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/*
* 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.collection.mutable
import org.apache.spark.annotation.AlphaComponent
import org.apache.spark.ml.UnaryTransformer
import org.apache.spark.ml.param.{IntParam, ParamValidators}
import org.apache.spark.ml.util.Identifiable
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, x * x, y, x * y, y * y)`.
*/
@AlphaComponent
class PolynomialExpansion(override val uid: String)
extends UnaryTransformer[Vector, Vector, PolynomialExpansion] {
def this() = this(Identifiable.randomUID("poly"))
/**
* The polynomial degree to expand, which should be >= 1. A value of 1 means no expansion.
* Default: 2
* @group param
*/
val degree = new IntParam(this, "degree", "the polynomial degree to expand (>= 1)",
ParamValidators.gt(1))
setDefault(degree -> 2)
/** @group getParam */
def getDegree: Int = $(degree)
/** @group setParam */
def setDegree(value: Int): this.type = set(degree, value)
override protected def createTransformFunc: Vector => Vector = { v =>
PolynomialExpansion.expand(v, $(degree))
}
override protected def outputDataType: DataType = new VectorUDT()
}
/**
* The expansion is done via recursion. Given n features and degree d, the size after expansion is
* (n + d choose d) (including 1 and first-order values). For example, let f([a, b, c], 3) be the
* function that expands [a, b, c] to their monomials of degree 3. We have the following recursion:
*
* {{{
* f([a, b, c], 3) = f([a, b], 3) ++ f([a, b], 2) * c ++ f([a, b], 1) * c^2 ++ [c^3]
* }}}
*
* To handle sparsity, if c is zero, we can skip all monomials that contain it. We remember the
* current index and increment it properly for sparse input.
*/
private[feature] object PolynomialExpansion {
private def choose(n: Int, k: Int): Int = {
Range(n, n - k, -1).product / Range(k, 1, -1).product
}
private def getPolySize(numFeatures: Int, degree: Int): Int = choose(numFeatures + degree, degree)
private def expandDense(
values: Array[Double],
lastIdx: Int,
degree: Int,
multiplier: Double,
polyValues: Array[Double],
curPolyIdx: Int): Int = {
if (multiplier == 0.0) {
// do nothing
} else if (degree == 0 || lastIdx < 0) {
if (curPolyIdx >= 0) { // skip the very first 1
polyValues(curPolyIdx) = multiplier
}
} else {
val v = values(lastIdx)
val lastIdx1 = lastIdx - 1
var alpha = multiplier
var i = 0
var curStart = curPolyIdx
while (i <= degree && alpha != 0.0) {
curStart = expandDense(values, lastIdx1, degree - i, alpha, polyValues, curStart)
i += 1
alpha *= v
}
}
curPolyIdx + getPolySize(lastIdx + 1, degree)
}
private def expandSparse(
indices: Array[Int],
values: Array[Double],
lastIdx: Int,
lastFeatureIdx: Int,
degree: Int,
multiplier: Double,
polyIndices: mutable.ArrayBuilder[Int],
polyValues: mutable.ArrayBuilder[Double],
curPolyIdx: Int): Int = {
if (multiplier == 0.0) {
// do nothing
} else if (degree == 0 || lastIdx < 0) {
if (curPolyIdx >= 0) { // skip the very first 1
polyIndices += curPolyIdx
polyValues += multiplier
}
} else {
// Skip all zeros at the tail.
val v = values(lastIdx)
val lastIdx1 = lastIdx - 1
val lastFeatureIdx1 = indices(lastIdx) - 1
var alpha = multiplier
var curStart = curPolyIdx
var i = 0
while (i <= degree && alpha != 0.0) {
curStart = expandSparse(indices, values, lastIdx1, lastFeatureIdx1, degree - i, alpha,
polyIndices, polyValues, curStart)
i += 1
alpha *= v
}
}
curPolyIdx + getPolySize(lastFeatureIdx + 1, degree)
}
private def expand(dv: DenseVector, degree: Int): DenseVector = {
val n = dv.size
val polySize = getPolySize(n, degree)
val polyValues = new Array[Double](polySize - 1)
expandDense(dv.values, n - 1, degree, 1.0, polyValues, -1)
new DenseVector(polyValues)
}
private def expand(sv: SparseVector, degree: Int): SparseVector = {
val polySize = getPolySize(sv.size, degree)
val nnz = sv.values.length
val nnzPolySize = getPolySize(nnz, degree)
val polyIndices = mutable.ArrayBuilder.make[Int]
polyIndices.sizeHint(nnzPolySize - 1)
val polyValues = mutable.ArrayBuilder.make[Double]
polyValues.sizeHint(nnzPolySize - 1)
expandSparse(
sv.indices, sv.values, nnz - 1, sv.size - 1, degree, 1.0, polyIndices, polyValues, -1)
new SparseVector(polySize - 1, polyIndices.result(), polyValues.result())
}
def expand(v: Vector, degree: Int): Vector = {
v match {
case dv: DenseVector => expand(dv, degree)
case sv: SparseVector => expand(sv, degree)
case _ => throw new IllegalArgumentException
}
}
}
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