[SPARK-13028] [ML] Add MaxAbsScaler to ML.feature as a transformer

jira: https://issues.apache.org/jira/browse/SPARK-13028
MaxAbsScaler works in a very similar way as MinMaxScaler, but scales in a way that the training data lies within the range [-1, 1] by dividing through the largest maximum value in each feature. The motivation to use this scaling includes robustness to very small standard deviations of features and preserving zero entries in sparse data.

Unlike StandardScaler and MinMaxScaler, MaxAbsScaler does not shift/center the data, and thus does not destroy any sparsity.

Something similar from sklearn:
http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.MaxAbsScaler.html#sklearn.preprocessing.MaxAbsScaler

Author: Yuhao Yang <hhbyyh@gmail.com>

Closes #10939 from hhbyyh/maxabs and squashes the following commits:

fd8bdcd [Yuhao Yang] add tag and some optimization on fit
648fced [Yuhao Yang] Merge remote-tracking branch 'upstream/master' into maxabs
75bebc2 [Yuhao Yang] Merge remote-tracking branch 'upstream/master' into maxabs
cb10bb6 [Yuhao Yang] remove minmax
91ef8f3 [Yuhao Yang] ut added
8ab0747 [Yuhao Yang] Merge remote-tracking branch 'upstream/master' into maxabs
a9215b5 [Yuhao Yang] max abs scaler

mllib/src/main/scala/org/apache/spark/ml/feature/MaxAbsScaler.scala

+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.spark.ml.feature
+
+import org.apache.hadoop.fs.Path
+
+import org.apache.spark.annotation.{Experimental, Since}
+import org.apache.spark.ml.{Estimator, Model}
+import org.apache.spark.ml.param.{ParamMap, Params}
+import org.apache.spark.ml.param.shared.{HasInputCol, HasOutputCol}
+import org.apache.spark.ml.util._
+import org.apache.spark.mllib.linalg.{Vector, Vectors, VectorUDT}
+import org.apache.spark.mllib.stat.Statistics
+import org.apache.spark.sql._
+import org.apache.spark.sql.functions._
+import org.apache.spark.sql.types.{StructField, StructType}
+
+/**
+ * Params for [[MaxAbsScaler]] and [[MaxAbsScalerModel]].
+ */
+private[feature] trait MaxAbsScalerParams extends Params with HasInputCol with HasOutputCol {
+
+   /** Validates and transforms the input schema. */
+  protected def validateAndTransformSchema(schema: StructType): StructType = {
+    validateParams()
+    val inputType = schema($(inputCol)).dataType
+    require(inputType.isInstanceOf[VectorUDT],
+      s"Input column ${$(inputCol)} must be a vector column")
+    require(!schema.fieldNames.contains($(outputCol)),
+      s"Output column ${$(outputCol)} already exists.")
+    val outputFields = schema.fields :+ StructField($(outputCol), new VectorUDT, false)
+    StructType(outputFields)
+  }
+}
+
+/**
+ * :: Experimental ::
+ * Rescale each feature individually to range [-1, 1] by dividing through the largest maximum
+ * absolute value in each feature. It does not shift/center the data, and thus does not destroy
+ * any sparsity.
+ */
+@Experimental
+class MaxAbsScaler @Since("2.0.0") (override val uid: String)
+  extends Estimator[MaxAbsScalerModel] with MaxAbsScalerParams with DefaultParamsWritable {
+
+  @Since("2.0.0")
+  def this() = this(Identifiable.randomUID("maxAbsScal"))
+
+  /** @group setParam */
+  def setInputCol(value: String): this.type = set(inputCol, value)
+
+  /** @group setParam */
+  def setOutputCol(value: String): this.type = set(outputCol, value)
+
+  override def fit(dataset: DataFrame): MaxAbsScalerModel = {
+    transformSchema(dataset.schema, logging = true)
+    val input = dataset.select($(inputCol)).map { case Row(v: Vector) => v }
+    val summary = Statistics.colStats(input)
+    val minVals = summary.min.toArray
+    val maxVals = summary.max.toArray
+    val n = minVals.length
+    val maxAbs = Array.tabulate(n) { i => math.max(math.abs(minVals(i)), math.abs(maxVals(i))) }
+
+    copyValues(new MaxAbsScalerModel(uid, Vectors.dense(maxAbs)).setParent(this))
+  }
+
+  override def transformSchema(schema: StructType): StructType = {
+    validateAndTransformSchema(schema)
+  }
+
+  override def copy(extra: ParamMap): MaxAbsScaler = defaultCopy(extra)
+}
+
+@Since("1.6.0")
+object MaxAbsScaler extends DefaultParamsReadable[MaxAbsScaler] {
+
+  @Since("1.6.0")
+  override def load(path: String): MaxAbsScaler = super.load(path)
+}
+
+/**
+ * :: Experimental ::
+ * Model fitted by [[MaxAbsScaler]].
+ *
+ */
+@Experimental
+class MaxAbsScalerModel private[ml] (
+    override val uid: String,
+    val maxAbs: Vector)
+  extends Model[MaxAbsScalerModel] with MaxAbsScalerParams with MLWritable {
+
+  import MaxAbsScalerModel._
+
+  /** @group setParam */
+  def setInputCol(value: String): this.type = set(inputCol, value)
+
+  /** @group setParam */
+  def setOutputCol(value: String): this.type = set(outputCol, value)
+
+  override def transform(dataset: DataFrame): DataFrame = {
+    transformSchema(dataset.schema, logging = true)
+    // TODO: this looks hack, we may have to handle sparse and dense vectors separately.
+    val maxAbsUnzero = Vectors.dense(maxAbs.toArray.map(x => if (x == 0) 1 else x))
+    val reScale = udf { (vector: Vector) =>
+      val brz = vector.toBreeze / maxAbsUnzero.toBreeze
+      Vectors.fromBreeze(brz)
+    }
+    dataset.withColumn($(outputCol), reScale(col($(inputCol))))
+  }
+
+  override def transformSchema(schema: StructType): StructType = {
+    validateAndTransformSchema(schema)
+  }
+
+  override def copy(extra: ParamMap): MaxAbsScalerModel = {
+    val copied = new MaxAbsScalerModel(uid, maxAbs)
+    copyValues(copied, extra).setParent(parent)
+  }
+
+  @Since("1.6.0")
+  override def write: MLWriter = new MaxAbsScalerModelWriter(this)
+}
+
+@Since("1.6.0")
+object MaxAbsScalerModel extends MLReadable[MaxAbsScalerModel] {
+
+  private[MaxAbsScalerModel]
+  class MaxAbsScalerModelWriter(instance: MaxAbsScalerModel) extends MLWriter {
+
+    private case class Data(maxAbs: Vector)
+
+    override protected def saveImpl(path: String): Unit = {
+      DefaultParamsWriter.saveMetadata(instance, path, sc)
+      val data = new Data(instance.maxAbs)
+      val dataPath = new Path(path, "data").toString
+      sqlContext.createDataFrame(Seq(data)).repartition(1).write.parquet(dataPath)
+    }
+  }
+
+  private class MaxAbsScalerModelReader extends MLReader[MaxAbsScalerModel] {
+
+    private val className = classOf[MaxAbsScalerModel].getName
+
+    override def load(path: String): MaxAbsScalerModel = {
+      val metadata = DefaultParamsReader.loadMetadata(path, sc, className)
+      val dataPath = new Path(path, "data").toString
+      val Row(maxAbs: Vector) = sqlContext.read.parquet(dataPath)
+        .select("maxAbs")
+        .head()
+      val model = new MaxAbsScalerModel(metadata.uid, maxAbs)
+      DefaultParamsReader.getAndSetParams(model, metadata)
+      model
+    }
+  }
+
+  @Since("1.6.0")
+  override def read: MLReader[MaxAbsScalerModel] = new MaxAbsScalerModelReader
+
+  @Since("1.6.0")
+  override def load(path: String): MaxAbsScalerModel = super.load(path)
+}

mllib/src/test/scala/org/apache/spark/ml/feature/MaxAbsScalerSuite.scala

+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.spark.ml.feature
+
+import org.apache.spark.SparkFunSuite
+import org.apache.spark.ml.util.{DefaultReadWriteTest, MLTestingUtils}
+import org.apache.spark.mllib.linalg.{Vector, Vectors}
+import org.apache.spark.mllib.util.MLlibTestSparkContext
+import org.apache.spark.sql.Row
+
+class MaxAbsScalerSuite extends SparkFunSuite with MLlibTestSparkContext with DefaultReadWriteTest {
+  test("MaxAbsScaler fit basic case") {
+    val data = Array(
+      Vectors.dense(1, 0, 100),
+      Vectors.dense(2, 0, 0),
+      Vectors.sparse(3, Array(0, 2), Array(-2, -100)),
+      Vectors.sparse(3, Array(0), Array(-1.5)))
+
+    val expected: Array[Vector] = Array(
+      Vectors.dense(0.5, 0, 1),
+      Vectors.dense(1, 0, 0),
+      Vectors.sparse(3, Array(0, 2), Array(-1, -1)),
+      Vectors.sparse(3, Array(0), Array(-0.75)))
+
+    val df = sqlContext.createDataFrame(data.zip(expected)).toDF("features", "expected")
+    val scaler = new MaxAbsScaler()
+      .setInputCol("features")
+      .setOutputCol("scaled")
+
+    val model = scaler.fit(df)
+    model.transform(df).select("expected", "scaled").collect()
+      .foreach { case Row(vector1: Vector, vector2: Vector) =>
+      assert(vector1.equals(vector2), s"MaxAbsScaler ut error: $vector2 should be $vector1")
+    }
+
+    // copied model must have the same parent.
+    MLTestingUtils.checkCopy(model)
+  }
+
+  test("MaxAbsScaler read/write") {
+    val t = new MaxAbsScaler()
+      .setInputCol("myInputCol")
+      .setOutputCol("myOutputCol")
+    testDefaultReadWrite(t)
+  }
+
+  test("MaxAbsScalerModel read/write") {
+    val instance = new MaxAbsScalerModel(
+      "myMaxAbsScalerModel", Vectors.dense(1.0, 10.0))
+      .setInputCol("myInputCol")
+      .setOutputCol("myOutputCol")
+    val newInstance = testDefaultReadWrite(instance)
+    assert(newInstance.maxAbs === instance.maxAbs)
+  }
+
+}