# Text Classification with Naive Bayes and NLTK

Feb 9, 2021
May 22, 2021 06:37 UTC

In the last post we talked about the theoretical side of naive Bayes in text classification. Here we will implement the model in Python, both from scratch and utilizing existing packages.

The corpus we use is a 26-line poem by T.S. Eliot. In each line a dummy string “ZZZ” or “XXX' has been inserted, representing the class of the line (“ZZZ” for class 0 and XXX for class 1).

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  corpus = [ "And indeed there will be time ZZZ", "For the yellow smoke that slides along the street XXX", "Rubbing its back upon the window-panes ZZZ", "There will be time, there will be time ZZZ", "To prepare a face to meet the faces that you meet XXX", "There will be time to murder and create ZZZ", "And time for all the works and days of hands ZZZ", "That lift and drop a question on your plate ZZZ", "Time for you and time for me ZZZ", "And time yet for a hundred indecisions XXX", "And for a hundred visions and revisions XXX", "Before the taking of a toast and tea ZZZ.", "In the room the women come and go XXX", "Talking of Michelangelo. XXX", "And indeed there will be time XXX", 'To wonder, "Do I dare?" and, "Do I dare?" ZZZ', "Time to turn back and descend the stair, ZZZ", "With a bald spot in the middle of my hair — XXX", '(They will say: "How his hair is growing thin!") XXX', "My morning coat, my collar mounting firmly to the chin, ZZZ", "My necktie rich and modest, but asserted by a simple pin — XXX", '(They will say: "But how his arms and legs are thin!") ZZZ', "Do I dare XXX", "Disturb the universe? XXX", "In a minute there is time ZZZ", "For decisions and revisions which a minute will reverse. XXX", ] targets = [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1] 

## Naive Bayes from scratch

The focus of this section is to get the maths right – we don’t care much about the efficiency or elegancy of the code.

The first thing we should think about is the data we’re feeding into the algorithm. The data at hand are sentences, so we need to parse them into words or tokens.

### The tokenizer

We’ll take a very simple approach here – given a sentence, our function returns a dictionary with words in the sentence as keys and counts of the words as values1. We also define a helper function that adds counts to our result dictionaries.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  import re def add_count(x, output_dict, count=1): if x not in output_dict: output_dict[x] = count else: output_dict[x] += count def tokenize(sentence): tokens = {} # Only keep tokens that are at least 2 characters long for token in re.findall(r"\b\w\w+\b", sentence): token = token.lower() add_count(token, tokens) return tokens 

### Naive Bayes core

Let’s take a minute to think about the parts needed to calculate the final probability for each class:

1. For each token, find its count in each of the classes.
2. Calculate and store $P(C)$, the frequencies of the classes.
3. Calculate the (log) probability of each token for each class using Bayes' Theorem. Laplace smoothing should be applied.
4. Predict the class of a given sentence by returning the class with maximum probability.

Let’s get started! First we take down everything that needs to be stored:

 1 2 3 4 5 6  class MyNaiveBayes: def __init__(self, laplace_smoothing_param=1): self.k = laplace_smoothing_param self.classes_count = {} self.class_tokens = {} self.all_tokens = set() 

We want to keep the class flexible and not limit the input to two classes. classes_count would have different classes as keys and their counts as values. class_tokens would be a nested dictionary – each element is a dictionary of token counts with the key as the class label.

Training the model is pretty easy as we only need to go through the corpus once. We first go through each sentence and count the words. Then we collect all the observed words into all_tokens and add the Laplace pseudo-counts to class_tokens.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  def train(self, corpus, labels): for label, s in zip(labels, corpus): add_count(label, self.classes_count) if label not in self.class_tokens: self.class_tokens[label] = {} tokens = tokenize(s) self.all_tokens.update(tokens.keys()) for token, token_count in tokens.items(): add_count(token, self.class_tokens[label], token_count) for label in self.class_tokens.keys(): for token in self.all_tokens: if token not in self.class_tokens[label]: self.class_tokens[label][token] = 0 self.class_tokens[label][token] += self.k # laplace 

Calculating the probability for each class is trivial:

 1 2 3 4  def calc_class_proba(self, classID): return self.classes_count[classID] / np.sum( [x for x in self.classes_count.values()] ) 

Finding the probability for each token given the class is only slightly harder – we run into cases where the word count is zero, so the Laplace estimator is plugged in:

 1 2 3  def calc_token_proba(self, token, classID): all_tokens_in_class = np.sum([x for x in self.class_tokens[classID].values()]) return self.class_tokens[classID][token] / all_tokens_in_class 

To get the probability for each class, we just apply Bayes' Theorem and scale the sum of the probabilities to one.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  def predict_proba(self, sentence): tokens = tokenize(sentence) res = {} for label in self.classes_count.keys(): # start from the class probability log_proba = np.log2(self.calc_class_proba(label)) for token, token_count in tokens.items(): # handle unseen words if token in self.class_tokens[label]: token_proba = self.calc_token_proba(token, label) log_proba += token_count * np.log2(token_proba) res[label] = np.exp2(log_proba) denom = np.sum([x for x in res.values()]) res = {label: proba / denom for label, proba in res.items()} return res 

And that’s pretty much the core part of our model! We’re just missing the functions to predict the final class, which is given below in the full class with all the other methods.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80  import re import numpy as np def add_count(x, output_dict, count=1): if x not in output_dict: output_dict[x] = count else: output_dict[x] += count def tokenize(sentence): tokens = {} # Only keep tokens that are at least 2 characters long for token in re.findall(r"\b\w\w+\b", sentence): token = token.lower() add_count(token, tokens) return tokens class MyNaiveBayes: def __init__(self, laplace_smoothing_param=1): self.k = laplace_smoothing_param self.classes_count = {} self.class_tokens = {} self.all_tokens = set() def train(self, corpus, labels): for label, s in zip(labels, corpus): add_count(label, self.classes_count) if label not in self.class_tokens: self.class_tokens[label] = {} tokens = tokenize(s) self.all_tokens.update(tokens.keys()) for token, token_count in tokens.items(): add_count(token, self.class_tokens[label], token_count) for label in self.class_tokens.keys(): for token in self.all_tokens: if token not in self.class_tokens[label]: self.class_tokens[label][token] = 0 self.class_tokens[label][token] += self.k # laplace def calc_class_proba(self, classID): return self.classes_count[classID] / np.sum( [x for x in self.classes_count.values()] ) def calc_token_proba(self, token, classID): all_tokens_in_class = np.sum([x for x in self.class_tokens[classID].values()]) # handle unseen words if token not in self.class_tokens[classID]: return 1 return self.class_tokens[classID][token] / all_tokens_in_class def predict_proba(self, sentence): tokens = tokenize(sentence) res = {} for label in self.classes_count.keys(): # start from the class probability log_proba = np.log2(self.calc_class_proba(label)) for token, token_count in tokens.items(): # handle unseen words if token in self.class_tokens[label]: token_proba = self.calc_token_proba(token, label) log_proba += token_count * np.log2(token_proba) res[label] = np.exp2(log_proba) denom = np.sum([x for x in res.values()]) res = {label: proba / denom for label, proba in res.items()} return res def predict(self, sentence): proba = self.predict_proba(sentence) max_proba = max([x for x in proba.values()]) res = [x for x in proba.keys() if proba[x] == max_proba] return res[0] 

### Checking the classifier

Now we check our model with the corpus given at the beginning. We have a test set given below:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  new_data = [ "For I have known them all already, known them all: ZZZ", "Have known the evenings, mornings, afternoons, ZZZ", "I have measured out my life with coffee spoons; XXX", "I know the voices dying with a dying fall XXX", "Beneath the music from a farther room. ZZZ", "So how should I presume? ZZZ", ] actual = [0, 0, 1, 1, 0, 0] cls = MyNaiveBayes() cls.train(corpus, targets) [cls.predict_proba(x) for x in new_data] # [{0: 0.9721513447351029, 1: 0.027848655264897063}, # {0: 0.9026159391741999, 1: 0.09738406082580003}, # {0: 0.02876761464981322, 1: 0.9712323853501869}, # {0: 0.021732005477143462, 1: 0.9782679945228566}, # {0: 0.8132271179857358, 1: 0.18677288201426423}, # {0: 0.9251393970016891, 1: 0.07486060299831092}] 

Well, we got all of the test cases right! Next we’ll compare our results to the output of scikit-learn to see if the probabilities are correct.

## Using scikit-learn

The CounterVectorizer class in scikit-learn can be used to convert each string in the corpus into a vector of word counts. The output is a compressed sparse row matrix (scipy.sparse.csr_matrix)2.

 1 2 3  from sklearn.feature_extraction.text import CountVectorizer count_vect = CountVectorizer() X_train_counts = count_vect.fit_transform(corpus.X) 

Once we have the vectorized input, we can create a naive Bayes classifier by fitting it to the corpus. Then we may invoke the predict method to classify new instances.

  1 2 3 4 5 6 7 8 9 10  from sklearn.naive_bayes import MultinomialNB clf = MultinomialNB().fit(X_train_counts, targets) clf.predict_proba(X_new_counts) # array([[0.97215134, 0.02784866], # [0.90261594, 0.09738406], # [0.02876761, 0.97123239], # [0.02173201, 0.97826799], # [0.81322712, 0.18677288], # [0.9251394 , 0.0748606 ]]) 

The output values are almost identical to that of our hand-written model above.

## Introducing NLTK

NLTK (the Natural Language ToolKit) provides a suite of text processing libraries for classification, tokenization, stemming, tagging, etc. It also provides interfaces to over 50 corpora and lexical resources such as WordNet. Here we’ll briefly introduce some of the most common methods. For detailed tutorials, see this book by Steven Bird et al..

### Tokenization

NLTK has tokenizers for splitting text into sentences (based on capitalization and punctuation) and into words. They should be much more robust than the one we used above.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  import nltk from nltk.corpus import wordnet from nltk.stem import PorterStemmer, WordNetLemmatizer from nltk.tokenize import sent_tokenize, word_tokenize poem = ". ".join(corpus) sentences = sent_tokenize(poem) print(sentences[:5]) # ['And indeed there will be time ZZZ.', # 'For the yellow smoke that slides along the street XXX.', # 'Rubbing its back upon the window-panes ZZZ.', # 'There will be time, there will be time ZZZ.', # 'To prepare a face to meet the faces that you meet XXX.'] words = word_tokenize(poem) print(words[:5]) # ['And', 'indeed', 'there', 'will', 'be'] 

### Stemming and lemmatization

As defined by the Stanford NLP group, the goal of both stemming and lemmatization is to reduce inflectional forms and sometimes derivationally related forms of a word to a common base form. Stemming usually refers to a crude heuristic process that chops off the ends of words in the hope of achieving this goal correctly most of the time, and often includes the removal of derivational affixes. Lemmatization usually refers to doing things properly with the use of a vocabulary and morphological analysis of words, normally aiming to remove inflectional endings only and to return the base or dictionary form of a word.

Let’s see the stemmed word tokens first. All characters are converted to lowercase, and some errors were introduced, e.g. “quickly” to “quickli”.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  text = "Run runs running ran. Tall tallest. Quick quickest quickly." words = word_tokenize(text) stemmer = PorterStemmer() stemmed = [(tok, stemmer.stem(tok)) for tok in words] print(stemmed) # [('Run', 'run'), # ('runs', 'run'), # ('running', 'run'), # ('ran', 'ran'), # ('.', '.'), # ('Tall', 'tall'), # ('tallest', 'tallest'), # ('.', '.'), # ('Quick', 'quick'), # ('quickest', 'quickest'), # ('quickly', 'quickli'), # ('.', '.')] 

We use WordNet Synset to demonstrate lemmatization. WordNet is a lexical database designed for NLP in English, and Synset is an interface to look up words in WordNet. It takes slightly longer to run, but the results are more accurate.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  lem = WordNetLemmatizer() lemmatized = [(tok, lem.lemmatize(tok)) for tok in words] print(lemmatized) # [('Run', 'Run'), # ('runs', 'run'), # ('running', 'running'), # ('ran', 'ran'), # ('.', '.'), # ('Tall', 'Tall'), # ('tallest', 'tallest'), # ('.', '.'), # ('Quick', 'Quick'), # ('quickest', 'quickest'), # ('quickly', 'quickly'), # ('.', '.')] 

### Part of speech tagging

Another common use case of NLTK is to tag the part of speech3 given a list of tokens. This is useful for identifying entities and relationships between entities in the text.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38  tokens = word_tokenize("The very first run was unsuccessful. ") tagged = nltk.pos_tag(tokens) for pair in tagged: print(pair) nltk.help.upenn_tagset(pair[1]) # ('The', 'DT') # DT: determiner # all an another any both del each either every half la many much nary # neither no some such that the them these this those # ('very', 'RB') # RB: adverb # occasionally unabatingly maddeningly adventurously professedly # stirringly prominently technologically magisterially predominately # swiftly fiscally pitilessly ... # ('first', 'JJ') # JJ: adjective or numeral, ordinal # third ill-mannered pre-war regrettable oiled calamitous first separable # ectoplasmic battery-powered participatory fourth still-to-be-named # multilingual multi-disciplinary ... # ('run', 'NN') # NN: noun, common, singular or mass # common-carrier cabbage knuckle-duster Casino afghan shed thermostat # investment slide humour falloff slick wind hyena override subhumanity # machinist ... # ('was', 'VBD') # VBD: verb, past tense # dipped pleaded swiped regummed soaked tidied convened halted registered # cushioned exacted snubbed strode aimed adopted belied figgered # speculated wore appreciated contemplated ... # ('unsuccessful', 'JJ') # JJ: adjective or numeral, ordinal # third ill-mannered pre-war regrettable oiled calamitous first separable # ectoplasmic battery-powered participatory fourth still-to-be-named # multilingual multi-disciplinary ... # ('.', '.') # .: sentence terminator # . ! ? 

1. Here we only keep tokens that are at least 2 characters long to stay consistent with the sklearn.feature_extraction.text.CountVectorizer method. ↩︎

2. We can check the data stored in the sparse matrix by converting it to a pandas data frame:

 1 2 3  names = count_vect.get_feature_names() arr = X_train_counts.toarray() counts_df = pd.DataFrame(arr, columns=names) 
↩︎
3. See nltk.help.upenn_tagset() for all of the tags. ↩︎

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