[SPARK-18408][ML] API Improvements for LSH

## What changes were proposed in this pull request?

(1) Change output schema to `Array of Vector` instead of `Vectors`
(2) Use `numHashTables` as the dimension of Array
(3) Rename `RandomProjection` to `BucketedRandomProjectionLSH`, `MinHash` to `MinHashLSH`
(4) Make `randUnitVectors/randCoefficients` private
(5) Make Multi-Probe NN Search and `hashDistance` private for future discussion

Saved for future PRs:
(1) AND-amplification and `numHashFunctions` as the dimension of Vector are saved for a future PR.
(2) `hashDistance` and MultiProbe NN Search needs more discussion. The current implementation is just a backward compatible one.

## How was this patch tested?
Related unit tests are modified to make sure the performance of LSH are ensured, and the outputs of the APIs meets expectation.

Author: Yun Ni <yunn@uber.com>
Author: Yunni <Euler57721@gmail.com>

Closes #15874 from Yunni/SPARK-18408-yunn-api-improvements.

(cherry picked from commit 05f7c6f)
Signed-off-by: Joseph K. Bradley <joseph@databricks.com>

Author: Yun Ni

…/spark/ml/feature/RandomProjection.scala …eature/BucketedRandomProjectionLSH.scalamllib/src/main/scala/org/apache/spark/ml/feature/RandomProjection.scala renamed to mllib/src/main/scala/org/apache/spark/ml/feature/BucketedRandomProjectionLSH.scala mllib/src/main/scala/org/apache/spark/ml/feature/RandomProjection.scala renamed to mllib/src/main/scala/org/apache/spark/ml/feature/BucketedRandomProjectionLSH.scala

@@ -34,9 +34,9 @@ import org.apache.spark.sql.types.StructType
 /**
  * :: Experimental ::
  *
- * Params for [[RandomProjection]].
+ * Params for [[BucketedRandomProjectionLSH]].
  */
-private[ml] trait RandomProjectionParams extends Params {
+private[ml] trait BucketedRandomProjectionLSHParams extends Params {
 
   /**
    * The length of each hash bucket, a larger bucket lowers the false negative rate. The number of
@@ -58,8 +58,8 @@ private[ml] trait RandomProjectionParams extends Params {
 /**
  * :: Experimental ::
  *
- * Model produced by [[RandomProjection]], where multiple random vectors are stored. The vectors
- * are normalized to be unit vectors and each vector is used in a hash function:
+ * Model produced by [[BucketedRandomProjectionLSH]], where multiple random vectors are stored. The
+ * vectors are normalized to be unit vectors and each vector is used in a hash function:
  *    `h_i(x) = floor(r_i.dot(x) / bucketLength)`
  * where `r_i` is the i-th random unit vector. The number of buckets will be `(max L2 norm of input
  * vectors) / bucketLength`.
@@ -68,18 +68,19 @@ private[ml] trait RandomProjectionParams extends Params {
  */
 @Experimental
 @Since("2.1.0")
-class RandomProjectionModel private[ml] (
+class BucketedRandomProjectionLSHModel private[ml](
     override val uid: String,
-    @Since("2.1.0") val randUnitVectors: Array[Vector])
-  extends LSHModel[RandomProjectionModel] with RandomProjectionParams {
+    private[ml] val randUnitVectors: Array[Vector])
+  extends LSHModel[BucketedRandomProjectionLSHModel] with BucketedRandomProjectionLSHParams {
 
   @Since("2.1.0")
-  override protected[ml] val hashFunction: (Vector) => Vector = {
+  override protected[ml] val hashFunction: Vector => Array[Vector] = {
     key: Vector => {
       val hashValues: Array[Double] = randUnitVectors.map({
         randUnitVector => Math.floor(BLAS.dot(key, randUnitVector) / $(bucketLength))
       })
-      Vectors.dense(hashValues)
+      // TODO: Output vectors of dimension numHashFunctions in SPARK-18450
+      hashValues.map(Vectors.dense(_))
     }
   }
 
@@ -89,27 +90,29 @@ class RandomProjectionModel private[ml] (
   }
 
   @Since("2.1.0")
-  override protected[ml] def hashDistance(x: Vector, y: Vector): Double = {
+  override protected[ml] def hashDistance(x: Seq[Vector], y: Seq[Vector]): Double = {
     // Since it's generated by hashing, it will be a pair of dense vectors.
-    x.toDense.values.zip(y.toDense.values).map(pair => math.abs(pair._1 - pair._2)).min
+    x.zip(y).map(vectorPair => Vectors.sqdist(vectorPair._1, vectorPair._2)).min
   }
 
   @Since("2.1.0")
   override def copy(extra: ParamMap): this.type = defaultCopy(extra)
 
   @Since("2.1.0")
-  override def write: MLWriter = new RandomProjectionModel.RandomProjectionModelWriter(this)
+  override def write: MLWriter = {
+    new BucketedRandomProjectionLSHModel.BucketedRandomProjectionLSHModelWriter(this)
+  }
 }
 
 /**
  * :: Experimental ::
  *
- * This [[RandomProjection]] implements Locality Sensitive Hashing functions for Euclidean
- * distance metrics.
+ * This [[BucketedRandomProjectionLSH]] implements Locality Sensitive Hashing functions for
+ * Euclidean distance metrics.
  *
  * The input is dense or sparse vectors, each of which represents a point in the Euclidean
- * distance space. The output will be vectors of configurable dimension. Hash value in the same
- * dimension is calculated by the same hash function.
+ * distance space. The output will be vectors of configurable dimension. Hash values in the
+ * same dimension are calculated by the same hash function.
  *
  * References:
  *
@@ -121,8 +124,9 @@ class RandomProjectionModel private[ml] (
  */
 @Experimental
 @Since("2.1.0")
-class RandomProjection(override val uid: String) extends LSH[RandomProjectionModel]
-  with RandomProjectionParams with HasSeed {
+class BucketedRandomProjectionLSH(override val uid: String)
+  extends LSH[BucketedRandomProjectionLSHModel]
+    with BucketedRandomProjectionLSHParams with HasSeed {
 
   @Since("2.1.0")
   override def setInputCol(value: String): this.type = super.setInputCol(value)
@@ -131,11 +135,11 @@ class RandomProjection(override val uid: String) extends LSH[RandomProjectionMod
   override def setOutputCol(value: String): this.type = super.setOutputCol(value)
 
   @Since("2.1.0")
-  override def setOutputDim(value: Int): this.type = super.setOutputDim(value)
+  override def setNumHashTables(value: Int): this.type = super.setNumHashTables(value)
 
   @Since("2.1.0")
   def this() = {
-    this(Identifiable.randomUID("random projection"))
+    this(Identifiable.randomUID("brp-lsh"))
   }
 
   /** @group setParam */
@@ -147,15 +151,16 @@ class RandomProjection(override val uid: String) extends LSH[RandomProjectionMod
   def setSeed(value: Long): this.type = set(seed, value)
 
   @Since("2.1.0")
-  override protected[this] def createRawLSHModel(inputDim: Int): RandomProjectionModel = {
+  override protected[this] def createRawLSHModel(
+    inputDim: Int): BucketedRandomProjectionLSHModel = {
     val rand = new Random($(seed))
     val randUnitVectors: Array[Vector] = {
-      Array.fill($(outputDim)) {
+      Array.fill($(numHashTables)) {
         val randArray = Array.fill(inputDim)(rand.nextGaussian())
         Vectors.fromBreeze(normalize(breeze.linalg.Vector(randArray)))
       }
     }
-    new RandomProjectionModel(uid, randUnitVectors)
+    new BucketedRandomProjectionLSHModel(uid, randUnitVectors)
   }
 
   @Since("2.1.0")
@@ -169,23 +174,25 @@ class RandomProjection(override val uid: String) extends LSH[RandomProjectionMod
 }
 
 @Since("2.1.0")
-object RandomProjection extends DefaultParamsReadable[RandomProjection] {
+object BucketedRandomProjectionLSH extends DefaultParamsReadable[BucketedRandomProjectionLSH] {
 
   @Since("2.1.0")
-  override def load(path: String): RandomProjection = super.load(path)
+  override def load(path: String): BucketedRandomProjectionLSH = super.load(path)
 }
 
 @Since("2.1.0")
-object RandomProjectionModel extends MLReadable[RandomProjectionModel] {
+object BucketedRandomProjectionLSHModel extends MLReadable[BucketedRandomProjectionLSHModel] {
 
   @Since("2.1.0")
-  override def read: MLReader[RandomProjectionModel] = new RandomProjectionModelReader
+  override def read: MLReader[BucketedRandomProjectionLSHModel] = {
+    new BucketedRandomProjectionLSHModelReader
+  }
 
   @Since("2.1.0")
-  override def load(path: String): RandomProjectionModel = super.load(path)
+  override def load(path: String): BucketedRandomProjectionLSHModel = super.load(path)
 
-  private[RandomProjectionModel] class RandomProjectionModelWriter(instance: RandomProjectionModel)
-    extends MLWriter {
+  private[BucketedRandomProjectionLSHModel] class BucketedRandomProjectionLSHModelWriter(
+    instance: BucketedRandomProjectionLSHModel) extends MLWriter {
 
     // TODO: Save using the existing format of Array[Vector] once SPARK-12878 is resolved.
     private case class Data(randUnitVectors: Matrix)
@@ -203,20 +210,22 @@ object RandomProjectionModel extends MLReadable[RandomProjectionModel] {
     }
   }
 
-  private class RandomProjectionModelReader extends MLReader[RandomProjectionModel] {
+  private class BucketedRandomProjectionLSHModelReader
+    extends MLReader[BucketedRandomProjectionLSHModel] {
 
     /** Checked against metadata when loading model */
-    private val className = classOf[RandomProjectionModel].getName
+    private val className = classOf[BucketedRandomProjectionLSHModel].getName
 
-    override def load(path: String): RandomProjectionModel = {
+    override def load(path: String): BucketedRandomProjectionLSHModel = {
       val metadata = DefaultParamsReader.loadMetadata(path, sc, className)
 
       val dataPath = new Path(path, "data").toString
       val data = sparkSession.read.parquet(dataPath)
       val Row(randUnitVectors: Matrix) = MLUtils.convertMatrixColumnsToML(data, "randUnitVectors")
         .select("randUnitVectors")
         .head()
-      val model = new RandomProjectionModel(metadata.uid, randUnitVectors.rowIter.toArray)
+      val model = new BucketedRandomProjectionLSHModel(metadata.uid,
+        randUnitVectors.rowIter.toArray)
 
       DefaultParamsReader.getAndSetParams(model, metadata)
       model