cs 5614: (big) data management...

CS5614:(Big)DataManagementSystems

B.AdityaPrakashLecture#16:Recommenda2on

Systems

Example:RecommenderSystems

§  CustomerX–  BuysMetallicaCD–  BuysMegadethCD

§  CustomerY–  DoessearchonMetallica–  RecommendersystemsuggestsMegadethfromdatacollectedaboutcustomerXVTCS5614 2Prakash2017

RecommendaCons

Items

Search Recommendations

Products, web sites, blogs, news items, …

3VTCS5614

Examples:

Prakash2017

FromScarcitytoAbundance§  ShelfspaceisascarcecommodityfortradiConalretailers– Also:TVnetworks,movietheaters,…

§ Webenablesnear-zero-costdisseminaConofinformaConaboutproducts– Fromscarcitytoabundance

§ MorechoicenecessitatesbeLerfilters– Recommenda2onengines– HowIntoThinAirmadeTouchingtheVoidabestseller:hQp://www.wired.com/wired/archive/12.10/tail.html

VTCS5614 4Prakash2017

Sidenote:TheLongTail

Source: Chris Anderson (2004) 5VTCS5614Prakash2017

Physicalvs.Online

Prakash2017 VTCS5614 6Read http://www.wired.com/wired/archive/12.10/tail.html to learn more!

TypesofRecommendaCons

§  Editorialandhandcurated– Listoffavorites– Listsof“essen2al”items

§  Simpleaggregates– Top10,MostPopular,RecentUploads

§  Tailoredtoindividualusers– Amazon,NeZlix,…

7VTCS5614Prakash2017

FormalModel

§ X=setofCustomers§  S=setofItems

§ UClityfuncConu:X× SàR– R=setofra2ngs– Risatotallyorderedset– e.g.,0-5stars,realnumberin[0,1]


UClityMatrix

0.410.2

0.30.50.21

Avatar LOTR Matrix Pirates

Alice

Bob

Carol

David


KeyProblems§  (1)Gathering“known”raCngsformatrix

– Howtocollectthedataintheu2litymatrix

§  (2)ExtrapolateunknownraCngsfromtheknownones– Mainlyinterestedinhighunknownra2ngs

• Wearenotinterestedinknowingwhatyoudon’tlikebutwhatyoulike

§  (3)EvaluaCngextrapolaConmethods– Howtomeasuresuccess/performanceofrecommenda2onmethods


(1)GatheringRaCngs

§  Explicit– Askpeopletorateitems– Doesn’tworkwellinprac2ce–peoplecan’tbebothered

§  Implicit– Learnra2ngsfromuserac2ons

•  E.g.,purchaseimplieshighra2ng

– Whataboutlowra2ngs?


(2)ExtrapolaCngUCliCes

§  Keyproblem:U2litymatrixUissparse– Mostpeoplehavenotratedmostitems–  Coldstart:

•  Newitemshavenora2ngs•  Newusershavenohistory

§  Threeapproachestorecommendersystems:–  1)Content-based–  2)Collabora2ve–  3)Latentfactorbased

12VTCS5614

Only briefly

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CONTENT-BASEDRECOMMENDERSYSTEMS

Prakash2017 VTCS5614 13

Content-basedRecommendaCons

§ Mainidea:Recommenditemstocustomerxsimilartopreviousitemsratedhighlybyx

Example:§ MovierecommendaCons

– Recommendmovieswithsameactor(s),director,genre,…

§ Websites,blogs,news– Recommendothersiteswith“similar”content


PlanofAcCon

likes

Item profiles

Red Circles

Triangles

User profile

match

recommend build


ItemProfiles§  Foreachitem,createanitemprofile

§  Profileisaset(vector)offeatures– Movies:author,2tle,actor,director,…–  Text:Setof“important”wordsindocument

§  Howtopickimportantfeatures?– Usualheuris2cfromtextminingisTF-IDF(Termfrequency*InverseDocFrequency)

•  Term…Feature•  Document…Item


Sidenote:TF-IDFfij=frequencyofterm(feature)iindoc(item)j

ni=numberofdocsthatmen2ontermiN=totalnumberofdocsTF-IDFscore:wij=TFij×IDFi

Docprofile=setofwordswithhighestTF-IDFscores,togetherwiththeirscores

17VTCS5614

Note: we normalize TF to discount for “longer” documents

Prakash2017

UserProfilesandPredicCon§  UserprofilepossibiliCes:

– Weightedaverageofrateditemprofiles– VariaCon:weightbydifferencefromaveragera2ngforitem

– …§  PredicConheurisCc:

– Givenuserprofilexanditemprofilei,es2mate𝑢(𝒙,𝒊) = cos(𝒙,𝒊) = 𝒙·𝒊/||𝒙||⋅||𝒊|| 


Pros:Content-basedApproach§  +:Noneedfordataonotherusers

– Nocold-startorsparsityproblems

§  +:Abletorecommendtouserswithuniquetastes

§  +:Abletorecommendnew&unpopularitems– Nofirst-raterproblem

§  +:AbletoprovideexplanaCons– Canprovideexplana2onsofrecommendeditemsbylis2ngcontent-featuresthatcausedanitemtoberecommended


Cons:Content-basedApproach§  –:Findingtheappropriatefeaturesishard

– E.g.,images,movies,music

§  –:RecommendaConsfornewusers– Howtobuildauserprofile?

§  –:OverspecializaCon– Neverrecommendsitemsoutsideuser’scontentprofile

– Peoplemighthavemul2pleinterests– Unabletoexploitqualityjudgmentsofotherusers


COLLABORATIVEFILTERING

Harnessingqualityjudgmentsofotherusers


CollaboraCveFiltering§  Consideruserx

§  FindsetNofotheruserswhosera2ngsare“similar”tox’sra2ngs

§  Es2matex’sra2ngsbasedonra2ngsofusersinN

22VTCS5614

x

N

Prakash2017

Finding“Similar”Users§  Letrxbethevectorofuserx’sra2ngs§  Jaccardsimilaritymeasure

–  Problem:Ignoresthevalueofthera2ng§  Cosinesimilaritymeasure

–  sim(x,y)=cos(rx,ry)–  Problem:Treatsmissingra2ngsas“nega2ve”

§  PearsoncorrelaConcoefficient–  Sxy=itemsratedbybothusersxandy

VTCS5614 23

rx = [*, _, _, *, ***] ry = [*, _, **, **, _]

rx, ry as sets: rx = {1, 4, 5} ry = {1, 3, 4}

rx, ry as points: rx = {1, 0, 0, 1, 3} ry = {1, 0, 2, 2, 0}

rx, ry … avg. rating of x, y

Prakash2017

sim(x, y) =(rxs − rx

−

)(s∈Sxy

∑ rys − ry−

)

(rxs − rx−

)2s∈Sxy

∑ (rys − ry−

)2s∈Sxy

∑

SimilarityMetric

§  IntuiCvelywewant:sim(A,B)>sim(A,C)§  Jaccardsimilarity:1/5<2/4§  Cosinesimilarity:0.386>0.322

–  Considersmissingra2ngsas“nega2ve”–  SoluCon:subtractthe(row)mean

VTCS5614 24

sim A,B vs. A,C: 0.092 > -0.559 Notice cosine sim. is correlation when data is centered at 0

Prakash2017

RaCngPredicCons


rxi

= 1/kP

y2N

ryi

rxi

=P

y2N

s

xy

r

yiPy2N

s

xy

Item-ItemCollaboraCveFiltering§  Sofar:User-usercollaboraCvefiltering§  Anotherview:Item-item

–  Foritemi,findothersimilaritems–  Es2matera2ngforitemibasedonra2ngsforsimilaritems

–  Canusesamesimilaritymetricsandpredic2onfunc2onsasinuser-usermodel

VTCS5614 26

∑∑

∈

∈⋅

=);(

);(

xiNj ij

xiNj xjijxi s

rsr

sij… similarity of items i and j rxj…rating of user u on item j N(i;x)… set items rated by x similar to i

Prakash2017

Item-ItemCF(|N|=2)

12 11 10 9 8 7 6 5 4 3 2 1

4 5 5 3 1 1

3 1 2 4 4 5 2

5 3 4 3 2 1 4 2 3

2 4 5 4 2 4

5 2 2 4 3 4 5

4 2 3 3 1 6

users

movies

- unknown rating - rating between 1 to 5 27VTCS5614Prakash2017

Item-ItemCF(|N|=2)

12 11 10 9 8 7 6 5 4 3 2 1

4 5 5 ? 3 1 1

3 1 2 4 4 5 2

5 3 4 3 2 1 4 2 3

2 4 5 4 2 4

5 2 2 4 3 4 5

4 2 3 3 1 6

users

- estimate rating of movie 1 by user 5 28VTCS5614

movies

Prakash2017

Item-ItemCF(|N|=2)

12 11 10 9 8 7 6 5 4 3 2 1

4 5 5 ? 3 1 1

3 1 2 4 4 5 2

5 3 4 3 2 1 4 2 3

2 4 5 4 2 4

5 2 2 4 3 4 5

4 2 3 3 1 6

users

Neighbor selection: Identify movies similar to movie 1, rated by user 5 29VTCS5614

movies

1.00

-0.18

0.41

-0.10

-0.31

0.59

sim(1,m)

Here we use Pearson correlation as similarity: 1) Subtract mean rating mi from each movie i m1 = (1+3+5+5+4)/5 = 3.6 row 1: [-2.6, 0, -0.6, 0, 0, 1.4, 0, 0, 1.4, 0, 0.4, 0] 2) Compute cosine similarities between rows Prakash2017

Item-ItemCF(|N|=2)

12 11 10 9 8 7 6 5 4 3 2 1

4 5 5 ? 3 1 1

3 1 2 4 4 5 2

5 3 4 3 2 1 4 2 3

2 4 5 4 2 4

5 2 2 4 3 4 5

4 2 3 3 1 6

users

Compute similarity weights: s1,3=0.41, s1,6=0.59

30VTCS5614

movies

1.00

-0.18

0.41

-0.10

-0.31

0.59

sim(1,m)

Prakash2017

Item-ItemCF(|N|=2)

12 11 10 9 8 7 6 5 4 3 2 1

4 5 5 2.6 3 1 1

3 1 2 4 4 5 2

5 3 4 3 2 1 4 2 3

2 4 5 4 2 4

5 2 2 4 3 4 5

4 2 3 3 1 6

users

Predict by taking weighted average:

r1.5 = (0.41*2 + 0.59*3) / (0.41+0.59) = 2.6 31VTCS5614

movies

Prakash2017∑∑

∈

∈⋅

=);(

);(

xiNj ij

xiNj xjijxi s

rsr

CF:CommonPracCce§  Definesimilaritysijofitemsiandj§  SelectknearestneighborsN(i;x)

–  Itemsmostsimilartoi,thatwereratedbyx

§  Es2matera2ngrxiastheweightedaverage:

VTCS5614 32

baselineesCmateforrxi μ=overallmeanmoviera2ngbx=ra2ngdevia2onofuserx=(avg.ra1ngofuserx)–μbi=ra2ngdevia2onofmoviei

∑∑

∈

∈=);(

);(

xiNj ij

xiNj xjijxi s

rsr

Before:

∑∑

∈

∈−⋅

+=);(

);()(

xiNj ij

xiNj xjxjijxixi s

brsbr

Prakash2017

bxi

= µ+ bx

+ bi

Item-Itemvs.User-User

0.418.010.90.30.5

0.81Avatar LOTR Matrix Pirates

Alice

Bob

Carol

David

33VTCS5614

¡  InpracCce,ithasbeenobservedthatitem-itemoqenworksbeLerthanuser-user

¡  Why?Itemsaresimpler,usershavemul2pletastesPrakash2017

Pros/ConsofCollaboraCveFiltering§  +Worksforanykindofitem

–  Nofeatureselec2onneeded§  -ColdStart:

–  Needenoughusersinthesystemtofindamatch§  -Sparsity:

–  Theuser/ra2ngsmatrixissparse–  Hardtofindusersthathaveratedthesameitems

§  -Firstrater:–  Cannotrecommendanitemthathasnotbeen

previouslyrated–  Newitems,Esotericitems

§  -Popularitybias:–  Cannotrecommenditemstosomeonewith

uniquetaste–  Tendstorecommendpopularitems


HybridMethods

§  ImplementtwoormoredifferentrecommendersandcombinepredicCons– Perhapsusingalinearmodel

§  Addcontent-basedmethodstocollaboraCvefiltering–  Itemprofilesfornewitemproblem– Demographicstodealwithnewuserproblem


LATENTFACTORMODELS


Gearedtowardsfemales

Gearedtowardsmales

Serious

Funny

LatentFactorModels(e.g.,SVD)

37VTCS5614

The Princess Diaries

The Lion King

Braveheart

Lethal Weapon

Independence Day

Amadeus The Color Purple

Dumb and Dumber

Ocean’s 11

Sense and Sensibility

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LatentFactorModels§  “SVD”onNeZlixdata:R≈Q·PT

§  Fornowlet’sassumewecanapproximatethera2ngmatrixRasaproductof“thin”Q·PT–  Rhasmissingentriesbutlet’signorethatfornow!

•  Basically,wewillwantthereconstruc2onerrortobesmallonknownra2ngsandwedon’tcareaboutthevaluesonthemissingones

VTCS5614 38

45531

312445

53432142

24542

522434

42331

.2 -.4 .1

.5 .6 -.5

.5 .3 -.2

.3 2.1 1.1

-2 2.1 -.7

.3 .7 -1

-.9 2.4 1.4 .3 -.4 .8 -.5 -2 .5 .3 -.2 1.1

1.3 -.1 1.2 -.7 2.9 1.4 -1 .3 1.4 .5 .7 -.8

.1 -.6 .7 .8 .4 -.3 .9 2.4 1.7 .6 -.4 2.1 ≈

users

item

s

PT

Q

item

s

users

R

SVD: A = U Σ VT

factors

factors

Prakash2017

RaCngsasProductsofFactors

§  HowtoesCmatethemissingraCngofuserxforitemi?

VTCS5614 39

45531

312445

53432142

24542

522434

42331

item

s

.2 -.4 .1

.5 .6 -.5

.5 .3 -.2

.3 2.1 1.1

-2 2.1 -.7

.3 .7 -1

-.9 2.4 1.4 .3 -.4 .8 -.5 -2 .5 .3 -.2 1.1

1.3 -.1 1.2 -.7 2.9 1.4 -1 .3 1.4 .5 .7 -.8

.1 -.6 .7 .8 .4 -.3 .9 2.4 1.7 .6 -.4 2.1

≈

item

s

users

users

?

PT

qi = row i of Q px = column x of PT

fact

ors

Q factors Prakash2017

RaCngsasProductsofFactors§  HowtoesCmatethemissingraCngof

userxforitemi?

VTCS5614 40

45531

312445

53432142

24542

522434

42331

item

s

.2 -.4 .1

.5 .6 -.5

.5 .3 -.2

.3 2.1 1.1

-2 2.1 -.7

.3 .7 -1

-.9 2.4 1.4 .3 -.4 .8 -.5 -2 .5 .3 -.2 1.1

1.3 -.1 1.2 -.7 2.9 1.4 -1 .3 1.4 .5 .7 -.8

.1 -.6 .7 .8 .4 -.3 .9 2.4 1.7 .6 -.4 2.1

≈

item

s

users

users

?

PT

fact

ors

Q factors


Prakash2017

RaCngsasProductsofFactors§  HowtoesCmatethemissingraCngof

userxforitemi?

VTCS5614 41

45531

312445

53432142

24542

522434

42331

item

s

.2 -.4 .1

.5 .6 -.5

.5 .3 -.2

.3 2.1 1.1

-2 2.1 -.7

.3 .7 -1

-.9 2.4 1.4 .3 -.4 .8 -.5 -2 .5 .3 -.2 1.1

1.3 -.1 1.2 -.7 2.9 1.4 -1 .3 1.4 .5 .7 -.8

.1 -.6 .7 .8 .4 -.3 .9 2.4 1.7 .6 -.4 2.1

≈

item

s

users

users

?

Q PT

2.4

f fac

tors

f factors


Prakash2017


Gearedtowardsmales

Serious

Funny

LatentFactorModels

42VTCS5614


The Lion King

Braveheart

Lethal Weapon

Independence Day


Dumb and Dumber

Ocean’s 11


Factor 1

Fact

or 2

Prakash2017


Gearedtowardsmales

Serious

Funny

LatentFactorModels

43VTCS5614


The Lion King

Braveheart

Lethal Weapon

Independence Day


Dumb and Dumber

Ocean’s 11


Factor 1

Fact

or 2

Prakash2017

Formoredetails

§  Readthetextbook!


REMARKS&PRACTICALTIPS

-EvaluaCon-Errormetrics-Complexity/Speed


EvaluaCon

1 3 4

3 5 5

4 5 5

3

3

2 2 2

5

2 1 1

3 3

1

movies

users


EvaluaCon

1 3 4

3 5 5

4 5 5

3

3

2 ? ?

?

2 1 ?

3 ?

1

Test Data Set

users

movies


EvaluaCngPredicCons§  ComparepredicConswithknownraCngs

–  Root-mean-squareerror(RMSE)•  whereispredicted,isthetruera2ngofxoni

–  Precisionattop10:•  %ofthoseintop10

–  RankCorrelaCon:•  Spearman’scorrela1onbetweensystem’sanduser’scompleterankings

§  Anotherapproach:0/1model–  Coverage:

•  Numberofitems/usersforwhichsystemcanmakepredic2ons–  Precision:

•  Accuracyofpredic2ons–  ReceiveroperaCngcharacterisCc(ROC)

•  Tradeoffcurvebetweenfalseposi2vesandfalsenega2ves


qPxi(r

xi � r⇤xi)2 r=predicted;r*=true

ra2ngofxoni

ProblemswithErrorMeasures

§  NarrowfocusonaccuracysomeCmesmissesthepoint– Predic2onDiversity– Predic2onContext– Orderofpredic2ons

§  InpracCce,wecareonlytopredicthighraCngs:– RMSEmightpenalizeamethodthatdoeswellforhighra2ngsandbadlyforothers


CollaboraCveFiltering:Complexity

§  Expensivestepisfindingkmostsimilarcustomers:O(|X|)

§  TooexpensivetodoatrunCme–  Couldpre-compute

§  Naïvepre-computa2ontakes2meO(k·|X|)–  X…setofcustomers

§  Wealreadyknowhowtodothis!– Near-neighborsearchinhighdimensions(LSH)–  Clustering– Dimensionalityreduc2on


Tip:AddData

§  Leverageallthedata– Don’ttrytoreducedatasizeinanefforttomakefancyalgorithmswork

– Simplemethodsonlargedatadobest

§  Addmoredata– e.g.,addIMDBdataongenres

§ MoredatabeatsbeLeralgorithmshttp://anand.typepad.com/datawocky/2008/03/more-data-usual.html


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