parceptron

build.sbt

name := "parceptron"

version := "1.0"

scalaVersion := "2.11.7"

libraryDependencies  ++= Seq(
  "org.scalanlp" %% "breeze" % "0.11.2",
  "org.scalanlp" %% "breeze-natives" % "0.11.2",
  "org.scalanlp" %% "breeze-viz" % "0.11.2"
)

resolvers ++= Seq(
  "Sonatype Snapshots" at "https://oss.sonatype.org/content/repositories/snapshots/",
  "Sonatype Releases" at "https://oss.sonatype.org/content/repositories/releases/"
)

iris.data

5.1,3.5,1.4,0.2,Iris-setosa
4.9,3.0,1.4,0.2,Iris-setosa
4.7,3.2,1.3,0.2,Iris-setosa
4.6,3.1,1.5,0.2,Iris-setosa
5.0,3.6,1.4,0.2,Iris-setosa
5.4,3.9,1.7,0.4,Iris-setosa
4.6,3.4,1.4,0.3,Iris-setosa
5.0,3.4,1.5,0.2,Iris-setosa
4.4,2.9,1.4,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
5.4,3.7,1.5,0.2,Iris-setosa
4.8,3.4,1.6,0.2,Iris-setosa
4.8,3.0,1.4,0.1,Iris-setosa
4.3,3.0,1.1,0.1,Iris-setosa
5.8,4.0,1.2,0.2,Iris-setosa
5.7,4.4,1.5,0.4,Iris-setosa
5.4,3.9,1.3,0.4,Iris-setosa
5.1,3.5,1.4,0.3,Iris-setosa
5.7,3.8,1.7,0.3,Iris-setosa
5.1,3.8,1.5,0.3,Iris-setosa
5.4,3.4,1.7,0.2,Iris-setosa
5.1,3.7,1.5,0.4,Iris-setosa
4.6,3.6,1.0,0.2,Iris-setosa
5.1,3.3,1.7,0.5,Iris-setosa
4.8,3.4,1.9,0.2,Iris-setosa
5.0,3.0,1.6,0.2,Iris-setosa
5.0,3.4,1.6,0.4,Iris-setosa
5.2,3.5,1.5,0.2,Iris-setosa
5.2,3.4,1.4,0.2,Iris-setosa
4.7,3.2,1.6,0.2,Iris-setosa
4.8,3.1,1.6,0.2,Iris-setosa
5.4,3.4,1.5,0.4,Iris-setosa
5.2,4.1,1.5,0.1,Iris-setosa
5.5,4.2,1.4,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
5.0,3.2,1.2,0.2,Iris-setosa
5.5,3.5,1.3,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
4.4,3.0,1.3,0.2,Iris-setosa
5.1,3.4,1.5,0.2,Iris-setosa
5.0,3.5,1.3,0.3,Iris-setosa
4.5,2.3,1.3,0.3,Iris-setosa
4.4,3.2,1.3,0.2,Iris-setosa
5.0,3.5,1.6,0.6,Iris-setosa
5.1,3.8,1.9,0.4,Iris-setosa
4.8,3.0,1.4,0.3,Iris-setosa
5.1,3.8,1.6,0.2,Iris-setosa
4.6,3.2,1.4,0.2,Iris-setosa
5.3,3.7,1.5,0.2,Iris-setosa
5.0,3.3,1.4,0.2,Iris-setosa
7.0,3.2,4.7,1.4,Iris-versicolor
6.4,3.2,4.5,1.5,Iris-versicolor
6.9,3.1,4.9,1.5,Iris-versicolor
5.5,2.3,4.0,1.3,Iris-versicolor
6.5,2.8,4.6,1.5,Iris-versicolor
5.7,2.8,4.5,1.3,Iris-versicolor
6.3,3.3,4.7,1.6,Iris-versicolor
4.9,2.4,3.3,1.0,Iris-versicolor
6.6,2.9,4.6,1.3,Iris-versicolor
5.2,2.7,3.9,1.4,Iris-versicolor
5.0,2.0,3.5,1.0,Iris-versicolor
5.9,3.0,4.2,1.5,Iris-versicolor
6.0,2.2,4.0,1.0,Iris-versicolor
6.1,2.9,4.7,1.4,Iris-versicolor
5.6,2.9,3.6,1.3,Iris-versicolor
6.7,3.1,4.4,1.4,Iris-versicolor
5.6,3.0,4.5,1.5,Iris-versicolor
5.8,2.7,4.1,1.0,Iris-versicolor
6.2,2.2,4.5,1.5,Iris-versicolor
5.6,2.5,3.9,1.1,Iris-versicolor
5.9,3.2,4.8,1.8,Iris-versicolor
6.1,2.8,4.0,1.3,Iris-versicolor
6.3,2.5,4.9,1.5,Iris-versicolor
6.1,2.8,4.7,1.2,Iris-versicolor
6.4,2.9,4.3,1.3,Iris-versicolor
6.6,3.0,4.4,1.4,Iris-versicolor
6.8,2.8,4.8,1.4,Iris-versicolor
6.7,3.0,5.0,1.7,Iris-versicolor
6.0,2.9,4.5,1.5,Iris-versicolor
5.7,2.6,3.5,1.0,Iris-versicolor
5.5,2.4,3.8,1.1,Iris-versicolor
5.5,2.4,3.7,1.0,Iris-versicolor
5.8,2.7,3.9,1.2,Iris-versicolor
6.0,2.7,5.1,1.6,Iris-versicolor
5.4,3.0,4.5,1.5,Iris-versicolor
6.0,3.4,4.5,1.6,Iris-versicolor
6.7,3.1,4.7,1.5,Iris-versicolor
6.3,2.3,4.4,1.3,Iris-versicolor
5.6,3.0,4.1,1.3,Iris-versicolor
5.5,2.5,4.0,1.3,Iris-versicolor
5.5,2.6,4.4,1.2,Iris-versicolor
6.1,3.0,4.6,1.4,Iris-versicolor
5.8,2.6,4.0,1.2,Iris-versicolor
5.0,2.3,3.3,1.0,Iris-versicolor
5.6,2.7,4.2,1.3,Iris-versicolor
5.7,3.0,4.2,1.2,Iris-versicolor
5.7,2.9,4.2,1.3,Iris-versicolor
6.2,2.9,4.3,1.3,Iris-versicolor
5.1,2.5,3.0,1.1,Iris-versicolor
5.7,2.8,4.1,1.3,Iris-versicolor
6.3,3.3,6.0,2.5,Iris-virginica
5.8,2.7,5.1,1.9,Iris-virginica
7.1,3.0,5.9,2.1,Iris-virginica
6.3,2.9,5.6,1.8,Iris-virginica
6.5,3.0,5.8,2.2,Iris-virginica
7.6,3.0,6.6,2.1,Iris-virginica
4.9,2.5,4.5,1.7,Iris-virginica
7.3,2.9,6.3,1.8,Iris-virginica
6.7,2.5,5.8,1.8,Iris-virginica
7.2,3.6,6.1,2.5,Iris-virginica
6.5,3.2,5.1,2.0,Iris-virginica
6.4,2.7,5.3,1.9,Iris-virginica
6.8,3.0,5.5,2.1,Iris-virginica
5.7,2.5,5.0,2.0,Iris-virginica
5.8,2.8,5.1,2.4,Iris-virginica
6.4,3.2,5.3,2.3,Iris-virginica
6.5,3.0,5.5,1.8,Iris-virginica
7.7,3.8,6.7,2.2,Iris-virginica
7.7,2.6,6.9,2.3,Iris-virginica
6.0,2.2,5.0,1.5,Iris-virginica
6.9,3.2,5.7,2.3,Iris-virginica
5.6,2.8,4.9,2.0,Iris-virginica
7.7,2.8,6.7,2.0,Iris-virginica
6.3,2.7,4.9,1.8,Iris-virginica
6.7,3.3,5.7,2.1,Iris-virginica
7.2,3.2,6.0,1.8,Iris-virginica
6.2,2.8,4.8,1.8,Iris-virginica
6.1,3.0,4.9,1.8,Iris-virginica
6.4,2.8,5.6,2.1,Iris-virginica
7.2,3.0,5.8,1.6,Iris-virginica
7.4,2.8,6.1,1.9,Iris-virginica
7.9,3.8,6.4,2.0,Iris-virginica
6.4,2.8,5.6,2.2,Iris-virginica
6.3,2.8,5.1,1.5,Iris-virginica
6.1,2.6,5.6,1.4,Iris-virginica
7.7,3.0,6.1,2.3,Iris-virginica
6.3,3.4,5.6,2.4,Iris-virginica
6.4,3.1,5.5,1.8,Iris-virginica
6.0,3.0,4.8,1.8,Iris-virginica
6.9,3.1,5.4,2.1,Iris-virginica
6.7,3.1,5.6,2.4,Iris-virginica
6.9,3.1,5.1,2.3,Iris-virginica
5.8,2.7,5.1,1.9,Iris-virginica
6.8,3.2,5.9,2.3,Iris-virginica
6.7,3.3,5.7,2.5,Iris-virginica
6.7,3.0,5.2,2.3,Iris-virginica
6.3,2.5,5.0,1.9,Iris-virginica
6.5,3.0,5.2,2.0,Iris-virginica
6.2,3.4,5.4,2.3,Iris-virginica
5.9,3.0,5.1,1.8,Iris-virginica

Main.scala

package parceptron

import breeze.linalg._
import breeze.plot._
import breeze.math._
import breeze.numerics._

import scala.annotation.tailrec
import scala.io.Source

sealed trait Klass
object Klass {
  case object A extends Klass
  case object B extends Klass
}

sealed trait State
case object Success extends State
case object Failure extends State

class Parceptron(rho: Double, xs: List[DenseMatrix[Double]], t: List[Klass], maxNumOfTrials: Int = 1000) {

  // (5) Xの全パターンを正しく識別できるまで (2) - (4) を繰り返す。
  @tailrec
  final def calc(omega: DenseMatrix[Double], numOfTrials: Int = 0): (DenseMatrix[Double], Int) = {
    if (numOfTrials > maxNumOfTrials) throw new Exception(s"$numOfTrials times tried but error.")
    else {
      optimizeOmega(omega) match {
        case (omg, 0) => (omg, numOfTrials)
        case (omg, err) => calc(omg, numOfTrials + 1)
      }
    }
  }

  private def optimizeOmega(omega: DenseMatrix[Double]): (DenseMatrix[Double], Int) = {
    // (4) Xの全パターンについて(2),(3)を行う。
    (xs zip t).foldLeft[(DenseMatrix[Double], Int)]((omega, 0)) { case ((_omega, err), (_x, _t)) =>
      // (2) 既知データXから学習パターンを１つ選ぶ。
      // (3)-1 識別関数g(x)によって識別を行い、
      val ev = g(_omega, _x)
      updateOmega(omega = _omega, ev = ev, x = _x, t = _t) match {
        case (newOmega, Success) => (newOmega, err)
        case (newOmega, Failure) => (newOmega, err + 1)
      }
    }
  }

  // evaluation function
  private def g(omega: DenseMatrix[Double], x: DenseMatrix[Double]): Double = sum(omega.t * x)

  // (3)-2 正しく識別できなかった場合はωを更新する。
  private def updateOmega(omega: DenseMatrix[Double], ev: Double, x: DenseMatrix[Double], t: Klass): (DenseMatrix[Double], State) = {
    if ((ev < 0 && t == Klass.A) || (ev > 0 && t == Klass.B)) (omega, Success)
    else if (ev >= 0) (omega - rho * x, Failure)
    else (omega + rho * x, Failure)
  }

}

object Main extends App {
  val source = Source.fromURL(getClass.getResource("/iris.data"))

  // 特徴量ベクトルXを作成
  // 
  // "5.1,3.5,1.4,0.2,Iris-setosa"
  // -> Array("5.1", "3.5", "1.4", "0.2", "Iris-setosa")
  // -> ([1, 5.1, 3.5, 1.4, 0.2] t, Klass.A)
  // 
  // List("5.1,3.5,1.4,0.2,Iris-setosa", "7.0,3.2,4.7,1.4,Iris-versicolor") 
  // -> (List([1.0, 5.1, 3.5, 1.4, 0.2] t, [1.0, 7.0, 3.2, 4.7, 1.4] t),   List(Klass.A, Klass.B))
  val (features, klasses) = source.getLines.toList.map(_.split(",") match {
    case Array(e0, e1, e2, e3, c) => (DenseMatrix(1.0d +: Array(e0.toDouble, e1.toDouble, e2.toDouble, e3.toDouble): _*), if (c == "Iris-setosa") Klass.A else Klass.B)
  }).unzip

  // (1) 重みベクトルωを適当に決める。
  val initialOmega = DenseMatrix(1.0d, 1.0d, 1.0d, 1.0d, 1.0d)

  val model = new Parceptron(rho = 0.05d, xs = features, t = klasses)
  val (optimizedOmega, numOfTrials) = model.calc(omega = initialOmega)

  println(s"optimized omega: ${optimizedOmega.t}, number of trials: ${numOfTrials}")
}