# Term Frequency Inverse Document Frequency

## Goal¶

This post aims to introduce term frequency-inverse document frequency as known as TF-IDF, which indicates the importance of the words in a document considering the frequency of them across multiple documents and used for feature creation.

Term Frequency (TF)

Term Frequency can be computed as the number of occurrence of the word $n_{word}$ divided by the total number of words in a document $N_{word}$.

\begin{equation*} TF = \frac{n_{word}}{N_{word}} \end{equation*}

Document Frequency (DF)

Document Frequency can be computed as the number of documents containing the word $n_{doc}$ divided by the number of documents $N_{doc}$.

\begin{equation*} DF = \frac{n_{doc}}{N_{doc}} \end{equation*}

Inverse Document Frequency (IDF)

The inverse document frequency is the inverse of DF.

\begin{equation*} IDF = \frac{N_{doc}}{n_{doc}} \end{equation*}

Practically, to avoid the explosion of IDF and dividing by zero, IDF can be computed by log format with adding 1 to denominator as below.

\begin{equation*} IDF = log(\frac{N_{doc}}{n_{doc}+1}) \end{equation*}

Reference

## Libraries¶

In [18]:
import pandas as pd
from sklearn.feature_extraction.text import TfidfVectorizer


## Create a document¶

In [36]:
documents = ['this is a sample.',
'this is another example. "this" also appears in the second example.']

documents

Out[36]:
['this is a sample.',
'this is another example. "this" also appears in the second example.']

## Apply TF-IDF vectorizer¶

Now applying TF-IDF to each sentence, we will obtain the feature vector for each document accordingly.

In [37]:
vectorizer = TfidfVectorizer()
X = vectorizer.fit_transform(documents)
df_tfidf = pd.DataFrame(X.todense(), columns=vectorizer.get_feature_names())
df_tfidf

Out[37]:
also another appears example in is sample second the this
0 0.00000 0.00000 0.00000 0.00000 0.00000 0.501549 0.704909 0.00000 0.00000 0.501549
1 0.28249 0.28249 0.28249 0.56498 0.28249 0.200994 0.000000 0.28249 0.28249 0.401988
In [38]:
# The highest TF-IDF for each document
df_tfidf.idxmax(axis=1)

Out[38]:
0     sample
1    example
dtype: object
In [39]:
# TF-IDF is zero if the word does not appear in a document
df_tfidf==0

Out[39]:
also another appears example in is sample second the this
0 True True True True True False False True True False
1 False False False False False False True False False False