What does tf-idf mean?
Tf-idf stands for term frequency-inverse document frequency, and the tf-idf weight is a weight often used in information retrieval and text mining. This weight is a statistical measure used to evaluate how important a word is to a document in a collection or corpus. The importance increases proportionally to the number of times a word appears in the document but is offset by the frequency of the word in the corpus. Variations of the tf-idf weighting scheme are often used by search engines as a central tool in scoring and ranking a document's relevance given a user query.
One of the simplest ranking functions is computed by summing the tf-idf for each query term; many more sophisticated ranking functions are variants of this simple model.
Tf-idf can be successfully used for stop-words filtering in various subject fields including text summarization and classification.
To learn more about tf-idf or the topics of information retrieval and text mining, we highly recommend Bruce Croft's practical tutorial Search Engines: Information Retrieval in Practice
How to Compute:
Typically, the tf-idf weight is composed by two terms: the first computes the normalized Term Frequency (TF), aka. the number of times a word appears in a document, divided by the total number of words in that document; the second term is the Inverse Document Frequency (IDF), computed as the logarithm of the number of the documents in the corpus divided by the number of documents where the specific term appears.
TF: Term Frequency, which measures how frequently a term occurs in a document. Since every document is different in length, it is possible that a term would appear much more times in long documents than shorter ones. Thus, the term frequency is often divided by the document length (aka. the total number of terms in the document) as a way of normalization:
IDF: Inverse Document Frequency, which measures how important a term is. While computing TF, all terms are considered equally important. However it is known that certain terms, such as "is", "of", and "that", may appear a lot of times but have little importance. Thus we need to weigh down the frequent terms while scale up the rare ones, by computing the following:
See below for a simple example.
Example:
Consider a document containing 100 words wherein the word cat appears 3 times. The term frequency (i.e., tf) for cat is then (3 / 100) = 0.03. Now, assume we have 10 million documents and the word cat appears in one thousand of these. Then, the inverse document frequency (i.e., idf) is calculated as log(10,000,000 / 1,000) = 4. Thus, the Tf-idf weight is the product of these quantities: 0.03 * 4 = 0.12.
More Resources:
For more information, please refer to some great textbooks on tf-idf and information retrieval
An open-source Python implementation of Tf-idf
References:
K. Sparck Jones. "A statistical interpretation of term specificity and its application in retrieval". Journal of Documentation, 28 (1). 1972.
G. Salton and Edward Fox and Wu Harry Wu. "Extended Boolean information retrieval". Communications of the ACM, 26 (11). 1983.
G. Salton and M. J. McGill. "Introduction to modern information retrieval". 1983
G. Salton and C. Buckley. "Term-weighting approaches in automatic text retrieval". Information Processing & Management, 24 (5). 1988.
H. Wu and R. Luk and K. Wong and K. Kwok. "Interpreting TF-IDF term weights as making relevance decisions". ACM Transactions on Information Systems, 26 (3). 2008.
TF(t) = (Number of times term t appears in a document) / (Total number of terms in the document).
IDF(t) = log_e(Total number of documents / Number of documents with term t in it).
