【Scala】MinHash for Jaccard Distance

来源：LSHMinHash

import org.apache.spark.ml.feature.MinHashLSH
import org.apache.spark.ml.linalg.Vectors
import org.apache.spark.sql.SparkSession
import org.apache.spark.sql.functions.col

val dfA = spark.createDataframe(Seq(
  (0, Vectors.sparse(6, Seq((0, 1.0), (1, 1.0), (2, 1.0)))),
  (1, Vectors.sparse(6, Seq((2, 1.0), (3, 1.0), (4, 1.0)))),
  (2, Vectors.sparse(6, Seq((0, 1.0), (2, 1.0), (4, 1.0))))
)).toDF("id", "features")

val dfB = spark.createDataframe(Seq(
  (3, Vectors.sparse(6, Seq((1, 1.0), (3, 1.0), (5, 1.0)))),
  (4, Vectors.sparse(6, Seq((2, 1.0), (3, 1.0), (5, 1.0)))),
  (5, Vectors.sparse(6, Seq((1, 1.0), (2, 1.0), (4, 1.0))))
)).toDF("id", "features")

val key = Vectors.sparse(6, Seq((1, 1.0), (3, 1.0)))

val mh = new MinHashLSH()
  .setNumHashTables(5)
  .setInputCol("features")
  .setOutputCol("hashes")

val model = mh.fit(dfA)

// Feature Transformation
println("The hashed dataset where hashed values are stored in the column 'hashes':")
model.transform(dfA).show(false)

// Compute the locality sensitive hashes for the input rows, then perform approximate
// similarity join.
// We could avoid computing hashes by passing in the already-transformed dataset, e.g.
// `model.approxSimilarityJoin(transformedA, transformedB, 0.6)`
println("Approximately joining dfA and dfB on Jaccard distance smaller than 0.6:")
model.approxSimilarityJoin(dfA, dfB, 0.6, "JaccardDistance")
  .select(col("datasetA.id").alias("idA"),
    col("datasetB.id").alias("idB"),
    col("JaccardDistance")).show()

// Compute the locality sensitive hashes for the input rows, then perform approximate nearest
// neighbor search.
// We could avoid computing hashes by passing in the already-transformed dataset, e.g.
// `model.approxNearestNeighbors(transformedA, key, 2)`
// It may return less than 2 rows when not enough approximate near-neighbor candidates are
// found.
println("Approximately searching dfA for 2 nearest neighbors of the key:")
model.approxNearestNeighbors(dfA, key, 2).show()

密集向量和稀疏向量的区别
密集向量的值是一个普通的Double数组，而稀疏向量由两个并列的数组indices和values组成。

例如：

向量(1.0, 0.0, 1.0, 3.0)

用密集格式表示为

[1.0, 0.0, 1.0, 3.0]

用稀疏格式表示为

Vectors.sparse(4,[0,2,3],[1.0, 1.0, 3.0]) 或者

Vectors.sparse(4, Seq((0, 1.0), (2, 1.0), (3, 3.0)))

其中，各个部分的含义如下表