# Cosine Similarity and Notion of Closeness

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To formalize the intuition of closeness between two word (vectors), we will
formally introduce the concept of cosine similarity.

## Motivation

Cosine similarity is a commonly used similarity measure in natural language
processing (NLP) tasks such as text classification, information retrieval, and
recommendation systems. The motivation behind using cosine similarity in NLP is
that it provides a way to compare the similarity of two documents, sentences or
words regardless of their size or the frequency of the terms they contain.

In NLP, text data is typically represented as high-dimensional vectors where
each dimension represents a term or a word in a corpus. The vector contains the
frequency or occurrence of each term or word in the text data. Cosine similarity
calculates the angle between two vectors and provides a measure of similarity
between them, regardless of their length or frequency. This makes it
particularly useful for comparing the similarity of two documents that have
different lengths or that use different words to express similar meanings.

## Table of Contents

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