Github user hhbyyh commented on a diff in the pull request:
https://github.com/apache/spark/pull/12957#discussion_r62627341
--- Diff: docs/ml-features.md ---
@@ -18,27 +18,58 @@ This section covers algorithms for working with
features, roughly divided into t
# Feature Extractors
-## TF-IDF (HashingTF and IDF)
-
-[Term Frequency-Inverse Document Frequency
(TF-IDF)](http://en.wikipedia.org/wiki/Tf%E2%80%93idf) is a common text
pre-processing step. In Spark ML, TF-IDF is separate into two parts: TF
(+hashing) and IDF.
+## 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 `$d$`, while
+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 `spark.mllib`, we separate TF and IDF to make them flexible.
--- End diff --
I think we can just say "in MLlib", sounds good?
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