Github user yinxusen commented on a diff in the pull request:
https://github.com/apache/spark/pull/5245#discussion_r28192764
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/feature/PolynomialMapper.scala ---
@@ -0,0 +1,170 @@
+/*
+ * 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 scala.annotation.tailrec
+
+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 ::
+ * Perform feature expansion in a polynomial space. As said in wikipedia
of Polynomial Expansion,
+ * which is available at
[[http://en.wikipedia.org/wiki/Polynomial_expansion]], "In mathematics, an
+ * expansion of a product of sums expresses it as a sum of products by
using the fact that
+ * multiplication distributes over addition". Take a 2-variable feature
vector as an example:
+ * `(x, y)`, if we want to expand it with degree 2, then we get `(x, y, x
* x, x * y, y * y)`.
+ */
+@AlphaComponent
+class PolynomialMapper extends UnaryTransformer[Vector, Vector,
PolynomialMapper] {
+
+ /**
+ * The polynomial degree to expand, which should be larger than 1.
+ * @group param
+ */
+ val degree = new IntParam(this, "degree", "the polynomial degree to
expand", Some(2))
+
+ /** @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
+ }
+
+ /**
+ * Given a pre-built array of Double, fill it with expanded monomials
until a given polynomial
+ * degree.
+ * @param values the array of Double, which represents a dense vector.
+ * @param prevStart the start offset of elements that filled in the last
function call.
+ * @param prevLen the length of elements that filled in the last
function.
+ * @param currDegree the current degree that we want to expand.
+ * @param finalDegree the final expected degree that we want to expand.
+ * @param nVariables number of variables in the original feature vector.
+ */
+ @tailrec
+ private def fillDenseVector(values: Array[Double], prevStart: Int,
prevLen: Int, currDegree: Int,
+ finalDegree: Int, nVariables: Int): Unit = {
+
+ if (currDegree > finalDegree) {
+ return
+ }
+
+ val currExpandedVecFrom = prevStart + prevLen
+ val currExpandedVecLen = numMonomials(currDegree, nVariables)
+
+ var leftIndex = 0
+ var currIndex = currExpandedVecFrom
+
+ while (leftIndex < nVariables) {
+ val numToKeep = numMonomials(currDegree - 1, nVariables - leftIndex)
+ val prevVecStartIndex = prevStart + prevLen - numToKeep
+
+ var rightIndex = 0
+ while (rightIndex < numToKeep) {
+ values(currIndex) =
+ values(leftIndex) * values(prevVecStartIndex + rightIndex)
+ currIndex += 1
+ rightIndex += 1
+ }
+
+ leftIndex += 1
+ }
+
+ fillDenseVector(values, currExpandedVecFrom, currExpandedVecLen,
currDegree + 1, finalDegree,
+ nVariables)
+ }
+
+ /**
+ * For polynomial expanding a `SparseVector`, we treat it as a dense
vector and call
+ * `fillDenseVector` to fill in the `values` of `SparseVector`. For its
`indices` part, we encode
+ * the indices from `nVariables` one by one, because we do not care of
the real indices.
+ */
+ private def fillPseudoSparseVectorIndices(indices: Array[Int],
startFrom: Int, startWith: Int) = {
--- End diff --
@mengxr I notice that it is not a feasible solution. We have to compute the
real indices of the sparse vector. I'll fix it ASAP.
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