Solutions for AMP Camp 2012 Machine Learning Exercises

> See the full AMP Camp 2012 exercise set

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]

(ja %E8%A5%BF%E5%B7%9D%E7%BE%8E%E5%92%8C,[D@16d19d73)

(ja %E7%A5%9D%E6%97%A5%E6%B3%95,[D@1bb7f4b9)

(ja %E3%82%A8%E3%83%AA%E3%83%BC%E3%82%BC%E3%81%AE%E3%81%9F%E3%82%81%E3%81%AB,[D@6beaaf10)

(ja %E5%B0%8F%E8%B0%B7%E5%B9%B8%E5%BC%98,[D@292a6200)

(ja DOUBLE,[D@1d88031d)

(ja P-3_(%E8%88%AA%E7%A9%BA%E6%A9%9F),[D@4c847410)

(ja %E7%84%A1%E9%87%8F%E5%A4%A7%E6%95%B0,[D@bdfedaf)

(ja Roman,[D@1a6d8240)

[0.018530166208031794,0.014164029467697646,0.011775435662179815,0.010682359375998917,0.010434563297147339,0.011733114542324872,0.015504242943136072,0.022969386777524067,0.03073608478499401,0.03718037182862875,0.041169148553117506,0.04339765324619536,0.049217061716337725,0.058553363000577154,0.06397029996914101,0.06819456022389997,0.07040081881858114,0.07065109592285682,0.07545585630364683,0.0744093165084814,0.07123832576597369,0.058321300507240874,0.04336448167990859,0.027946962896378505]

(es Melendi,[D@778e7e6a)

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(pl Dmitrij_Mendelejew,[D@67a2997e)

(pl Jurij_Gagarin,[D@640b5459)

(de Konjunktur,[D@5f556d56)

[0.04004400475581517,0.038118787030749966,0.03801015733643086,0.03967369502072206,0.04151351988591238,0.04308393683465291,0.044778057420320046,0.04384191817330043,0.04327253705198659,0.04337169109087168,0.04206913431317084,0.040278518303564805,0.04101954271722155,0.038450206013100216,0.0418555337240833,0.043012543561769416,0.04353482943994479,0.043243093996798466,0.04369268461921003,0.04282953399927644,0.042365251465160035,0.04139263576836268,0.040894906504096745,0.03965328097347838]

(en Dick_Fuld,[D@25a97638)

(en Stargate_SG-1_(season_10),[D@189069d9)

(en Recollection,[D@31153228)

(en John_Taverner,[D@668ff944)

(en Category:Computer_languages,[D@763613f6)

(en Dream_Job,[D@5858b81b)

(en Fictional,[D@289f21ed)

(en Brazilian_films_of_2008,[D@676c6370)

(en Breville,[D@7cf4831b)

(en Intel_P35,[D@18cba1b4)

[0.0374891593665341,0.03647933999115497,0.03490100360527816,0.03515709593165882,0.03469511934394539,0.03467025288539275,0.03329515631628146,0.03368583693510732,0.03477995751228721,0.036139262146712585,0.036710028791579495,0.037891229499294896,0.042674988377533606,0.08459747304988914,0.047525076105976734,0.04547605472166529,0.045894075497203375,0.04573279489946979,0.04511827746337737,0.04541791931578055,0.04559712807618702,0.04402081145055172,0.042593234700449276,0.039458724016689144]

(en Passenger_rail_transport_in_China,[D@33984c9e)

(en Sentimental_novel,[D@53ce3388)

(en BBC_Online,[D@69950b4)

(en Len_Bosack,[D@3b815cce)

(en Fuji-Servetto,[D@29f3f6e7)

(ja %E5%B6%8B%E6%9D%91%E4%BE%91,[D@4fd6cd35)

(en Lechitic_languages,[D@1f3a7b86)

(en Digital_subtraction_angiography,[D@3883aa6e)

(ru.q %D0%A1%D0%B5%D0%BA%D1%81,[D@4c2a38be)

[0.050561001862224196,0.05109208279218707,0.052605718164506036,0.05403393713172642,0.05214285050352309,0.04787392679595907,0.039443144422478656,0.03296110630434489,0.02877417857709431,0.0266050285603666,0.02535277917627233,0.025495577756069122,0.027674046032043615,0.03230355314426185,0.036812246876504216,0.039516779336855566,0.04251301869056978,0.04416092811265632,0.045521754846991565,0.04708016847807021,0.049128276676792884,0.04986530476895841,0.04976581264907038,0.0487167783404734]

(en Alydar,[D@6b8a24e9)

(en AJ_Buckley,[D@3a7d7427)

(en The_Old_Regime_and_the_Revolution,[D@254ca71)

(en File:Evstafiev-bosnia-sarajevo-serbs-toast.jpg,[D@cb6c1e9)

(en Underground_(soundtrack),[D@3274ae84)

(en Pandamonium_(TV_series),[D@a6d75fd)

(en Joe_B._Hall,[D@185d3a64)

(en Nicotina,[D@10a487bb)

(en The_Sandman_(DC_Comics/Vertigo),[D@21cb0e86)

(en Deep_Water_Slang_V2.0,[D@1a2690bf)

[0.041710303207894095,0.038279529726798316,0.03633519156675436,0.036137178058335974,0.03588734746680139,0.03511199697067867,0.03273275085363018,0.031182210413119978,0.0309164565152981,0.031029341057239656,0.031292135138417894,0.03203783496775679,0.03456017008357846,0.03721815744086422,0.04064688332473918,0.0426120213468905,0.044877155468792694,0.04537918193846189,0.04616844847291527,0.04909265938711985,0.05946311232478101,0.0735443794073923,0.06434038325303444,0.04944517160870489]

(en Vice_Chief_of_Naval_Operations,[D@3f686e67)

(en Cleaver_(The_Sopranos),[D@1cc4728f)

(es 18_de_abril,[D@253d190a)

(en Yuya_Ozeki,[D@4e36f29f)

(en File:Gray557.png,[D@7972ccd6)

(en Paperback_Hero_(1999_film),[D@258eeec)

(en Crawler-transporter,[D@55716fcd)

[0.07083508476656544,0.06248561700630076,0.05226199674927553,0.04391332021512457,0.0362388948836421,0.028771811915904597,0.021766912642120367,0.017851811183800522,0.016547718864265582,0.016204081338222126,0.01609928843778344,0.01793340743858376,0.02167101081510387,0.026905775933065687,0.03476028008247919,0.04174969217701337,0.04556642622981125,0.0502964960299522,0.05343915640099257,0.05633593277960072,0.05930919417599005,0.06268432745911172,0.07100232753007056,0.07536943494521993]

(es Cocci%C3%B3n_del_pan,[D@4113dfa1)

(en Incest_(book),[D@7fbee467)

(es Rigidez,[D@4d8567b6)

(en It%27s_a_Big_Big_World,[D@715c057c)

(es Xena,_la_princesa_guerrera,[D@506c4a08)

(en Canine_degenerative_myelopathy,[D@2bfba4dd)

(es Napalm_Death,[D@1604bfba)

(es Bill_Weasley,[D@11c757a1)

[0.015940518515149795,0.013132258953179704,0.011945897552640562,0.011861991244436657,0.012805831491068948,0.015679187263148014,0.02262443064726532,0.035556345120969696,0.04741118399400519,0.05668415262778178,0.06092749528188912,0.06019468009188924,0.06382755672329135,0.06871833451187394,0.06897048207607162,0.06478477925594898,0.060607724418520206,0.055794153506566455,0.05487181360690192,0.05290308482272885,0.04992589295590789,0.04168858732173386,0.03152206946939797,0.02162154854763272]

(fr Alain_Duhamel,[D@5dd22216)

(ru %D0%A2%D1%83%D0%B9%D0%BE%D0%BD,[D@ebc0279)

(fr NFFNSNC,[D@59465d7d)

(de Michael_Diekmann,[D@1aa3e755)

(ru %D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%97%D0%B0%D1%8F%D0%B2%D0%BA%D0%B8_%D0%BD%D0%B0_%D1%81%D1%82%D0%B0%D1%82%D1%83%D1%81_%D0%BF%D0%B0%D1%82%D1%80%D1%83%D0%BB%D0%B8%D1%80%D1%83%D1%8E%D1%89%D0%B5%D0%B3%D0%BE,[D@7ea88b1c)

(de Mini_(BMW),[D@6b0ce311)

(de Fusion_(Wirtschaft),[D@1b0fa7ff)

(ru %D0%A5%D0%B0%D0%BD%D0%BA%D0%B0,[D@20de643a)

[0.03352617350252567,0.03079052991999171,0.02964440457103978,0.029540020953520832,0.029461836540902554,0.029905089678931806,0.029808884916087165,0.03200541174382243,0.03512436551351589,0.039966520210524596,0.04240044988606437,0.04418582216021132,0.04632109711997721,0.04557993800971453,0.05757313899096623,0.05831192867593248,0.0564793332541563,0.051774310974806004,0.049047699260265844,0.049311394625994494,0.049607769417391215,0.047604845887662825,0.04413031817168932,0.03789871601430566]

(es Stamford_Bridge,[D@273f5150)

(en Santa_Fe_Institute,[D@2df36f51)

(ru %D0%9A%D0%BE%D0%BD%D1%82%D0%B5%D0%B9%D0%BD%D0%B5%D1%80%D0%BE%D0%B2%D0%BE%D0%B7,[D@49114668)

(ru %D0%92%D0%BE%D1%82%D0%BA%D0%B8%D0%BD%D1%81%D0%BA%D0%B8%D0%B9_%D0%B7%D0%B0%D0%B2%D0%BE%D0%B4,[D@17c34b3c)

(en V%C3%A9hicule_de_l%27Avant_Blind%C3%A9,[D@16805c54)

(en Lobengula,[D@452d9a56)

(en Magdalene_College,_Cambridge,[D@61e34259)

(en Garth_Jennings,[D@f191344)

[0.04397009580374622,0.04162512759241117,0.03956298146407021,0.03880084655148732,0.03722109162254666,0.03461427673659028,0.03034563252301237,0.027899146946995145,0.02672476183219311,0.02700962431341052,0.02676881490505619,0.027838522610068694,0.03097753816972948,0.03720679918909251,0.04442681935077926,0.04892967621461186,0.053597342502344755,0.057160187311227316,0.06022186015740068,0.06160813428878053,0.05672625533767601,0.051335667357740755,0.049207945989977214,0.04622085122905136]

(en Saliva_(band),[D@946421a)

(en Queue,[D@639dbdb7)

(en Tufted_Titmouse,[D@9126c79)

(en Keystone_(architecture),[D@188f8096)

(en George_Jones,[D@75430472)

(en Jason_&_the_Scorchers,[D@2d91483)

(en File:Lamb_of_God-0358-Randy_Blythe.jpg,[D@79d1a5ea)

(en Beneath_the_Sky,[D@32e3e421)

(en Pajeon,[D@f964ca1)

Centroids with some articles for K-means with K=50:

Centroids with some articles:

[0.013690037692894869,0.010981137438827645,0.009832182695759195,0.009747683964607061,0.01062609887924154,0.013795931813798259,0.022683117107498634,0.041557225413187376,0.058233651817725204,0.07006137710396709,0.0714935795862924,0.06678149417967616,0.06815596753041171,0.0727939164406252,0.06914650297633196,0.06319227057504655,0.055070747215743086,0.04834312245154153,0.04703580574392569,0.04624735116600365,0.04519051524010059,0.038067519497170195,0.028328931218810187,0.01894383225081437]

(en Energy_systems,[D@44f55289)

(de Flughafen_Berlin-Tegel,[D@45fdc3bd)

(fr API,[D@173dd131)

(fr AXA,[D@5b70f3e2)

(fi Kosovo,[D@549ba954)

(de Ich_heirate_eine_Familie,[D@3789f531)

(pl Rumie%C5%84_zaka%C5%BAny,[D@42408073)

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