How Bag of Words Documents work? Explain with Numerical Examples.

The Bag of Words (BoW) model is a representation used in natural language processing (NLP) to convert a piece of text into a numerical feature vector. It simplifies text data by discarding information about the order and structure of words, focusing only on the frequency of words in the document. Here's how the Bag of Words model works:

1. Tokenization:

   • The first step is to break down a document or piece of text into individual words or tokens. This process is called tokenization.

2. Vocabulary Construction:

   • Create a vocabulary, which is a unique set of all the words present in the entire dataset. Each unique word in the vocabulary is assigned a unique index.

3. Vectorization:

   • Represent each document as a vector in the space of the vocabulary. The length of the vector is the size of the vocabulary, and each element of the vector corresponds to the count of the corresponding word in the document.

   • For example, if the vocabulary consists of ["apple", "orange", "banana"], and a document is "apple orange orange banana," the vector representation would be [1, 2, 1].

4. Sparse Matrix:

   • Since most documents only contain a small subset of the words in the vocabulary, the resulting vectors are usually sparse, with many zero values.

Let's consider a simple example:

Example: Suppose we have a collection of three documents:

1. Document 1: "The cat in the hat."
2. Document 2: "The quick brown fox."
3. Document 3: "The hat is black."

Step 1: Tokenization:

Document 1: ["The", "cat", "in", "the", "hat"] Document 2: ["The", "quick", "brown", "fox"] Document 3: ["The", "hat", "is", "black"]

Step 2: Vocabulary Construction:

Vocabulary: ["The", "cat", "in", "hat", "quick", "brown", "fox", "is", "black"]
Step 3: Vectorization:
Vector representation:
Document 1: [1, 1, 1, 1, 0, 0, 0, 0, 0]
Document 2: [1, 0, 0, 0, 1, 1, 1, 0, 0]
Document 3: [1, 0, 0, 1, 0, 0, 0, 1, 1]

In this way, each document is represented as a sparse vector, and the Bag of Words model captures the frequency of each word across the entire corpus. While BoW is a simple and effective method for text representation, it does not consider the order or structure of words, which may limit its performance in capturing more complex language patterns.