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Converted from custom Linalg routines to Breeze: added JavaDoc commen…
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…ts; added Markdown documentation
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@sboeschhuawei
sboeschhuawei committed Jan 28, 2015
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15 changes: 15 additions & 0 deletions data/mllib/pic-15.txt
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91 2.1419053155 1.919407949 0.0501333631 -0.1069902864 1.2809776381 1.6846227956 0.1827785926 -0.3966434027 0.8090554869 2.4862133924
82 1.8023071497 0.8784870753 2.4105062239 0.3597672178 -0.2096444593 1.3537576979 0.5096503508 1.5507215383 -0.203551002 1.3210160806
73 2.5511476389 1.4385302862 1.4815980608 2.519631079 0.7231682708 0.9160610215 2.2558330058 0.6747272061 0.8267096669 -0.8585851446
64 2.4238069456 -0.3637260241 -0.9646660988 0.0814051561 -1.5488873934 -0.6309606578 0.8779952254 2.2891590718 0.7308611443 1.2574914085
55 0.680085624 -0.7684998593 0.5165496871 0.4900095346 2.116673377 0.9590527985 -0.1076715169 2.8623214176 2.1457411377 -0.0586772049
46 2.0725991339 -0.931744152 1.3010252161 1.2475231583 2.4061568492 -0.5202207204 1.2709294127 1.5612492848 0.470170422 1.5390221915
37 3.2123402142 0.3670664312 -0.8831759122 1.3865659854 1.3258292709 0.0986956805 0.9973196911 0.526040745 0.4520218452 0.9808998515
28 2.6468163883 -0.1070625922 1.5938103927 0.8443353789 1.6632872929 2.2267933607 1.8839698438 1.2217245467 1.919702086 0.2606241814
19 1.8035177495 0.7460582552 0.2361611395 -0.8645567427 -0.8613062 0.4234001189 0.5910061938 1.2484609376 0.5190870451 1.4462120574
10 0.5534111111 1.0456386879 1.7045663273 0.7281759816 1.0807487792 2.2590964696 1.7635098382 2.7220810802 1.1459500541 0.0053369875
911 1.200749626 1.8962364439 2.5117192131 -0.4034737281 -0.9069696484 2.3685654487 0.4403269676 1.7446081537 2.5736655957 2.1280434418
812 0.8079184133 -1.2544936618 1.4398518629 1.6568003266 0.2550498386 2.1994753269 2.7797467522 1.0674041521 2.295064022 0.4173234715
713 1.7688682382 1.4176645502 0.530907764 1.4141481733 1.6630227275 1.8671946375 1.2967008778 1.3215230565 3.2242953581 1.8358482078
614 -0.193302298 1.118805146 1.5580410346 -0.9527104651 2.4960553383 0.2374178113 1.8951776489 0.8173290971 1.929763464 0.5625196402
515 0.895089061 0.3885617561 1.3527646645 -0.1445166108 0.3461682011 3.6770971085 1.1513217164 2.8470372001 1.440743315 1.8773090852
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30 changes: 30 additions & 0 deletions docs/mllib-pic-clustering.md
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---
layout: global
title: Clustering - MLlib
displayTitle: <a href="mllib-guide.html">MLlib</a> - Power Iteration Clustering
---

* Table of contents
{:toc}


## Power Iteration Clustering

Power iteration clustering is a scalable and efficient algorithm for clustering points given pointwise mutual affinity values. Internally the algorithm:

* computes the Gaussian distance between all pairs of points and represents these distances in an Affinity Matrix
* calculates a Normalized Affinity Matrix
* calculates the principal eigenvalue and eigenvector
* Clusters each of the input points according to their principal eigenvector component value

Details of this algorithm are found within [Power Iteration Clustering, Lin and Cohen]{www.icml2010.org/papers/387.pdf}

Example outputs for a dataset inspired by the paper - but with five clusters instead of three- have he following output from our implementation:

<p style="text-align: center;">
<img src="img/PIClusteringFiveCirclesInputsAndOutputs.png"
title="The Property Graph"
alt="The Property Graph"
width="50%" />
<!-- Images are downsized intentionally to improve quality on retina displays -->
</p>
104 changes: 19 additions & 85 deletions mllib/src/main/scala/org/apache/spark/mllib/clustering/PICLinalg.scala
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Expand Up @@ -22,14 +22,17 @@ import org.apache.spark.mllib.linalg.Vectors
import scala.reflect.ClassTag
import scala.util.Random
import breeze.linalg.{DenseVector => BDV,DenseMatrix => BDM}
import scala.language.existentials
import scala.language.implicitConversions

/**
* PICLinalg
* Linear Algebra helper routines associated with the PIClustering implementation
*
*/

object PICLinalg {

import breeze.linalg.DenseVector._
import breeze.linalg.DenseMatrix._
type DMatrix = BDM[Double]

type LabeledVector = (Long, BDV[Double])
Expand All @@ -38,68 +41,17 @@ object PICLinalg {

type Vertices = Seq[LabeledVector]

// implicit def arrayToVect(darr: Array[Double]): BDV[Double] = new BDV(darr)
implicit def bdvToSeq[T](vect: BDV[T])(implicit ct: ClassTag[T]): Seq[T] = vect.toArray.toSeq
implicit def bdvToArray[T](vect: BDV[T])(implicit ct: ClassTag[T]): Array[T] = vect.toArray
// implicit def arrayToSeq(arr: Array[Double]) = Predef.doubleArrayOps(arr)
def add(v1: BDV[Double], v2: BDV[Double]) =
v1.zip(v2).map { x => x._1 + x._2}

def norm(darr: Array[Double]): Double = {
Math.sqrt(darr.foldLeft(0.0) { case (sum, dval) => sum + Math.pow(dval, 2)})
}

def norm(darr: BDV[Double]): Double = {
darr.norm(2)
}

//
//
// // Implicits to convert between Breeze DenseVector's and Arrays
// implicit def arrToSeq[T](arr: Array[T]): Seq[T] = arr.toSeq
//// implicit def arrayToBDV(darr: Array[Double]): BDV[Double]
//// = Vectors.dense(darr).asInstanceOf[BDV[Double]]
//// implicit def bdvToArray[T](vect: BDV[T])(implicit ct: ClassTag[T]): Array[T] = vect.toArray
//// implicit def bdvToSeq[T](vect: BDV[T])(implicit ct: ClassTag[T]): Seq[T] = vect.toArray.toSeq
//
// def add(v1: BDV[Double], v2: BDV[Double]) =
// v1.zip(v2).map { x => x._1 + x._2}

def mult(v1: BDV[Double], d: Double) = {
v1 * d
}

def mult(v1: BDV[Double], v2: BDV[Double]) = {
v1 * v2
}

def multColByRow(v1: BDV[Double], v2: BDV[Double]) = {
val mat = v1 * v2.t
mat
}

def norm(vect: BDV[Double]): Double = {
vect.norm
}

// def norm(darr: Array[Double]): Double = {
// Math.sqrt(darr.foldLeft(0.0) { case (sum, dval) => sum + Math.pow(dval, 2)})
// }

def manhattanNorm(vect: BDV[Double]): Double = {
vect.norm(1)
Vectors.norm(Vectors.fromBreeze(vect),2.0)
}

def dot(v1: BDV[Double], v2: BDV[Double]) : Double = {
v1.dot(v2)
}

def onesVector(len: Int): BDV[Double] = {
BDV.ones(len)
}

val calcEigenDiffs = true

def withinTol(d: Double, tol: Double = DefaultTolerance) = Math.abs(d) <= tol

val DefaultTolerance: Double = 1e-8
Expand All @@ -112,17 +64,17 @@ object PICLinalg {
}
}

def transpose(mat: DMatrix) = {
mat.t
}

def printMatrix(mat: BDM[Double]): String
= printMatrix(mat, mat.rows, mat.cols)

def printMatrix(mat: BDM[Double], numRows: Int, numCols: Int): String = {
printMatrix(mat.toArray, numRows, numCols)
}

def printMatrix(vectors: Array[BDV[Double]]) : String = {
printMatrix(vectors.map{_.toArray}.flatten, vectors.length, vectors.length)
}

def printMatrix(vect: Array[Double], numRows: Int, numCols: Int): String = {
val darr = vect
val stride = darr.length / numCols
Expand Down Expand Up @@ -185,12 +137,13 @@ object PICLinalg {
cnorm = makeNonZero(norm(eigen))
eigen = eigen.map(_ / cnorm)
}
val signum = Math.signum(dot(mat(0), eigen))
val lambda = dot(mat(0), eigen) / eigen(0)
val matDotEigen = mat(::,0) dot eigen
val signum = Math.signum(matDotEigen)
val lambda = matDotEigen / eigen(0)
eigen = eigen.map(_ * signum)
println(s"lambda=$lambda eigen=${printVector(eigen)}")
if (expLambda.toArray.length > 0) {
val compareVect = eigen.zip(expdat(k)).map { case (a, b) => a / b}
val compareVect = eigen.toArray.zip(expdat(::,k)).map { case (a, b) => a / b}
println(s"Ratio to expected: lambda=${lambda / expLambda(k)} " +
s"Vect=${compareVect.mkString("[", ",", "]")}")
}
Expand All @@ -216,11 +169,8 @@ object PICLinalg {
}

def deflate(mat: DMatrix, lambda: Double, eigen: BDV[Double]) = {
// mat = mat.map(subtractProjection(_, mult(eigen, lambda)))
val eigT = eigen
val projected = (eigen * eigen.t) * lambda
// println(s"projected matrix:\n${printMatrix(projected,
// eigen.length, eigen.length)}")
val matOut = mat - projected
println(s"Updated matrix:\n${
printMatrix(mat,
Expand All @@ -234,29 +184,12 @@ object PICLinalg {
outMat
}

// def mult(mat: DMatrix, vect: BDV[Double]): DMatrix = {
// val outMat = mat.map { m =>
// mult(m, vect)
// }
// outMat
// }
//
// def mult(vect: BDV[Double], mat: DMatrix): DMatrix = {
// for {d <- vect.zip(transpose(mat)) }
// yield mult(d._2, d._1)
// }

def scale(mat: DMatrix, d: Double): DMatrix = {
mat * d
}

def transpose(vector: BDV[Double]) = {
vector.map { d => Array(d)}
}

def toMat(dvect: Array[Double], ncols: Int) = {
val m = dvect.toSeq.grouped(ncols).map(_.toArray)
m
def matToCols(mat: DMatrix) = {
mat.toArray.grouped(mat.cols)
}

def schurComplement(mat: DMatrix, lambda: Double, eigen: BDV[Double]) = {
Expand All @@ -273,9 +206,10 @@ object PICLinalg {
printMatrix(numerat2,
eigen.length, eigen.length)
}")
val denom1 = eigT * mat
val denom1 = eig * mat
val denom2 = denom1 * eigen
val denom = denom2.toArray(0)
val denomTmp = denom2.toArray
val denom = denomTmp(0)
println(s"denom is $denom")
val projMat = scale(numerat2, 1.0 / denom)
println(s"Updated matrix:\n${
Expand Down
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