Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/5245#discussion_r27925704
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/feature/PolynomialMapper.scala ---
@@ -0,0 +1,137 @@
+/*
+ * 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.annotation.AlphaComponent
+import org.apache.spark.ml.UnaryTransformer
+import org.apache.spark.ml.param.{IntParam, ParamMap}
+import org.apache.spark.mllib.linalg._
+import org.apache.spark.sql.types.DataType
+
+/**
+ * :: AlphaComponent ::
+ * Polynomially expand a vector into a larger one.
+ */
+@AlphaComponent
+class PolynomialMapper extends UnaryTransformer[Vector, Vector,
PolynomialMapper] {
+
+ /**
+ * The polynomial degree to expand, which should be larger than or equal
to 1.
+ * @group param
+ */
+ val degree = new IntParam(this, "degree", "the polynomial degree to
expand", Some(1))
+
+ /** @group getParam */
+ def getDegree: Int = get(degree)
+
+ /** @group setParam */
+ def setDegree(value: Int): this.type = set(degree, value)
+
+ override protected def createTransformFunc(paramMap: ParamMap): Vector
=> Vector = {
+ PolynomialMapper.transform(getDegree)
+ }
+
+ override protected def outputDataType: DataType = new VectorUDT()
+}
+
+object PolynomialMapper {
+ /**
+ * The number that combines k items from N items without repeat, i.e.
the binomial coefficient.
+ */
+ private def binomialCoefficient(N: Int, k: Int): Int = {
+ (N - k + 1 to N).product / (1 to k).product
+ }
+
+ /**
+ * The number of monomials of a `numVariables` vector after expanding at
a specific polynomial
+ * degree `degree`.
+ */
+ private def numMonomials(degree: Int, numVariables: Int): Int = {
+ binomialCoefficient(numVariables + degree - 1, degree)
+ }
+
+ /**
+ * The number of monomials of a `numVariables` vector after expanding
from polynomial degree 1 to
+ * polynomial degree `degree`.
+ */
+ private def numExpandedDims(degree: Int, numVariables: Int): Int = {
+ binomialCoefficient(numVariables + degree, numVariables) - 1
+ }
+
+ /**
+ * Multiply two polynomials, the first is the original vector, i.e. the
expanded vector with
+ * degree 1, while the second is the expanded vector with degree
`currDegree - 1`. A new expanded
+ * vector with degree `currDegree` will be generated after the function
call.
+ *
+ * @param lhs original vector with degree 1
+ * @param rhs expanded vector with degree `currDegree - 1`
+ * @param nDim the dimension of original vector
+ * @param currDegree the polynomial degree that need to be achieved
+ */
+ private def expandVector(lhs: Vector, rhs: Vector, nDim: Int,
currDegree: Int): Vector = {
+ (lhs, rhs) match {
+ case (l: DenseVector, r: DenseVector) =>
+ val rLen = rhs.size
+ val allExpansions = l.toArray.zipWithIndex.flatMap { case (lVal,
lIdx) =>
+ val numToKeep = numMonomials(currDegree - 1, nDim - lIdx)
+ r.toArray.slice(rLen - numToKeep, rLen).map(rVal => lVal * rVal)
+ }
+ Vectors.dense(allExpansions)
+
+ case (SparseVector(lLen, lIdx, lVal), SparseVector(rLen, rIdx,
rVal)) =>
+ val len = numMonomials(currDegree, nDim)
+ var numToKeepCum = 0
+ val allExpansions = lVal.zip(lIdx).flatMap { case (lv, li) =>
+ val numToKeep = numMonomials(currDegree - 1, nDim - li)
+ val currExpansions = rVal.zip(rIdx).map { case (rv, ri) =>
+ val realIdx = ri - (rLen - numToKeep)
+ (if (realIdx >= 0) lv * rv else 0.0, numToKeepCum + realIdx)
+ }
+ numToKeepCum += numToKeep
+ currExpansions
+ }.filter(_._1 != 0.0)
+ Vectors.sparse(len, allExpansions.map(_._2),
allExpansions.map(_._1))
+
+ case _ => throw new Exception("vector types are not match.")
+ }
+ }
+
+ /**
+ * Transform a vector of variables into a larger vector which stores the
polynomial expansion from
+ * degree 1 to degree `degree`.
+ */
+ private def transform(degree: Int)(feature: Vector): Vector = {
+ val nDim = feature.size
+ feature match {
+ case f: DenseVector =>
+ (2 to degree).foldLeft(Array(feature.copy)) { (vectors,
currDegree) =>
--- End diff --
The implementation is too expensive. We already know the output size and it
should be easy to fill in the values one by one.
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