Efficient cosine similarity computation

[Stevens, Clay]

There are several ways I can compute the cosine similarities between a Spark ML 
vector to each ML vector in a Spark DataFrame column then sorting for the 
highest results.  However, I can't come up with a method that is faster than 
replacing the `/data/` in a Spark ML Word2Vec model, then using 
`.findSynonyms()`.  The problem is the Word2Vec model is held entirely in the 
driver which can cause memory issues if the data set I want to compare to gets 
too big.

1. Is there a more efficient method than the ones I have shown below?
2. Could the data for the Word2Vec model be distributed across the cluster?
3. Could the the `.findSynonyms()` [Scala 
code](https://github.com/apache/spark/blob/master/mllib/src/main/scala/org/apache/spark/mllib/feature/Word2Vec.scala#L571toL619)
 be modified to make a spark sql function that can operate efficiently over a 
whole Spark DataFrame?


Methods I have tried:

#1 rdd function:
```

    # vecIn = vector of same dimensions as 'vectors' column
    def cosSim(row, vecIn):
        return (
            tuple(( Vectors.dense( Vectors.dense(row.vectors.dot(vecIn)) /
                        (Vectors.dense(np.sqrt(row.vectors.dot(row.vectors))) *
                          Vectors.dense(np.sqrt(vecIn.dot(vecIn)))))
                ).toArray().tolist()))

    df.rdd.map(lambda row: cosSim(row, 
vecIn)).toDF(['CosSim']).show(truncate=False)
```

#2  `.toIndexedRowMatrix().columnSimilarities()` then filter the results (not 
shown):

```

    spark.createDataFrame(
        IndexedRowMatrix(df.rdd.map(lambda row: (row.vectors.toArray())))
        .toBlockMatrix()
        .transpose()
        .toIndexedRowMatrix()
        .columnSimilarities()
        .entries)
```

#3 replace Word2Vec model `/data/` with my own, then load 'revised' model and 
use `.findSynonyms()`:
```
    df_words_vectors.schema
    ## 
StructType(List(StructField(word,StringType,true),StructField(vector,ArrayType(FloatType,true),true)))

    df_words_vectors.write.parquet("exiting_Word2Vec_model/data/", 
mode='overwrite')

    new_Word2Vec_model = Word2VecModel.load("exiting_Word2Vec_model")

    ## vecIn = vector of same dimensions as 'vector' column in DataFrame saved 
over Word2Vec model /data/
    new_Word2Vec_model.findSynonyms(vecIn, 20).show()
```


Clay Stevens