[SPARK-2842][MLlib]Word2Vec documentation

mengxr
Documentation for Word2Vec

Author: Liquan Pei <liquanpei@gmail.com>

Closes #2003 from Ishiihara/Word2Vec-doc and squashes the following commits:

4ff11d4 [Liquan Pei] minor fix
8d7458f [Liquan Pei] code reformat
6df0dcb [Liquan Pei] add Word2Vec documentation

docs/mllib-feature-extraction.md

@@ -9,4 +9,65 @@ displayTitle: <a href="mllib-guide.html">MLlib</a> - Feature Extraction
 
 ## Word2Vec 
 
-## TFIDF
+Word2Vec computes distributed vector representation of words. The main advantage of the distributed
+representations is that similar words are close in the vector space, which makes generalization to 
+novel patterns easier and model estimation more robust. Distributed vector representation is 
+showed to be useful in many natural language processing applications such as named entity 
+recognition, disambiguation, parsing, tagging and machine translation.
+
+### Model
+
+In our implementation of Word2Vec, we used skip-gram model. The training objective of skip-gram is
+to learn word vector representations that are good at predicting its context in the same sentence. 
+Mathematically, given a sequence of training words `$w_1, w_2, \dots, w_T$`, the objective of the
+skip-gram model is to maximize the average log-likelihood 
+`\[
+\frac{1}{T} \sum_{t = 1}^{T}\sum_{j=-k}^{j=k} \log p(w_{t+j} | w_t)
+\]`
+where $k$ is the size of the training window.  
+
+In the skip-gram model, every word $w$ is associated with two vectors $u_w$ and $v_w$ which are 
+vector representations of $w$ as word and context respectively. The probability of correctly 
+predicting word $w_i$ given word $w_j$ is determined by the softmax model, which is 
+`\[
+p(w_i | w_j ) = \frac{\exp(u_{w_i}^{\top}v_{w_j})}{\sum_{l=1}^{V} \exp(u_l^{\top}v_{w_j})}
+\]`
+where $V$ is the vocabulary size. 
+
+The skip-gram model with softmax is expensive because the cost of computing $\log p(w_i | w_j)$ 
+is proportional to $V$, which can be easily in order of millions. To speed up training of Word2Vec, 
+we used hierarchical softmax, which reduced the complexity of computing of $\log p(w_i | w_j)$ to
+$O(\log(V))$
+
+### Example 
+
+The example below demonstrates how to load a text file, parse it as an RDD of `Seq[String]`,
+construct a `Word2Vec` instance and then fit a `Word2VecModel` with the input data. Finally,
+we display the top 40 synonyms of the specified word. To run the example, first download
+the [text8](http://mattmahoney.net/dc/text8.zip) data and extract it to your preferred directory.
+Here we assume the extracted file is `text8` and in same directory as you run the spark shell.  
+
+<div class="codetabs">
+<div data-lang="scala">
+{% highlight scala %}
+import org.apache.spark._
+import org.apache.spark.rdd._
+import org.apache.spark.SparkContext._
+import org.apache.spark.mllib.feature.Word2Vec
+
+val input = sc.textFile("text8").map(line => line.split(" ").toSeq)
+
+val word2vec = new Word2Vec()
+
+val model = word2vec.fit(input)
+
+val synonyms = model.findSynonyms("china", 40)
+
+for((synonym, cosineSimilarity) <- synonyms) {
+  println(s"$synonym $cosineSimilarity")
+}
+{% endhighlight %}
+</div>
+</div>
+
+## TFIDF
\ No newline at end of file