
    "Note that the prediction from the regression model doesn't necessary match the data point.\n",
    "\n",
    "This is a good thing as the data points can have noises."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overfitting\n",
    "\n",
    "If we do force the model to go through the data points, then it is modeling the noise rather than the underlying relationship."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "X_10 = PolynomialFeatures(degree=10).fit_transform(X.reshape(-1, 1))\n",
    "x_10 = PolynomialFeatures(degree=10).fit_transform(x.reshape(-1, 1))\n",
    "\n",
    "reg_10 = LinearRegression().fit(X_10, Y.reshape(-1, 1))\n",
    "y_10 = reg_10.predict(x_10)\n",
    "\n",
    "plt.scatter(X, Y, s=10)\n",
    "plt.plot(x, y, 'r', label='Underlying relationship')\n",
    "plt.plot(x, y_10, 'g', label=\"Overfitted model\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is undesired as the noises are random in nature. So the noise in one set of data is usually different than another set.\n",
    "\n",
    "Let us set up a way to measure the performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To measure the two models we have trained, we will use a metric called mean square error. We will talk about it in detail in a later lesson. \n",
    "\n",
    "For now, think it as the distance between to set of data. In our case, the real data and predicted data from our model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we test on the three center point of our data points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26.463736327032947"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_2 = reg_2.predict(X_2)\n",
    "\n",
    "mean_squared_error(Y[3:6], Y_2.reshape(-1)[3:6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5774665631853171e-13"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_10 = reg_10.predict(X_10)\n",
    "\n",
    "mean_squared_error(Y[3:6], Y_10.reshape(-1)[3:6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first result is the original model, the second result is the overfitted model.\n",
    "\n",
    "The overfitted model should have a lower distance between the data points and prediction as the overfitted model go through the data points.\n",
    "\n",
    "However, the overfitted model probability would not model a different set of data points from the same underlying model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make the testing more fair, we should generate a new set of data points from the same underlying model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate new data points\n",
    "x_t = np.linspace(-10, 10, 10)\n",
    "X_t = np.random.normal(x_t, 0.2)  # Add noise to data\n",
    "Y_t = X_t ** 2\n",
    "Y_t = np.random.normal(Y_t, 10)  # Add noise to data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.scatter(X_t, Y_t, s=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now make prediction with models and measure them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "179.74767661656546"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_2_t = PolynomialFeatures(degree=2).fit_transform(X_t.reshape(-1, 1))\n",
    "Y_2_t = reg_2.predict(X_2_t)\n",
    "\n",
    "mean_squared_error(Y_t, Y_2_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1316.0508028945383"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_10_t = PolynomialFeatures(degree=10).fit_transform(X_t.reshape(-1, 1))\n",
    "Y_10_t = reg_10.predict(X_10_t)\n",
    "\n",
    "mean_squared_error(Y_t, Y_10_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The original model should perform better than the overfitted model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training data and test data\n",
    "\n",
    "In practice, given a dataset, we split into training data and test data. Only the training data is used for training. The test data is not used for training at all. Else the test would not be accurate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preprocessing of the data\n",
    "\n",
    "In machine learning, it is important to process the dataset prior to training.\n",
    "\n",
    "First import the packages and load in the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_20newsgroups\n",
    "\n",
    "dataset = fetch_20newsgroups(data_home=\"data\", remove=('headers', 'footers', 'quotes'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset contains newsgroup posts. Here is one example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Do you have Weitek's address/phone number?  I'd like to get some information\n",
      "about this chip.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(dataset.data[3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### spaCy\n",
    "This a python package for preprocessing of text. It is optimized and aimed for deep learning. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tokenization\n",
    "\n",
    "In NLP, it is common to convert a sentence to an array of words.\n",
    "\n",
    "For English, we just need to cut along the space and punctuation for the most part. This is called tokenization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from spacy.tokenizer import Tokenizer\n",
    "from spacy.lang.en import English\n",
    "eng = English()\n",
    "tokenizer = Tokenizer(eng.vocab)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[,\n",
       " Do,\n",
       " you,\n",
       " have,\n",
       " Weitek's,\n",
       " address/phone,\n",
       " number?,\n",
       "  ,\n",
       " I'd,\n",
       " like,\n",
       " to,\n",
       " get,\n",
       " some,\n",
       " information,\n",
       " ,\n",
       " about,\n",
       " this,\n",
       " chip.,\n",
       " ]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(tokenizer(dataset.data[3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sentence became a list of words."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lemmatization\n",
    "In certain cases, it may be helpful to convert the words into their root forms. \n",
    "\n",
    "Examples: \"apples\" $\\to$ \"apple\", \"bought\" $\\to$ \"buy\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from spacy.lemmatizer import Lemmatizer\n",
    "from spacy.lang.en import LEMMA_INDEX, LEMMA_EXC, LEMMA_RULES\n",
    "\n",
    "lemmatizer = Lemmatizer(LEMMA_INDEX, LEMMA_EXC, LEMMA_RULES)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['apple']"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lemmatizer(\"apples\", \"NOUN\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['buy']"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lemmatizer(\"bought\", \"VERB\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This can help with the model to deal with variation in the data.\n",
    "\n",
    "As NLP moves toward deep learning, lemmatization becomes increasingly uncommon. After all, lemmatization removes some information in the process, and deep learning deals with variation better than traditional statistical approaches. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stop Word\n",
    "\n",
    "Sometimes it is also helpful to remove high-frequency words. These high-frequency words are called stop words. There is no standard list of stop words."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['did', 'those', 'hereafter', 'his', 'herself', 'still', 'can', 'wherein', 'many', 'per']\n"
     ]
    }
   ],
   "source": [
    "from spacy.lang.en.stop_words import STOP_WORDS\n",
    "print(list(STOP_WORDS)[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like lemmatization, it tends to be unnecessary to remove stop words for deep learning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preprocess with spaCy\n",
    "Instead of processing it step by step like in the preprocess section. SpaCy offers a pipeline approach to preprocessing data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many functions in spaCy requires a statistic model that must be downloaded first. Different language requires different models. These models can be downloaded [here](https://spacy.io/models)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will be needing a model for English, which will be downloaded by the following code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\u001b[93m    Linking successful\u001b[0m\n",
      "    /home/user/anaconda3/envs/nlp-course/lib/python3.7/site-packages/en_core_web_sm\n",
      "    -->\n",
      "    /home/user/anaconda3/envs/nlp-course/lib/python3.7/site-packages/spacy/data/en_core_web_sm\n",
      "\n",
      "    You can now load the model via spacy.load('en_core_web_sm')\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import spacy\n",
    "\n",
    "spacy.cli.download(\"en_core_web_sm\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "nlp = spacy.load(\"en_core_web_sm\", disable=['tagger', 'parser', 'ner'])\n",
    "sentencizer = nlp.create_pipe(\"sentencizer\")\n",
    "nlp.add_pipe(sentencizer, first=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model provided by spaCy comes with many components in the pipeline by default which we disabled during loading.\n",
    "A sentencizer is added as it is not a part of the default pipeline. Lemmatization is included by default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I -> I\n",
      "was -> be\n",
      "wondering -> wonder\n",
      "if -> if\n",
      "anyone -> anyone\n",
      "out -> out\n",
      "there -> there\n",
      "could -> can\n",
      "enlighten -> enlighten\n",
      "me -> me\n",
      "on -> on\n",
      "this -> this\n",
      "car -> car\n",
      "I -> I\n",
      "saw -> see\n",
      "\n",
      " -> \n",
      "\n",
      "the -> the\n",
      "other -> other\n",
      "day -> day\n",
      ". -> .\n"
     ]
    }
   ],
   "source": [
    "for doc in nlp.pipe(dataset.data):\n",
    "    for sent in doc.sents:\n",
    "        for token in sent:\n",
    "            # Do NLP stuff\n",
    "            \n",
    "            # Example: print out each word and the lemma of each word.\n",
    "            print(f\"{token} -> {token.lemma_}\")\n",
    "            \n",
    "        # Remove the two break statements to process the whole document.\n",
    "        break  \n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output is a single sentence before and after lemmatization. Remove the break statements to process the whole dataset."
   ]
  }
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