Solutions for AMP Camp 2012 Machine Learning Exercises

> http://ampcamp.berkeley.edu

> See the full AMP Camp 2012 exercise set

Table of Contents

Solution for Shark Queries

Full code solution for featurization

Solution to Featurization problem 2a

Solution to Featurization problem 2b

Solution for K means

Solution for Shark Queries

- Count the number of distinct date/times for English pages

select count(distinct dt) from wikistats_cached;

- How many hits are there on pages with Berkeley in the title throughout the entire period?

select count(page_views) from wikistats_cached where page_name like "%berkeley%";

- Generate a histogram for the number of hits for each hour on May 6, 2009; sort the output by date/time. Based on the output, which hour is Wikipedia most popular?

select dt, sum(page_views) from wikistats_cached where dt like "20090506%" group by dt order by dt;

Full code solution for featurization

Place the following code within a Scala object and call the featurization function from a main function:

  import scala.io.Source

  import spark.SparkContext

  import SparkContext._

  lazy val hostname = Source.fromFile("/root/mesos-ec2/masters").mkString.trim

  def featurization(sc: SparkContext) {

    val featurizedRdd = sc.textFile("hdfs://"+hostname+":9000/wikistats_20090505-07_restricted").map{line => {

      val Array(dateTime, projectCode, pageTitle, numViews, numBytes) = line.trim.split("\\s+")

      val hour = dateTime.substring(dateTime.indexOf("-")+1, dateTime.indexOf("-")+3).toInt

      (projectCode+" "+pageTitle, hour -> numViews.toInt)

    }}.groupByKey.map{grouped => {

      val (article, hoursViews) = grouped

      val sums = Array.fill[Int](24)(0)

      val counts = Array.fill[Int](24)(0)

      for((hour, numViews) <- hoursViews) {

        sums(hour) += numViews

        counts(hour) += 1

      }

      val avgs: Array[Double] =

        for((sum, count) <- sums zip counts) yield

          if(count > 0) sum/count.toDouble else 0.0

      article -> avgs

    }}.filter{t => {

      t._2.forall(_ > 0)

    }}.map{t => {

      val avgsTotal = t._2.sum

      t._1 -> t._2.map(_ / avgsTotal)

    }}

    featurizedRdd.cache()

    println("Number of records in featurized dataset: " + featurizedRdd.count)

    println("Selected feature vectors:")

    featurizedRdd.filter{t => {

      t._1 == "en Computer_science" || t._1 == "en Machine_learning"

    }}.collect.map{t => t._1 -> t._2.mkString("[",",","]")}.foreach(println)

    featurizedRdd.map{t => t._1 -> t._2.mkString(",")}.saveAsSequenceFile("hdfs://"+hostname+":9000/wikistats_featurized")

  }

Solution to Featurization problem 2a

Number of records in the preprocessed data: 802450

Solution to Featurization problem 2b

(en Machine_learning, [0.03708182184602984,0.027811366384522376,0.031035872632003234,0.033454252317613876,0.033051189036678766,0.023780733575171308,0.03224506247480856,0.029826682789197912,0.04997984683595326,0.04433696090286176,0.04997984683595326,0.04474002418379687,0.04272470777912134,0.054816606207174545,0.054816606207174545,0.04474002418379687,0.054010479645304324,0.049173720274083045,0.049173720274083045,0.05038291011688836,0.04594921402660219,0.04957678355501815,0.03667875856509473,0.030632809351068126])

(en Computer_science, [0.03265137425087828,0.057656540607563554,0.03306468278569953,0.033374664186815464,0.03709444100020666,0.03947096507542881,0.03502789832610044,0.03637115106426948,0.036577805331680105,0.0421574705517669,0.04267410622029345,0.03885100227319695,0.03885100227319695,0.046083901632568716,0.04691051870221121,0.050320314114486474,0.05259351105600331,0.04649721016738996,0.04732382723703245,0.048357098574085565,0.04236412481917752,0.043190741888820015,0.03626782393056417,0.03626782393056417])

Solution for K-means

Place the following code within a Scala object and call the clustering function from a main function:

  import scala.io.Source

  import scala.util.Random

  import spark.SparkContext

  import SparkContext._

  lazy val hostname = Source.fromFile("/root/mesos-ec2/masters").mkString.trim

  //computes the Euclidean distance between vectors a1 and a2

  def distL2(a1: Array[Double], a2: Array[Double]): Double = {

    require(a1.size == a2.size)

    var sum: Double = 0.0

    for(i <- a1.indices) sum += math.pow(a1(i) - a2(i), 2)

    math.sqrt(sum)

  }

  //class for computing running averages of real vectors

  class ArrAvg extends Serializable {

    private var avg: Array[Double] = null

    private var count: Int = 0      //number of vectors averaged thus far

    //constructor initializing this ArrAvg to be the average of the single vector arr

    def this(arr: Array[Double]) { this(); this += arr }

    //incorporate arr into this running average

    def +=(arr: Array[Double]): ArrAvg = {

      if(avg == null) avg = arr.clone    //if this average is currently empty

      else {

        //update avg to include arr

        require(avg.size == arr.size)

        for(i <- avg.indices) avg(i) = avg(i)*count/(count+1).toDouble + arr(i)/(count+1).toDouble

      }

      count += 1

      this

    }

    //incorporate all vectors averaged in other into this running average

    def ++=(other: ArrAvg): ArrAvg = {

      if(other.count == 0) return this   //if other is empty

      else if(avg == null) {

        //if this average is currently empty, set it equal to other

        avg = other.avg.clone

        count = other.count

      }

      else {

        //update this.avg and this.count based on the contents of other

        require(avg.size == other.avg.size)

        for(i <- avg.indices) {

          avg(i) *= count.toDouble/(count+other.count)

          avg(i) += other.avg(i)*other.count/(count+other.count).toDouble

        }

        count += other.count

      }

      this

    }

    def getAvg = avg

  }

  def clustering(sc: SparkContext) {

    //define settings

    //desired number of clusters

    val K = 10

    //stopping criterion for K-means iterations (threshold on average centroid change)

    val eps = 1e-6

    //load and cache the featurized data

    val rdd = sc.sequenceFile[String, String]("hdfs://"+hostname+":9000/wikistats_featurized").map{t => {

      //parse the string representation of the feature vectors used for data storage

      t._1 -> t._2.split(",").map(_.toDouble)

    }}.cache()

    //select a random subset of the data points as initial centroids

    var centroids = rdd.sample(false, 0.005, 23789).map(_._2).collect.map(_ -> Random.nextDouble).sortBy(_._2).map(_._1).take(K)

    println("Done selecting initial centroids")

    //run the K-means iterative procedure to find centroids

    var iterI = 0

    var oldCentroids = centroids

    var delta = 0.0

    //iterate until average centroid change (measured by Euclidean distance) is <= eps

    do {

      //store the previous set of centroids

      oldCentroids = centroids

      //compute new centroids; the aggregate() function on RDDs is analogous to

      //  the aggregate() function on Iterables

      centroids = rdd.map(_._2).aggregate(Array.fill(K)(new ArrAvg))((aa: Array[ArrAvg], arr: Array[Double]) => {

        //determine the centroid closest to feature vector arr

        val centroidI = centroids.indices.minBy{i => distL2(centroids(i), arr)}

        //incorporate arr into the ArrAvg corresponding to this closest centroid

        aa(centroidI) += arr

        aa

      }, (aa1: Array[ArrAvg], aa2: Array[ArrAvg]) => {

        //combine ArrAvgs computed for each new centroid

        (aa1 zip aa2).map(t => t._1 ++= t._2)

      }).map(_.getAvg)

      /* NOTE: if no points are assigned to a given centroid, then _.getAvg above will

               yield null; we do not currently handle this case, as this is only an

               exercise, and this situation is unlikely to occur on the given data;

               however, a proper implementation should handle this case */

      //compute the average change between elements of oldCentroids and new centroids

      delta = (centroids zip oldCentroids).map{t => distL2(t._1, t._2)}.reduce(_+_)/K.toDouble

      println("Finished iteration "+iterI+" (delta="+delta+")")

      iterI += 1

    } while(delta > eps)

    //print results

    println("Centroids with some articles:")

    val numArticles = 10

    for((centroid, centroidI) <- centroids.zipWithIndex) {

      //print centroid

      println(centroid mkString ("[",",","]"))

      //print numArticles articles which are assigned to this centroid’s cluster

      rdd.filter{t => {

        centroids.indices.minBy{i => distL2(centroids(i), t._2)} == centroidI

      }}.take(numArticles).foreach(println)

      println()

    }

  }

Centroids with some articles for K-means with K=10:

[0.022147691025988934,0.028446757284088322,0.03401348051181095,0.04028622120760124,0.044808787400008564,0.05102000676659651,0.054746875714012155,0.056997844456603025,0.06023923286538736,0.05995930437707476,0.05484747876276983,0.052368291791386884,0.05836844829674058,0.06332469983469591,0.06252944032549862,0.05669573830648844,0.04611266361220511,0.036162554227650384,0.02705067763648778,0.021163652272439472,0.017747384624005096,0.016299762995042936,0.016537288598262062,0.018125717107154878]

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