Bag of Words and Tf-idf Explained

Pio Calderon · May 4, 2017

Text analytics is one of the most interesting applications of computing. It involves taking raw text, converting it into a set of numerical features, and applying a natural language processing (NLP) or machine learning (ML) algorithm on it to derive some insight. Let’s focus on the second step. How do we actually transform raw text into numerical features?

In this post, I will explore two ways this can be done: the Bag-of-words model and tf-idf.

Bag-of-words Model

You can think of the bag-of-words (BoW) model as a machine which takes as input a set of documents and outputs a table containing the frequency counts of each word in each document.

In the simplest case, let’s suppose that our set of documents consists of only one document — a sentence:

Let’s apply our BoW model to this document.

The BoW outputs a table wherein each row corresponds to a document and each column represents a unique word. The entries are the counts of each word in each document.

We can’t really derive any insight from the table, since we’re only considering one document. Each entry in the table is 1, since the first document obviously contains all unique words in the first document.

The BoW model was created as a means to compare a set of documents. There really is no point if you only have a single document.

Suppose our set of documents consists of three sentences:

Applying the BoW to this set, we get a table with three rows.

Let’s zoom in on the table.

OK. This is a lot more interesting.

BoW only takes into consideration the frequency of words in a document. A document’s important words, in the BoW-sense, are words that occur a lot of times in said document.

We can see in the table that the word love appears only in the first document, hate only appears in the second, and hobby and passion only appear in the third. Using the BoW model, we can identify the important — that is, signature — words in the different documents by visual inspection.

The question now is, can we actually quantify the signature words?

Well, yes we can. By applying another transformation.


The BoW model is a perfectly acceptable model to convert raw text to numbers. However, if our purpose is to identify signature words in a document, there is a better transformation that we can apply.

tf-idf is shorthand for term frequency — inverse document frequency. So, two things: term frequency and inverse document frequency.

Term frequency (tf) is basically the output of the BoW model. For a specific document, it determines how important a word is by looking at how frequently it appears in the document. Term frequency measures the local importance of the word. If a word appears a lot of times, then the word must be important. For example, if our document is “I am a cat lover. I have a cat named Steve. I feed a cat outside my room regularly,” we see that the words with the highest frequency are I, a, and cat. This agrees with our intuition that high term frequency = higher importance since the document is all about my fascination with cats.

The second component of tf-idf is inverse document frequency (idf). For a word to be considered a signature word of a document, it shouldn’t appear that often in the other documents. Thus, a signature word’s document frequency must be low, meaning its inverse document frequency must be high. The idf is usually calculated as

The tf-idf is the product of these two frequencies. For a word to have high tf-idf in a document, it must appear a lot of times in said document and must be absent in the other documents. It must be a signature word of the document.

Let’s zoom in on the output of our three-sentence example.

We can see here that tf-idf highlights love as a signature word in the first document, hate in the second, and is, my, hobby and passion in the third.

What’s Next

BoW and tf-idf are the first step in the text analytics pipeline. These two tools are mainly used to convert raw text to numerical features which are then fed to natural language processing (NLP) or machine learning (ML) algorithms.

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