TF-IDF — Term Frequency-Inverse Document Frequency – LearnDataSci (2024)

Term Frequency - Inverse Document Frequency (TF-IDF) is a widely used statistical method in natural language processing and information retrieval. It measures how important a term is within a document relative to a collection of documents (i.e., relative to a corpus).

Words within a text document are transformed into importance numbers by a text vectorization process. There are many different text vectorization scoring schemes, with TF-IDF being one of the most common.

As its name implies, TF-IDF vectorizes/scores a word by multiplying the word’s Term Frequency (TF) with the Inverse Document Frequency (IDF).

Term Frequency: TF of a term or word is the number of times the term appears in a document compared to the total number of words in the document.

$$ TF = \frac {\textrm{number of times the term appears in the document} }{ \textrm{total number of terms in the document}} $$

Inverse Document Frequency: IDF of a term reflects the proportion of documents in the corpus that contain the term. Words unique to a small percentage of documents (e.g., technical jargon terms) receive higher importance values than words common across all documents (e.g., a, the, and).

$$ IDF = log (\frac {\textrm{number of the documents in the corpus}} {\textrm{number of documents in the corpus contain the term}}) $$

The TF-IDF of a term is calculated by multiplying TF and IDF scores.

$$ \textit{TF-IDF} = TF * IDF $$

Translated into plain English, importance of a term is high when it occurs a lot in a given document and rarely in others. In short, commonality within a document measured by TF is balanced by rarity between documents measured by IDF. The resulting TF-IDF score reflects the importance of a term for a document in the corpus.

TF-IDF is useful in many natural language processing applications. For example, Search Engines use TF-IDF to rank the relevance of a document for a query. TF-IDF is also employed in text classification, text summarization, and topic modeling.

Note that there are some different approaches to calculating the IDF score. The base 10 logarithm is often used in the calculation. However, some libraries use a natural logarithm. In addition, one can be added to the denominator as follows in order to avoid division by zero.

$$ IDF = log (\frac {\textrm{number of the documents in the corpus}} {\textrm{number of documents in the corpus contain the term} +1}) $$

Imagine the term $t$ appears 20 times in a document that contains a total of 100 words. Term Frequency (TF) of $t$ can be calculated as follow:

$$ TF= \frac{20}{100} = 0.2 $$

Assume a collection of related documents contains 10,000 documents. If 100 documents out of 10,000 documents contain the term $t$, Inverse Document Frequency (IDF) of $t$ can be calculated as follows

$$ IDF = log \frac{10000}{100} = 2 $$

Using these two quantities, we can calculate TF-IDF score of the term $t$ for the document.

$$ \textit{TF-IDF} = 0.2 * 2 = 0.4 $$

Some popular python libraries have a function to calculate TF-IDF. The popular machine learning library Sklearn has TfidfVectorizer() function (docs).

We will write a TF-IDF function from scratch using the standard formula given above, but we will not apply any preprocessing operations such as stop words removal, stemming, punctuation removal, or lowercasing. It should be noted that the result may be different when using a native function built into a library.

import pandas as pdimport numpy as np
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corpus = ['data science is one of the most important fields of science', 'this is one of the best data science courses', 'data scientists analyze data' ]
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words_set = set()for doc in corpus: words = doc.split(' ') words_set = words_set.union(set(words)) print('Number of words in the corpus:',len(words_set))print('The words in the corpus: \n', words_set)
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Out:

Number of words in the corpus: 14The words in the corpus: {'important', 'scientists', 'best', 'courses', 'this', 'analyze', 'of', 'most', 'the', 'is', 'science', 'fields', 'one', 'data'}
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n_docs = len(corpus) #Number of documents in the corpusn_words_set = len(words_set) #Number of unique words in the df_tf = pd.DataFrame(np.zeros((n_docs, n_words_set)), columns=words_set)# Compute Term Frequency (TF)for i in range(n_docs): words = corpus[i].split(' ') # Words in the document for w in words: df_tf[w][i] = df_tf[w][i] + (1 / len(words)) df_tf
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print("IDF of: ")idf = {}for w in words_set: k = 0 # number of documents in the corpus that contain this word for i in range(n_docs): if w in corpus[i].split(): k += 1 idf[w] = np.log10(n_docs / k) print(f'{w:>15}: {idf[w]:>10}' )
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Out:

IDF of: important: 0.47712125471966244 scientists: 0.47712125471966244 best: 0.47712125471966244 courses: 0.47712125471966244 this: 0.47712125471966244 analyze: 0.47712125471966244 of: 0.17609125905568124 most: 0.47712125471966244 the: 0.17609125905568124 is: 0.17609125905568124 science: 0.17609125905568124 fields: 0.47712125471966244 one: 0.17609125905568124 data: 0.0
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df_tf_idf = df_tf.copy()for w in words_set: for i in range(n_docs): df_tf_idf[w][i] = df_tf[w][i] * idf[w] df_tf_idf
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from sklearn.feature_extraction.text import TfidfVectorizer
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tr_idf_model = TfidfVectorizer()tf_idf_vector = tr_idf_model.fit_transform(corpus)
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After vectorizing the corpus by the function, a sparse matrix is obtained.

Here's the current shape of the matrix:

print(type(tf_idf_vector), tf_idf_vector.shape)
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Out:

<class 'scipy.sparse.csr.csr_matrix'> (3, 14)
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tf_idf_array = tf_idf_vector.toarray()print(tf_idf_array)
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Out:

[[0. 0. 0. 0.18952581 0.32089509 0.32089509 0.24404899 0.32089509 0.48809797 0.24404899 0.48809797 0. 0.24404899 0. ] [0. 0.40029393 0.40029393 0.23642005 0. 0. 0.30443385 0. 0.30443385 0.30443385 0.30443385 0. 0.30443385 0.40029393] [0.54270061 0. 0. 0.64105545 0. 0. 0. 0. 0. 0. 0. 0.54270061 0. 0. ]]
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words_set = tr_idf_model.get_feature_names()print(words_set)
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Out:

['analyze', 'best', 'courses', 'data', 'fields', 'important', 'is', 'most', 'of', 'one', 'science', 'scientists', 'the', 'this']
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df_tf_idf = pd.DataFrame(tf_idf_array, columns = words_set)df_tf_idf
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