Applying Multinomial Naive Bayes to NLP Problems

Naive Bayes Classifier Algorithm is a family of probabilistic algorithms based on applying Bayes’ theorem with the “naive” assumption of conditional independence between every pair of a feature.
Bayes theorem calculates probability P(c|x) where c is the class of the possible outcomes and x is the given instance which has to be classified, representing some certain features.

P(c|x) = P(x|c) * P(c) / P(x)

Naive Bayes are mostly used in natural language processing (NLP) problems. Naive Bayes predict the tag of a text. They calculate the probability of each tag for a given text and then output the tag with the highest one.

How Naive Bayes Algorithm Works ?

Let’s consider an example, classify the review whether it is positive or negative.

Training Dataset:

Text Reviews
“I liked the movie” positive
“It’s a good movie. Nice story” positive
“Nice songs. But sadly boring ending. ” negative
“Hero’s acting is bad but heroine looks good. Overall nice movie” positive
“Sad, boring movie” negative

We classify whether the text “overall liked the movie” has a positive review or a negative review. We have to calculate,
P(positive | overall liked the movie) — the probability that the tag of a sentence is positive given that the sentence is “overall liked the movie”.
P(negative | overall liked the movie) — the probability that the tag of a sentence is negative given that the sentence is “overall liked the movie”.

Before that, first, we apply Removing Stopwords and Stemming in the text.

Removing Stopwords: These are common words that don’t really add anything to the classification, such as an able, either, else, ever and so on.

Stemming: Stemming to take out the root of the word.

Now After applying these two techniques, our text becomes

Text Reviews
“ilikedthemovi” positive
“itsagoodmovienicestori” positive

Feature Engineering:
The important part is to find the features from the data to make machine learning algorithms works. In this case, we have text. We need to convert this text into numbers that we can do calculations on. We use word frequencies. That is treating every document as a set of the words it contains. Our features will be the counts of each of these words.

In our case, we have P(positive | overall liked the movie), by using this theorem:

P(positive | overall liked the movie) = P(overall liked the movie | positive) * P(positive) / P(overall liked the movie)

Since for our classifier we have to find out which tag has a bigger probability, we can discard the divisor which is the same for both tags,

P(overall liked the movie | positive)* P(positive) with P(overall liked the movie | negative) * P(negative)

There’s a problem though: “overall liked the movie” doesn’t appear in our training dataset, so the probability is zero. Here, we assume the ‘naive’ condition that every word in a sentence is independent of the other ones. This means that now we look at individual words.

We can write this as:

P(overall liked the movie) = P(overall) * P(liked) * P(the) * P(movie)

The next step is just applying the Bayes theorem:-

P(overall liked the movie| positive) = P(overall | positive) * P(liked | positive) * P(the | positive) * P(movie | positive)

And now, these individual words actually show up several times in our training data, and we can calculate them!

Calculating probabilities:

First, we calculate the a priori probability of each tag: for a given sentence in our training data, the probability that it is positive P(positive) is 3/5. Then, P(negative) is 2/5.

Then, calculating P(overall | positive) means counting how many times the word “overall” appears in positive texts (1) divided by the total number of words in positive (11). Therefore, P(overall | positive) = 1/17, P(liked/positive) = 1/17, P(the/positive) = 2/17, P(movie/positive) = 3/17.

If probability comes out to be zero then By using Laplace smoothing: we add 1 to every count so it’s never zero. To balance this, we add the number of possible words to the divisor, so the division will never be greater than 1. In our case, the total possible words count are 21.

Applying smoothing, The results are:

Word P(word | positive) P(word | negative)
overall 1 + 1/17 + 21 0 + 1/7 + 21
liked 1 + 1/17 + 21 0 + 1/7 + 21
the 2 + 1/17 + 21 0 + 1/7 + 21
movie 3 + 1/17 + 21 1 + 1/7 + 21

Now we just multiply all the probabilities, and see who is bigger:

P(overall | positive) * P(liked | positive) * P(the | positive) * P(movie | positive) * P(postive ) = 1.38 * 10^{-5} = 0.0000138

P(overall | negative) * P(liked | negative) * P(the | negative) * P(movie | negative) * P(negative) = 0.13 * 10^{-5} = 0.0000013

Our classifier gives “overall liked the movie” the positive tag.

Below is the implementation :

 # cleaning texts import pandas as pd import re import nltk from nltk.corpus import stopwords from nltk.stem.porter import PorterStemmer from sklearn.feature_extraction.text import CountVectorizer    dataset = [["I liked the movie", "positive"],            ["It’s a good movie. Nice story", "positive"],            ["Hero’s acting is bad but heroine looks good.\             Overall nice movie", "positive"],             ["Nice songs. But sadly boring ending.", "negative"],             ["sad movie, boring movie", "negative"]]                dataset = pd.DataFrame(dataset) dataset.columns = ["Text", "Reviews"]    nltk.download('stopwords')    corpus = []    for i in range(0, 5):     text = re.sub('[^a-zA-Z]', '', dataset['Text'][i])     text = text.lower()     text = text.split()     ps = PorterStemmer()     text = ''.join(text)     corpus.append(text)    # creating bag of words model cv = CountVectorizer(max_features = 1500)    X = cv.fit_transform(corpus).toarray() y = dataset.iloc[:, 1].values

 # splitting the data set into training set and test set from sklearn.cross_validation import train_test_split    X_train, X_test, y_train, y_test = train_test_split(            X, y, test_size = 0.25, random_state = 0)

 # fitting naive bayes to the training set from sklearn.naive_bayes import GaussianNB from sklearn.metrics import confusion_matrix    classifier = GaussianNB(); classifier.fit(X_train, y_train)    # predicting test set results y_pred = classifier.predict(X_test)    # making the confusion matrix cm = confusion_matrix(y_test, y_pred) cm

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