Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/5245#discussion_r28846227
--- Diff:
mllib/src/main/scala/org/apache/spark/ml/feature/PolynomialMapper.scala ---
@@ -0,0 +1,240 @@
+/*
+ * 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 scala.collection.mutable.ArrayBuffer
+
+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
--- End diff --
`choose(n + 1, k) - 1`?
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