Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/2061#discussion_r16504078
--- Diff: docs/mllib-feature-extraction.md ---
@@ -7,9 +7,87 @@ displayTitle: <a href="mllib-guide.html">MLlib</a> -
Feature Extraction
* Table of contents
{:toc}
+
+## TF-IDF
+
+[Term frequency-inverse document frequency
(TF-IDF)](http://en.wikipedia.org/wiki/Tf%E2%80%93idf) is a feature
+vectorization method widely used in text mining to reflect the importance
of a term to a document in the corpus.
+Denote a term by `$t$`, a document by `$d$`, and the corpus by `$D$`.
+Term frequency `$TF(t, d)$` is the number of times that term `$t$` appears
in document `$d$`.
+And document frequency `$DF(t, D)$` is the number of documents that
contains term `$t$`.
+If we only use term frequency to measure the importance, it is very easy
to over-emphasize terms that
+appear very often but carry little information about the document, e.g.,
"a", "the", and "of".
+If a term appears very often across the corpus, it means it doesn't carry
special information about
+a particular document.
+Inverse document frequency is a numerical measure of how much information
a term provides:
+`\[
+IDF(t, D) = \log \frac{|D| + 1}{DF(t, D) + 1},
+\]`
+where `$|D|$` is the total number of documents in the corpus.
+Since logarithm is used, if a term appears in all documents, its IDF value
becomes 0.
+Note that a smoothing term is applied to avoid dividing by zero for terms
outside the corpus.
+The TF-IDF measure is simply the product of TF and IDF:
+`\[
+TFIDF(t, d, D) = TF(t, d) \cdot IDF(t, D).
+\]`
+There are several variants on the definition of term frequency and
document frequency.
+In MLlib, we separate TF and IDF to make them flexible.
+
+Our implementation of term frequency utilizes the
+[hashing trick](http://en.wikipedia.org/wiki/Feature_hashing).
+A raw feature is mapped into an index (term) by applying a hash function.
+Then term frequencies are calculated based on the mapped indices.
+This approach saves the global term-to-index map, which is expensive for a
large corpus,
+but it suffers from hash collision, where different raw features may
become the same term after hashing.
+To reduce the chance of collision, we can increase the target feature
dimension, i.e.,
+the number of buckets of the hash table.
--- End diff --
We use `2^20`. I will mention the default value.
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