MathorCup优秀论文B题.docx
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MathorCup优秀论文B题.docx
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MathorCup优秀论文B题
Thejudgesscoring,note
Teamnumber:
10469
Thejudgesscoring,note
Thejudgesscoring,note
Problem:
B
Thejudgesscoring,note
Title:
BookRecommendation
Thispapermainlystudiesthebooksrecommendproblem,andanalyzesthefactorsthatinfluencethescoreofbooksbycollaborativefilteringalgorithmandbookssimilarityanalysis,thenpredictsthescoresofthesebookswhichspecifiedreaderswhohavenotread.Atlast,itrespectivelyrecommendsthreebookstothespecifiedreadersbasedontagsimilarityandreadingpreferencemodel.
Problem1:
Thispaper,accordingtothecorrelationanalysisandclassificationofdatastatistics,foundthattheaveragescoresofbooks,theuser'shabitsofscoringandusers'readingpreference(tag)havedifferentimpactonusers’score.
Problem2:
Forthespecifiedreaders,thispaperadoptsthecosinesimilaritytocalculatesimilaritybetweeneachbookwhichneedtopredictandallbooksthatthisreaderhavescoredandrankedthebookbytheirsimilarity,selectedthetop10booksasaneighborset,accordingtothisbooks’scoreofneighborsetbythisreadertopredicthisscoreforthisbook.Inordertocheckuptheaccuracyoftheprediction,thispaperputasmallpartofthescoringrecordasatestset,thenuseMAEindextomeasurepredictionerror,theresultsshowthatpredictionisgood.
Problem3:
Thispaperusethecosinesimilaritytocalculateperbook’stagsymbiosisofsimilarity,setauserreadingpreferencemodeltocalculatethesimilaritybetweenusersandmatched-degreebetweenusers’readingpreferencesandtags,integratedthetwoindexestogettherecommendedindex.Accordingtotherecommendedindex,werecommendthreebookstothespecifiedusers.
Keywords:
Collaborativefiltering,Cosinesimilarity,Labelsimilarity,Readingpreferencemodel,Recommendindex
Modelhypothesis
1.Thereadinginterestsofusersthroughoutthegradingprocesshavenotchanged.
2.Theuserwouldliketoreadthebookthatheinterestedin.
3.Differentlabelsrepresentdifferentcategoriesofbooks.
4.Theuserwouldliketoreadabookseveraltimesifheisinterestedinthisbook.
Symboldescription
Symbol
Details
Bookquality
Thepopularityofthebooks
Users’scorepreference
Users’bookpreference
Influenceofthesocialcycle
Thesimilarityofbooks
Co-occurrenceofthebooktags
Users’similarity
Thematched-degreebetweenuserandbook
Recommendationindex
Questionanalysis
Questionone:
Objectively,thescoreofbooksarebasedonthequality,anditisalsoinfluencedbytheindividualpreference.Accordingtothedatathatisgivenbytheaccessory,inthefirstplace,wedefinethequalityofbookQ,thepopularitydegreeofthebookP,user’sindividualpreferenceofscoreIP,user’spreferenceofbookBP,andtheinfluenceofpersonalsocialcircleSI.Thenweanalyzetheinfluenceofthesefactorstothescorerespectively.
Questiontwo:
Inconditionsthatdonottakeintoaccountsubjectivefactors,thesameuserhassimilartobooksshouldbeofthesamequalitygrading.Firstofall,weusecollaborativefilteringrecommendationalgorithmbasedonsimilarityofbookstofindbookssimilarityoftheneighborwiththeprojectionsset;then,weusetheneighborssetforpredictingbooksgiveapredictionscore.
Questionthree:
Torecommendbooks,itshouldasfaraspossibleinlinewiththeuser'sreadingpreferences.Firstofall,wederiveuserattentiontobooks.Secondly,wefindthereadingpreferencesofusers,thenpleaserecommendbooksthatmeetusers'preferencesontheuser'sindexand,finally,findthehighestrecommendindexbooksrecommendedtotheuser.
ModelSolution
Questionone
TheimpactofthebookqualityQ
WeassumetheaveragescoreofbookcanindicatethebookqualityQ,anddefineitasfollows:
The
showsthescoreofbookiwhichismarkedbytheuserj.
representsthenumberofuserwhomarkedthebooki.
Werandomlyselect100usersfromtheaccessoryofuserbookscore,andthenmakethreestepstoanalyzeit,theprocessareasfollows:
Step1:
Findhebookswhichismarkedbytheuseranditsscore.
Step2:
Calculatetheaveragescoreofthesebook.
Step3:
Calculatethecorrelation coefficientbetweenthebookscoreandbookqualityandmakeahypothesistestingtoexaminewhetheritisrelevant.
Hereistheresulttable:
BookID
score
numbers
Bookquality
962729
4
959
4.116788
356405
4
463
4.164147
836383
4
588
4.061224
284550
4
998
3.942886
723581
4
1145
4.135371
827305
4
478
3.920502
572786
4
232
4.025862
473690
4
319
3.833856
964695
4
1063
4.235183
929118
4
497
4.046278
ThecorrelationcoefficientR=0.57359,confidencelevelP=1.4614e-046.
Theimpactofthebookpopularitydegree
Becausethenumberofbooktagreflectthepopularitydegreeofbook,wedefinethepopularitydegreePasfollows:
The
showsthej-thtagofbooki.
Werandomlyselect100usersfromtheaccessoryofuserbookscore,andthenmakethreestepstoanalyzeit,theprocessareasfollows:
Step1:
Findhebookswhichismarkedbytheuseranditsscore.
Step2:
Calculatethepopularitydegreeofthesebooks.
Step3:
Calculatethecorrelation coefficientbetweenthebookscoreandbookpopularitydegreeandmakeahypothesistestingtoexaminewhetheritisrelevant.
Hereistheresulttable:
BookID
score
Tagnumber
304070
3
17
419461
3
0
394406
4
17
995198
4
18
523511
4
0
471206
4
24
726758
4
17
798662
3
13
877201
3
20
378626
3
16
ThecorrelationcoefficientR=0.1368,confidencelevelP=0.0018234.
IP:
User’sscorepreference
Firstly,wecandefinetheIP:
Inthisformula,
Werandomlyselect100usersfromtheaccessoryofuserbookscore,andmakeaprocesstoeachindividual:
Step1:
Findthemarkedbookandthescoreoftheusers
Step2:
CalculatetheIP.
ThereareanexampleofauserwhichIDis7245481,theresultisasfollows:
Score
Appearingtimes
1
1
2
7
3
131
4
359
5
19
IP=3.909
Questiontwo
Thisquestionweadoptthecollaborativefilteringrecommendationalgorithmbasedonthebooksimilarity,andthenpredictthebookscoreofaccessorypredict.txt.
1.Firstly,weneedtodefinethesimilaritybetweenthebooks,theprocessareasfollows:
Findtheuserwhomarkedthebookiandj,nrepresentsthenumberoftheseusers,sothebookiandjhaveitsvector
and
respectivelyinndimensionspace,thesimilaritybetweenbookiandjis
2.EstablishthescorematrixS.
ThefirstsixcolumnofthematrixSindicatethebookswhichisneededtopredictfortheuser
andmarkeditas
thenextncolumnindicatethebookswhichismarkedbytheuser.Wecansettherearennumberofbooks,sothematrixwillhaven+6column.ThefirstrowofmatrixSshowstheusers,thenextmrowsindicatetheuserwhoparticipatedinthemarking.Supposingtherearemnumberusers,sothematrixwouldhavem+1row.
3.Predictingthescore
Thedetailprocessesareasfollows:
Step1:
takematrixSinthe1thcolumnelementandsubsectionjcolumnelement,
respectivelyrememberfor
and
;
Step2:
takein
andinthe
whicharenotcontaining0ofline,rememberfor
and
ifnotaketo,wecandefine
and
ofsimilardegreesfor0;orwithformula
(1)begged
and
ofsimilardegrees
;
Step3:
takesimilardegrees
supremeof10books,composedneighborsset
whichbooks
and
ofsimilardegreessupreme
books
and
ofsimilardegreesfollowed,andsoon.
Step4:
askstheuserforthepredictedscore:
4.Makeaforecastforthesixusers
Theresultsareasfollows:
7245481
794171
381060
776002
980705
354292
738735
4
3.8
3.6
3.8
3.6
3.6
7625225
473690
929118
235338
424691
916469
793936
3.800161
3.399658
4
4
3.800061
3.799982
4156658
175031
422711
585783
412990
134003
443948
4.6
3.4
4
4
3.6
3.8
5997834
346935
144718
827305
219560
242057
803508
4.599925
4.799826
4.400263
4.600099
4.400368
4.599396
9214078
310411
727635
724917
325721
105962
235338
4
4
4.2
3.6
3.8
4.2
2515537
900197
680158
770309
424691
573732
210973
3.399379
3.199388
3.799433
3.799829
4
3.799717
Inordertoexaminetheprediction,weusethemeanabsoluteerror(MAE)tojudgetheaccuracyoftheforecast.Wesupposethepredictionsetas
realscoresetas
.
Therearethetableofthecomparabledata.
7245481
BookID
962729
356405
836383
284550
723581
827305
Forecastscore
3.846279
3.846045
4
3.99992
3.845464
3.922996
Actual
Score
4
4
4
4
4
4
7625225
BookID
702699
962729
642256
794171
836383
284550
Forecastscore
3.845917
4
4
3.845978
4
4
Actual
Score
4
4
4
4
4
4
4156658
BookID
345849
220930
732533
566113
500788
242605
Forecastscore
3.690256
3.230769
3.615385
3.230769
3.384615
3.921765
Actual
Score
4
4
4
4
4
4
5997834
BookID
885390
702699
962729
723581
381060
964695
Forecastscore
4
5
5
4
4
4
Actual
Score
4
5
5
4
4
4
9214078
BookID
776002
144718
242462
424691
557713
438265
Forecastscore
4.07757
4.07708
4.154254
3.922162
4.076416
3.999463
Actual
Score
4
4
4
4
4
4
2515537
BookID
284550
981616
585307
916469
131620
549623
Forecastscore
3.537614
3.230474
3.461628
3.307315
3.614623
3.614518
Actual
Score
4
4
4
4
4
4
Questionthree
Inordertoexpresstheuser’spreferencesmoreaccurately,weadoptthebookrecommendationalgorithmwhichbasedonlabelsimilarityforthequestionthree.Becau
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