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Term frequency–inverse document frequency (TF-IDF), is a numerical statistic that is intended to reflect how important a word is to a document in a collection or corpus. It is often used as a weighting factor in searches of information retrieval, text mining, and user modeling. The TF-IDF value increases proportionally to the number of times a word appears in the document and is offset by the frequency of the word in the corpus, which helps to adjust for the fact that some words appear more frequently in general.

Put simply, the higher the TF*IDF score (weight), the rarer the term and vice versa.

TF: Term Frequency, which measures how frequently a term occurs in a document. Since every document is different in length, it is possible that a term would appear much more times in long documents than shorter ones. Thus, the term frequency is often divided by the document length (aka. the total number of terms in the document) as a way of normalization:

TF(t) = (Number of times term t appears in a document) / (Total number of terms in the document).

IDF: Inverse Document Frequency, which measures how important a term is. While computing TF, all terms are considered equally important. However it is known that certain terms, such as “is”, “of”, and “that”, may appear a lot of times but have little importance. Thus we need to weigh down the frequent terms while scale up the rare ones, by computing the following:

IDF(t) = (Total number of documents / Number of documents with term t in it).


Consider a document containing 100 words wherein the word cat appears 3 times. The term frequency (i.e., tf) for cat is then (3 / 100) = 0.03. Now, assume we have 10 million documents and the word cat appears in one thousand of these. Then, the inverse document frequency (i.e., idf) is calculated as log(10,000,000 / 1,000) = 4.

Thus, the Tf-idf weight is the product of these quantities: 0.03 * 4 = 0.12.

Using TF-IDF

A good rule of thumb is, the more your content “makes sense” to the user, the more weight it is assigned by the search engine. With words having a high TF*IDF weight in your content, your content will always be among the top search results, so you can:

  • stop worrying about using the stop-words,
  • successfully hunt words with higher search volumes and lower competition,
  • be sure to have words that make your content unique and relevant to the user, etc.

Code: Available on Github Repo

Written on March 20, 2018