Github user holdenk commented on a diff in the pull request:
https://github.com/apache/spark/pull/12957#discussion_r62556107
--- 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.
**TF**: Both `HashingTF` and `CountVectorizer` can be used to generate the
term frequency vectors.
`HashingTF` is a `Transformer` which takes sets of terms and converts
those sets into
fixed-length feature vectors. In text processing, a "set of terms" might
be a bag of words.
-The algorithm combines Term Frequency (TF) counts with the
-[hashing trick](http://en.wikipedia.org/wiki/Feature_hashing) for
dimensionality reduction.
+`HashingTF` 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 avoids the need
to compute a global
+term-to-index map, which can be expensive for a large corpus, but it
suffers from potential hash
+collisions, 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. The default feature dimension is `$2^{20} = 1,048,576$`.
`CountVectorizer` converts text documents to vectors of term counts. Refer
to [CountVectorizer
](ml-features.html#countvectorizer) for more details.
**IDF**: `IDF` is an `Estimator` which is fit on a dataset and produces an
`IDFModel`. The
-`IDFModel` takes feature vectors (generally created from `HashingTF` or
`CountVectorizer`) and scales each column.
-Intuitively, it down-weights columns which appear frequently in a corpus.
+`IDFModel` takes feature vectors (generally created from `HashingTF` or
`CountVectorizer`) and
+scales each column. Intuitively, it down-weights columns which appear
frequently in a corpus.
+
+Please refer to the [MLlib user guide on
TF-IDF](mllib-feature-extraction.html#tf-idf) for RDD-based API.
--- End diff --
I don't know if we want to link the RDD based API given we are deprecating
it?
---
If your project is set up for it, you can reply to this email and have your
reply appear on GitHub as well. If your project does not have this feature
enabled and wishes so, or if the feature is enabled but not working, please
contact infrastructure at [email protected] or file a JIRA ticket
with INFRA.
---
---------------------------------------------------------------------
To unsubscribe, e-mail: [email protected]
For additional commands, e-mail: [email protected]
