Explain with suitable example how the Term Frequency

Term Frequency-Inverse Document Frequency (TF-IDF) is a statistical measure used in information retrieval and text mining to evaluate the importance of a term within a document relative to a collection of documents. It helps in quantifying the relevance of a term in a document within a larger corpus.
Example:
Let’s consider a corpus of documents consisting of articles from a news website. We want to retrieve articles related to “climate change” from this corpus. We’ll use TF-IDF to rank the documents based on their relevance to the search query.

1. Term Frequency (TF):
   • Term Frequency measures how frequently a term occurs in a document relative to the total number of terms in the document.
   • Example: Suppose we have a document containing 100 words, and the term “climate change” appears 5 times in that document. The term frequency of “climate change” in this document is TF=5100=0.05TF=1005​=0.05.
2. Inverse Document Frequency (IDF):
   • Inverse Document Frequency measures the rarity of a term across the entire corpus of documents. It’s calculated as the logarithm of the ratio of the total number of documents to the number of documents containing the term.
   • Example: If there are 1,000 documents in the corpus and the term “climate change” appears in 100 of them, then the IDF of “climate change” is IDF=log⁡(1000100)=log⁡(10)=1IDF=log(1001000​)=log(10)=1.
3. TF-IDF Score:
   • The TF-IDF score is calculated by multiplying the term frequency (TF) and the inverse document frequency (IDF).
   • Example: If the TF of “climate change” in a document is 0.05 and the IDF is 1, then the TF-IDF score for “climate change” in that document is TF-IDF=0.05×1=0.05TF-IDF=0.05×1=0.05.

Application in Information Retrieval:

• Ranking Documents: Documents containing rare terms that are highly relevant to the search query will have higher TF-IDF scores, thus ranking them higher in the search results.
• Filtering Stop Words: Common words like “the,” “and,” “is” have high term frequencies but low IDF scores, so they receive low TF-IDF scores and are filtered out from search results.
• Identifying Key Terms: Terms with high TF-IDF scores are likely to be important keywords or phrases that capture the essence of a document’s content.