Artificial Intelligence Algorithms for Collaborative Book Recommender Systems

Annals o Da a Science (2024) 11(5):1705–1739 h ps://doi.o g/10.1007/s40745-023-00474-4 A i icial In elligence Algo i hms o Collabo a i e Book Recommende Sys ems Clemens Tege meie 1·A ne Johannssen1·Na aliya Chukh o a2 Recei ed: 24 No embe 2022 / Re ised: 10 May 2023 / Accep ed: 13 May 2023 / Published online: 8 June 2023 © The Au ho (s) 2023 Abs ac Book ecommende sys ems p o ide pe sonalized ecommenda ions o books o use s based on hei p e ious sea ches o pu chases. As online ading o books has become inc easinglyimpo an in ecen yea s,a i icialin elligence(AI)algo i hmsa eneeded o ecommend sui able books o use s and encou age hem o make pu chasing deci- sions in he sho and he long un. In his pape , we conside AI algo i hms o so called collabo a i e book ecommende sys ems, especially he ma ix ac o - iza ion algo i hm using he s ochas ic g adien descen me hod and he book-based k-nea es -neighbo algo i hm. We pe o m a comp ehensi e case s udy based on he Book-C ossing benchma k da a se , and implemen a ious a ian s o bo h AI algo- i hms o p edic unknown book a ings and o ecommend books o indi idual use s based on he highes p edic ed a ings. This s udy aims o e alua e he quali y o he implemen ed me hods in ecommending books by using selec ed e alua ion me ics o AI algo i hms. Keywo ds A i icial in elligence ·Book ecommende sys ems ·knn algo i hm · Machine lea ning ·Ma ix ac o iza ion algo i hm ·S ochas ic g adien descen me hod BA ne Johannssen a ne.johannssen@uni-hambu g.de Clemens Tege meie [email p o ec ed] Na aliya Chukh o a na aliya.chukh o a@hcu-hambu g.de 1Uni e si y o Hambu g, Hambu g, Ge many 2Ha enCi y Uni e si y, Hambu g, Ge many 123 1706 Annals o Da a Science (2024) 11(5):1705–1739 1 In oduc ion Book ecommende sys ems a e o en used by companies o p esen in e es ing and pe sonalized book ecommenda ions o hei cus ome s. The ecommenda ions a e supposed ocon ince hecus ome obuybooksin hesho unand ouse hebook ec- ommende sys em o u he pu chases in he long un. As online ading o books has conside ably inc eased in ecen yea s [1], book ecommende sys ems ha e become mo e impo an . Online bookselle s such as Amazon, Ba nes & Noble, Wa e s ones, and Thalia ha e played an impo an ole in his de elopmen . Fo ins ance, cu en challenges o ecommende sys ems a e aking in o accoun he use ’s con ex , e.g., ime o mood [2–4], ensu ing di e si y [5] and including implici a ings o a g ea e ex en [6] when gene a ing book ecommenda ions. Gene ally, he esea ch ocus has u ned o A i icial In elligence (AI) algo i hms, e.g., he numbe o pape s conside ing deep lea ning echniques has inc eased signi ican ly in ecen yea s and is equen ly applied o ecommende sys ems [7–9]. No e ha AI, like machine lea ning, deep lea ning, da a mining, and Big Da a analy ics, is based on Da a Science echniques, so hese a eas a e closely ela ed [10–12]. While AI e e s o he de elopmen o in elligen echniques ha can pe o m asks ha ypically equi e human in elligence [13], Da a Science is an in e disciplina y ield ha in ol es he ex ac ion, p ocessing, analysis, and in e p e a ion o la ge and complex da a se s. In pa icula , deep lea ning and a ious a ian s o neu al ne wo ks o e a new way o add ess cu en challenges o ecommende sys ems [14] and beyond [15–19]. Howe e , when using hese black box algo i hms, he p oblem o missing explainabili y o how he ecommenda ions a e gene a ed needs o be conside ed [20–22]. Inbook ecommende sys ems, AI algo i hms ha e he ask o sugges ingbooks ha buye s a e po en ially in e es ed in and ha ha e no been ead by hem. Depending on how he AI algo i hms a e supposed o ecommend books, a dis inc ion is made be ween collabo a i e,con en -based, and hyb id book ecommende sys ems. In a collabo a i e book ecommende sys em, AI algo i hms access all book a ings ha ha ebeensubmi edbyuse so hebook ecommende sys em.Basedon hesubmi ed book a ings, he AI algo i hms p edic o each use he a ings o he books hey ha e no ye a ed. Then, he books wi h he highes p edic ed a ings can be ecommended o each use [23]. Use s mos ly ha e a ed a e y small p opo ion o he books ha exis in he da a. Thus, AI algo i hms ha e o p edic mo e o he book a ings han a e known. In his pape , we ocus on AI algo i hms in collabo a i e ecommende sys ems. Two popula AI algo i hms in collabo a i e ecommende sys ems a e he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod and he book- based k-nea es -neighbo (knn) algo i hm [24]. In his pape , bo h hese algo i hms a e conside ed in he amewo k o he modi ied Book-C ossing da a se . This da a se om Cai–Nicolas Ziegle [25] is a kind o benchma k da a basis o esea ch on AI algo i hms in collabo a i e ecommende sys ems [26]. We in es iga e a subse consis ing o 42,137 explici a ings o he Book-C ossing da a se ha o ms he da a basis. The ask o bo h AI algo i hms is o p edic he unknown book a ings o he modi ied Book-C ossing da a se , and hen o ecommend he books wi h he highes p edic ed a ings o each use . By using di e en a ian s o bo h AI algo i hms, his 123 Annals o Da a Science (2024) 11(5):1705–1739 1707 pape aims o e alua e bo h hese algo i hms in ecommending books based on he modi ied Book-C ossing da a se . Fo his aim, he quali y o bo h AI algo i hms is measu ed by selec ed e alua ion me ics o AI algo i hms. This pape is o ganized as ollows. In Sec .2, a e in oducing he basics o collab- o a i e book ecommende sys ems, a sho o e iew o AI algo i hms and common e alua ion me ics is gi en. Sec ion3p esen s he book-based knn-algo i hm and he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod. In Sec .4, we p o ide a comp ehensi e case s udy based on he Book-C ossing da a se . In pa - icula , we es ablish modi ica ions o he da a basis, p esen ou me hodology and p oposed p ocedu e, gi e he esul s o he s udy, and discuss hem in de ail. In he amewo ko hecases udyweshowhow hequali yo bo hAIalgo i hmsismeasu ed using selec ed e alua ion me ics. Fo his pu pose, he s a is ical so wa e Rand he co esponding package Recommende lab, which was de eloped o collabo a i e ecommende sys ems [27], is used. Finally, Sec .5concludes he pape . 2 AI Algo i hms in Collabo a i e Book Recommende Sys ems 2.1 Essen ials AI algo i hms in collabo a i e book ecommende sys ems a e equi alen o AI algo- i hms ha a e gene ally used in en e ainmen ecommende sys ems (e.g., mo ie ecommende sys ems), whe e he en e ainmen p oduc s a e e e ed o as i ems. The esea ch on book ecommende sys ems depends e y much on he esea ch low on en e ainmen ecommende sys ems, and mos o he esul s a e ans e able o book ecommende sys ems. AI algo i hms need da a abou he book a ings by use s, which can be explici o implici book a ings. A book a ing is called an explici book a ing i a use ac i ely assigns a a ing on a speci ic scale (e.g., a scale om 1 o 10, whe e 10 ep esen s he mos posi i e expe ience and 1 is he mos nega i e expe ience) o a book, see Table 1. In con as , an implici book a ing is no di ec ly gi en by a use . Ins ead, he book a ings a e p edic ed based on he use ’s beha io [28]. Fo example, a a ing o 1 is assigned o a book i a use eads he comple e book whe eas he book ge s a a ing o 0 i a use only spends a sho ime wi h he book. In he ollowing, howe e , we ocus on explici book a ings. Table 1 Example o explici book a ings by use s (on a scale om 1 o 10) Book 1 Book 2 Book 3 Book 4 Book 5 Use 19––1– Use 2–––64 Use 31010–1– Use 4–109–9 Use 5–109–– 123 1708 Annals o Da a Science (2024) 11(5):1705–1739 A collabo a i e book ecommende sys em includes da a abou pbook a ings. The e a e nuse s u1,...,unwho ha e a ed books, and mbooks i1,...im ha ha e ecei ed a a ing by a use . The pbook a ings a e ep esen ed in an n×m use -book ma ix B,see(2.1). B= i1i2··· im u1 u2 . . . un ⎛ ⎜ ⎜ ⎜ ⎝ 11 12 ··· 1m 21 22 ··· 2m . . ..... . . n1··· ··· nm ⎞ ⎟ ⎟ ⎟ ⎠ (2.1) A use can a e a book only once. E e y ow shows he a ings by one use and e e y column ep esen s he a ings o one book. Thus, e e y en y in he use -book ma ix is a a ing by one use o one book. Fo mally his means ha he en y ui is he a ing by use u o book i. Ra ing all mbooks is he maximum amoun o a ings a use can gi e. A book can ecei e a maximum o n a ings meaning ha e e y use has a ed his book. In his pape , we conside a ing p edic ions o use s who ha e al eady a ed a leas one book and o books ha ha e al eady ecei ed a leas one a ing by a use . The e o e, he cold s a p oblem [29] ha deals wi h he ques ion o how o p edic a a ingo ause o o a book wi hou anyknowledgeabou pas a ings is no add essed. Mos use s ha e a ed only a small pe cen age o he mbooks, which implies ha B is a spa se ma ix. The densi y DB=p nm ·100 o he use -book ma ix measu es he pe cen age o he known pbook a ings in ela ion o he heo e ically possible book a ings (i.e., nm a ings). I is impo an o he AI algo i hms o be able o p edic he la ge numbe o unknown a ings by a small numbe o known a ings. I should be no ed ha each use has a di e en iew on he ques ion o which a ing co esponds o a ce ain book quali y. One use may a gue ha he a ing 6 is a good a ing on a scale om 1 o 10, whe eas ano he use conside s only a ings g ea e o equal o 9 as good a ings. The mean u ep esen s he a e age book a ing by a use . Based on he s anda d de ia ion σ( u)o a use ’s book a ings, conclusions can be d awn whe he a use has gi en simila book a ings (low s anda d de ia ion) o a ying book a ings (high s anda d de ia ion). The mean o he a ings o a book iindica es how well use s ha e a ed he book on a e age. Addi ionally, he s anda d de ia ion σ( i)desc ibes he size o he a ing ange o a speci ic book. The mean o all p a ings o he use -book ma ix is gi en by μ. Based on he gi en book a ings, AI algo i hms p edic he unknown a ings o he use -book ma ix B. This enables he AI algo i hms o c ea e an o de ed lis o each use wi h he Nbooks ha ecei ed he highes p edic ion. As a consequence, he books on he lis a e ecommended o each use . How AI algo i hms deal wi h di e en pe cep ions o he a ing scale by use s is explained in Sec s.3.1 and 3.2. 123 Annals o Da a Science (2024) 11(5):1705–1739 1709 2.2 Memo y-Based Ve sus Model-Based AI Algo i hms The AI algo i hms in book ecommende sys ems a e dis inguished be ween memo y- based and model-based AI algo i hms. Memo y-based AI algo i hms access he en i e use -book ma ix o ecommend books o use s [23,30]. In con as , model-based AI algo i hms c ea e a model om he use -book ma ix. Based on his model, use s ge book ecommenda ions. Wi hin he memo y-based AI algo i hms, a dis inc ion is made be ween use -based and book-based AI algo i hms. They employ wo di e en app oaches o o ecas he unknown a ings o he use -book ma ix. Use -based AI algo i hms p edic he missing a ings o e e y use based on simila use a ings. In con as , book-based AI algo i hms o ecas he unknown a ings o e e y book by conside ing he a ings o simila a ed books. Based on he o ecas s o he unknown book a ingse e yuse ge s hebooks ecommended ha ecei ed hehighes p edic ed a ings. The knn-algo i hm is a popula memo y-based AI algo i hm in collabo a i e book ecommende sys ems [23,31]. Model-based AI algo i hms can be classi ied in o he ields o eg ession, clus e - ing, neu al ne wo ks, deep lea ning and dimensionali y educ ion [31]. Model-based AI algo i hms a e mos ly dimension- educing algo i hms, and ma ix ac o iza ion algo i hms a e o en applied in his con ex . The ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod and he ma ix ac o iza ion algo i hm using he al e na ing leas squa es me hod a e wo popula ma ix ac o iza ion algo i hms [23,24]. Addi ionally, esea ch on neu al ne wo ks and deep lea ning in collabo a- i e ecommende sys ems has inc eased signi ican ly in ecen yea s and can also be applied o collabo a i e book ecommende sys ems [7–9]. 2.3 E alua ion Me ics o AI Algo i hms in Book Recommende Sys ems AI algo i hms in book ecommende sys ems p edic he unknown book a ings o he use -book ma ix B. Based on he p edic ions, he AI algo i hms sugges Nbooks o e e y use as an o de ed lis . The quali y o he AI algo i hms depends on he g ade o sa is ac ion o he use s in ela ion o he p oposed books. Howe e , he sa is ac ion is ha dly measu able in eali y. Thus, he quali y o he algo i hms can only be app oxima ed by online o o line es s [28,32]. In he ollowing, we ocus on o line es s and he co esponding e alua ion measu es. The e alua ion me ics can be di ided in o he ields o p edic ion accu acy,classi ica ion accu acy and di e si y [23]. The alues o he e alua ion me ics depend on he cha ac e is ics o he conside ed da a se (e.g., he ange o he a ing scale). The e o e, i is impo an o compa e he quali y o di e en AI algo i hms using he same da a se [28]. Spli ,boo s apping and c oss- alida ion a e me hods ha can be used o e alua e he AI algo i hms [27]. In pa icula , in a c oss- alida ion, use s a e di ided in o a p ede e mined numbe o g oups o equal size. The numbe o g oups is equi alen o he numbe o i e a ions pe o med. In each i e a ion, one g oup is he es g oup and all o he g oups a e conside ed o be he aining g oups. The es g oup is changed in e e yi e a ion, so ha a e all i e a ions each use wasin he es g oup once. The use s o he aining g oups a e e e ed o as aining use s and he use s o he es g oup 123 1710 Annals o Da a Science (2024) 11(5):1705–1739 Table 2 O e iew o he classi ica ion accu acy (con usion ma ix) Recommended No ecommended All Rele an books m e (TP) m n (FN) m I ele an books mie (FP) min (TN) mi All memnm a e e e ed o as es use s. In each i e a ion, a model is de eloped based on he gi en a ings o he aining use s. This model is hen es ed on he es use s. In his p ocess, some o he known a ings a e employed o es he model and some o he known a ings o he es use s a e wi hheld o alida e he model. Mos o line e alua ion me ics a e measu ed by he p edic ed alues o he wi hheld a ings. This is mos ly done by aking he mean o he alues ega ding he o line assessmen me ics in all i e a ions [27]. P edic ion accu acy me ics measu e how p ecisely an AI algo i hm es ima es he a ings. The la ge he de ia ion o he p edic ed alue om he ue alue is, he la ge is he alue o he me ics, and he wo se he p edic ion accu acy o he AI algo i hm. In he ollowing, we conside h ee common p edic ion accu acy me ics, i.e., he Roo Mean Squa e E o (RMSE), he Mean Squa e E o (MSE), and he Mean Absolu e E o (MAE): RMSE = ui ∈ es (ˆ ui − ui)2 p es MSE = ui ∈ es (ˆ ui − ui)2 p es MAE = ui ∈ es |ˆ ui − ui| p es He e, es deno es he a ings o he es da a se ha need o be alida ed and p es deno es hei numbe . The eal a ings a e e e ed o as ui, whe eas ˆ ui ep esen s he p edic ed a ings o use u o book i. Classi ica ion accu acy me ics de e mine whe he a use ecei es book ecom- menda ions ha a e ele an o he use [23]. The la ge he alue o a classi ica ion accu acy me ic, he la ge he classi ica ion accu acy. P ecision and Recall a e he wo mos popula classi ica ion accu acy me ics and can be compu ed based on he con usion ma ix gi en in Table 2: P ecision =m e me Recall =m e m No e ha i holds 0 ≤P ecision,Recall ≤1. 123 Annals o Da a Science (2024) 11(5):1705–1739 1711 In Table 2, he ollowing ac onyms a e used: T ue Posi i es (TP), False Nega i es (FN), False Posi i es (FP), T ue Nega i es (TN). Following Table 2, he ecommended bu i ele an numbe o books mie co esponds o he ype I e o . Addi ionally, he numbe o books m n ha is no ecommended bu ele an can be in e p e ed as ype II e o . P ecision measu es how many o he ecommended books a e ele an , whe easRecall speci ies howmanyo he ele an booksa e ecommended. The e o e, P ecision minimizes he ype I e o , while Recall minimizes he ype II e o . No e ha minimizing one e o ype inc eases he o he e o ype in many cases. This leads o a ade-o be ween he maximiza ion o Recall on he one hand and he maximiza ion o P ecision on he o he hand [23]. Ano he impo an e alua ion me ic is Di e si y. The main idea is ha use s do no app ecia e o ha e he same books sugges ed o e and o e again. Di e si y can be measu ed in di e en ways [5,33]. One app oach is o de e mine how many o he mbooks o he da a se a e ecommended o he use s. This abili y is called Co e age. I he e a e many books ha a e no ecommended o any use , his could mean a lack o di e si ica ion. Bobadilla e al. [34] de ined a use ’s co e age as he p opo ion o books no a ed by he use ha ha e been a ed by one o he use ’s nea es neighbo s (a use ’s nea es neighbo s a e use s who ha e a ed books simila ly o he conside ed use ). Yang e al. [23] p esen ed a di e en app oach o measu e Di e si y ha akes in o accoun he simila i y o books ecommended o one use and he simila i y o books ecommended o wo di e en use s. 3 AI Algo i hms 3.1 Book-Based knn Algo i hm The knn algo i hm is a nonpa ame ic algo i hm [35]. In collabo a i e book ecom- mende sys ems, i is used as a eg ession algo i hm o es ima e he missing alues o he use -book ma ix B. A dis inc ion is made be ween he use -based and he book- based knn-algo i hm. We will mainly ocus on he book-based knn-algo i hm in he ollowing. Fi s , o e e y book, he simila i y o all o he books is measu ed by a simila i y measu e. Two books a e conside ed o be simila , i use s ha e gi en hem a simila a ing. The knea es neighbo s o a book a e he kbooks ha a e mos simila o he book. E e y book has use s who ha e no a ed he book. Based on one use ’s a ings o he knea es neighbo s o he book he use ’s a ing o he book can be p edic ed. The e o e, he use ’s a ings o he knea es neighbo s a e weigh ed wi h he alue o he co esponding simila i y measu e. Fo example, in Table 1, books 2 and 3 ha e ecei ed simila a ings by use s 4 and 5. Book 2 has been highly a ed by use 3. The e o e, he p edic ed a ing o use 3 o book 3 could also be high. Wi h his app oach, he knn algo i hm ies o p edic all unknown book a ings. A e ob aining he p edic ions, he Nbooks wi h he highes p edic ed a ings a e sugges ed o each use [23]. 123 1712 Annals o Da a Science (2024) 11(5):1705–1739 The simila i y o wo books is measu ed by a simila i y measu e. A common sim- ila i y measu e is he B a ais-Pea son co ela ion coe icien [36] wi gh =u∈U ug − g·( uh − h) u∈U ug − g2·u∈U( uh − h)2(3.1) wi h−1≤wi gh ≤1,whe ewi gh indica es hesimila i yo hebooksigandihmeasu ed by he B a ais-Pea son co ela ion coe icien . No e ha only he use s who ha e a ed bo h books (i.e., u∈U) a e used o he calcula ion. Some books may gene ally ha e been a ed highe han o he books. This is aken in o accoun by sub ac ing he espec i e mean. The mean o book igis gi en by gand he mean o book ihis gi en by h. The e o e, a use ’s a ing coun s as a posi i e a ing only i i exceeds he mean o he book’s a ings. The denomina o con ains he s anda d de ia ion o he a ings om he mean. A la ge s anda d de ia ion indica es ha a book has ecei ed di e en a ings. In con as , a low s anda d de ia ion means ha a book has ecei ed mos ly he same a ings. In his way he di e ences o he a ings om he mean conside ed in he nume a o a e scaled. Thus, he B a ais-Pea son co ela ion coe icien akes in o accoun gene al a ing di e ences be ween books. A alue o “1” implies a high simila i y be ween wo books, whe eas a alue o “−1” means ha wo books ha e ecei ed opposi e a ings by use s and a e he e o e no simila . The adjus ed cosine simila i y and he Euclidean dis ance a e also popula simila i y measu es bu a e no conside ed in his pape [37]. To imp o e he quali y o he simila i y measu e, he numbe o use s who ha e a ed bo h books could be conside ed. This ensu es ha books a e only coun ed as simila i hey ha e been a ed simila ly by mul iple use s [23,37]. This app oach can be ep esen ed o he calcula ion o he simila i y o wo books as ollows [23]: wi gh =2·|Ug∩Uh| |Ug|+|Uh|·wi gh (3.2) In (3.2), |Ug| ep esen s he numbe o use s who ha e a ed he book ig,|Uh|indica es how many use s ha e a ed he book ihand |Ug∩Uh|co esponds o he numbe o use s who ha e a ed bo h books. The ac ion ge s smalle i ewe use s ha e a ed bo hbooks. Mul iplying he ac ion by wi gh ensu es ha e y ewcommonuse a ings esul in a lowe simila i y o wo books [23]. A e calcula ing he simila i y measu es o all books, he knea es neighbo s a e de e mined o each book. The knea es neighbo s o a book a e he books ha ha e he highes simila i y alue [23]. The unknown a ings o use s o a book a e de e mined by weigh ing he a ings o hese use s a he knea es neighbo s o he book wi h he simila i y measu e [36,37]: P(ug)= g+σ( g)·ga∈N(g) uga− ga σ( ga)·wi gga ga∈N(g)wi gga (3.3) 123 Annals o Da a Science (2024) 11(5):1705–1739 1713 He e, P(ug)is he p edic ion o he a ing o a use o book ig.Thekmos simila books o book iga ein hese N(g). These books a e deno ed by ga,...,gk.Only he books ha ha e been a ed by a gi en use a e conside ed as nea es neighbo s in he p edic ion. To accoun o di e ences in a ings be ween books, he a ings o he books a e no malized. Addi ionally, he no malized a ings a e weigh ed by he simila i y measu e wi gga. The use ’s weigh ed no malized a ings o he books a e ans o med in o he book’s a ing scale by mul iplying he s anda d de ia ion σ( g)o he book’s a ings. The esul ing alue is added o he mean go book ig. I book ighas a la ge s anda d de ia ion, he mul iplica ion by he s anda d de ia ion ensu es ha a posi i e alue should cause a g ea e de ia ion o he p edic ed alue om he mean go book ig. Thisapp oachisknownas z-sco e.Ano he commonapp oachisgi enby hede ia ion om he mean. This app oach does no ake in o accoun he s anda d de ia ion o he conside ed book and he book’s nea es neighbo s [36,37]. In his way, he unknown a ings o use s a e es ima ed o each book. As explained la e in his sec ion, i may no be possible o p edic all a ings. Fo each use , he books no ye a ed by he use a e so ed in a descending o de acco ding o he heigh o he p edic ed a ing. The book-based knn algo i hm can be classi ied as ei he a memo y-based [23,31] o a model-based AI algo i hm [38]. I depends on whe he each ime a lis o book ecommenda ions is c ea ed o a use , he simila i y measu es a e ecalcula ed using he use -book ma ix. I his is ue, he book-based knn algo i hm is a memo y-based AI algo i hm. In con as , he book-based knn algo i hm can be conside ed as a model- based algo i hm i he simila i y measu es a e ecompu ed only a egula in e als. The model is he simila i y ma ix ha con ains he simila i y be ween he books. The classi ica ion o he book-based knn algo i hm as a model-based AI algo i hm is suppo ed by esea ch esul s showing ha he simila i ies be ween he books a e s able o e ime [38]. Thequali yo he knnalgo i hm dependson he choiceo hesimila i ymeasu e and he possible conside a ion o he numbe o common use s o wo books. Addi ionally, he choice o he numbe o knea es neighbo s plays an impo an ole: choosing a small numbe o nea es neighbo s could esul in an o e i ing o he a ings o he nea es neighbo s [28]. Mo eo e , he e is a isk ha he nea es neighbo s ha e no ecei edany a ings by he use . This implies ha i is no possible o p edic a a ing o he book. Co e age (see Sec .2.3) is a measu e o de e mine he ex en o he p oblem [34,36]. In con as , choosing a la ge numbe o nea es neighbo s could lead o he p oblem o unde i ing [35]. Use ’s a ings o books ha a e no simila enough o he book migh in luence he p edic ion oo much. In ex eme cases his could lead o unsa is ac o y book ecommenda ions. The e o e, i is o en sugges ed o ake a alue in he ange be ween 20 and 50 o he numbe o knea es neighbo s o sol e he ade-o be ween o e i ing and unde i ing [36,37]. 3.2 Ma ix Fac o iza ion Algo i hm Using he S ochas ic G adien Descen Me hod The ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod is a model-based AI algo i hm. The main assump ion behind he ma ix ac o iza ion is 123 1720 Annals o Da a Science (2024) 11(5):1705–1739 examine he impac o di e si y in book ecommenda ions on use ’s sa is ac ion wi h he ecommended books. Adamopoulos/Tuzhilin [42] conside ed di e en subse s o he da a se and p oposed unexpec edness as an addi ional oppo uni y o imp o e he ecommenda ion quali y. Pa k/Tuzhilin [43] p esen ed an app oach o sol ing he long- ail p oblem (e.g., how o deal wi h books wi h ew a ings) o ecommende sys ems. Deldjoo e al. [44] used he da a se as pa o hei s udy which examined he in luence o da a cha ac e is ics on he accu acy and ai ness (e.g., measu ing o wha ex en he quali y o he ecommenda ion depends on being in a speci ic g oup as age) o ecommende sys ems. 4.2 P ocedu e and Me hodology In his sec ion, he me hodology and he p ocedu e o analyze he quali y o he book-based knn-algo i hm and he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod o ecommend books om he modi ied Book-C ossing da a se is p esen ed. 4.2.1 P ocedu e On he one hand, he quali y o 31 a ian s o book-based knn-algo i hms, in which he numbe o knea es neighbo s is a ied om 20 o 50, is measu ed. On he o he hand, he quali y o 11 a ian s o he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod, in which he numbe o la en ac o s is a ied om 5 o 15, is measu ed. In o de o measu e he quali y o he a ian s o bo h algo i hms, he alues o he p edic ion accu acy me ics RMSE, MSE, and MAE and o he classi- ica ion me ics P ecision and Recall (see Sec .2.3) a e conside ed. As an addi ional check on he quali y o he a ian s, hey a e compa ed wi h he alues o he e alua- ion me ics in a “ andom” algo i hm ( ecommends books andomly) and a “popula ” algo i hm ( ecommends equen ly a ed books). The alues o he e alua ion me - ics a e de e mined using he R-package Recommende lab ha was de eloped by Michael Hahsle o es and e alua e collabo a i e ecommende sys ems [27]. To compa e he a ian s o bo h AI algo i hms, hey need o ha e he same ain- ing and es da a se . Addi ionally, mo e han one aining da a se and one es da a se should be used o he e alua ion. This may educe he isk ha he di i- sion in o a aining and a es da a se would a ec he quali y o he algo i hms. To sa is y hese impo an equi emen s o quali y compa abili y, he op ion o he Recommende lab package o de e mine an e alua ion scheme is employed. Using he command se .seed ensu es ha he e alua ion scheme is he same o all es ed a ian s. We apply c oss- alida ion wi h 10 pa i ions and 10 i e a ions o each a ian o bo h AI algo i hms. The e o e, he 1842 use s o he modi ied Book-C ossing da a se we e di ided in o 10 pa i ions consis ing o abou 184 use s. In each i e a ion, use s o 9 pa i ions o m he aining da a se and de elop a model. This model is es ed using he es da a se , which consis s o he use s o one pa i ion. Thus, each use is nine imes in he aining da a se and once in he es da a se (see Table 6). 123 Annals o Da a Science (2024) 11(5):1705–1739 1721 Table 6 O e iew o he se ings a he a ing scheme Me hod Pe cen age o aining use s I e a ions Gi en GoodRa ing C oss- alida ion 90% 10 9 9 4.2.2 E alua ion Me ics To be able o measu e he e alua ion me ics, he a ing scheme uses he op ion Gi en o speci y how many o a es use ’s known a ings should be used o es ing and how many should be used o alida ion. The alue “9” is se o Gi en. Thus, om each es use , 9 o he known a ings a e u ilized o es he model de eloped by he aining da a se . Based on he es ima ion o he emaining known a ings o he es use s, he algo i hms a e alida ed. Since each use has submi ed a leas 10 a ings in he modi ied Book-C ossing da a se , a leas one a ing is used o alida ion o e e y es use . The p edic ion accu acy me ics RMSE, MSE, and MAE a e measu ed by he known a ings used o alida ion. A e 10 i e a ions, he p edic ion accu acy me ics a e de e mined as he mean o hei alues om hese i e a ions. To measu e he classi ica ion accu acy me ics P ecision and Recall, he alue o GoodRa ing was decisi e o he a ing scheme. The alue o GoodRa ing indica es he a ing om which on a book belonging o a alida ing a ing is so ele an o a es use ha i should be ecommended o he es use . This is a hypo he ical assump ion since, in eali y, he use has al eady a ed he book. The book a ings o he modi ied Book-C ossing da a se a e on a scale o 1 o 10, whe e a alue o “9” is chosen o GoodRa ing. This choice is based on he assump ion ha he use would like o ecei e a ecommenda ion o a book ha he use has a ed 9 o 10. Addi ionally, his assumes ha he use would no know he book ye . The numbe o a ings o alida e wi h a a ing o 9 o 10 is de e mined o each es use . Then, o each es use , he a ings o he 2056 emaining books a e p edic ed, since 9 o he known a ings a e used o es he model. O he 2056 books, each es use was ecommended once he 10 and once he 20 books wi h he highes p edic ed a ings. The main assump ion o choosing he wo lis sizes is ha a use would mos ly only look a he ecommenda ions placed a he op o he lis . Fo each es use , P ecision is measu ed as he p opo ion o books in he lis om ecommended books ha we e p e iously de e mined o be ele an books o alida e. Recall is measu ed as he p opo ion o he ele an books o be alida ed. A e 10 i e a ions, he alues o Recall and P ecision a e aken as he mean o he esul s om he 10 i e a ions. 4.2.3 Book-Based knn Algo i hm P e ious esea ch on collabo a i e ecommende sys ems (as discussed in Sec .3.1) conside sanumbe o 20–50knea es neighbo sasop imum.Basedon hissugges ion, 31 a ian s wi h alues o k om k=20 o k=50 o he book-based knn algo i hm a e es ed. 123 1722 Annals o Da a Science (2024) 11(5):1705–1739 Table 7 O e iew o he a ian s o he book-based knn-algo i hm na.as.ze o kNo malize Me hod no malize_sim_ma ix alpha FALSE 20–50 z-sco e Pea son FALSE 0.5 Table 8 O e iew o he a ian s o he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod kγλmin_epochs max_epochs min_imp o emen No malize 5–15 0.001 0.015 50 200 0.000001 z-sco e The B a ais-Pea son co ela ion coe icien (3.1) is chosen as simila i y measu e. Fo no maliza ion, he z-sco e app oach (3.3) is used. The unknown book a ings a e no se o 0 (op ion na.as.ze o) because he simila i y o wo books in he B a ais-Pea son co ela ion coe icien is only based on he use s who a ed bo h books. The meaning o alpha is no de ined in he Recommende lab package and ela ed ins uc ions, so he alue was le a he de aul alue o 0.5 (no e ha p e- es s showed no change in he sco ing me ics a di e en alues o alpha). The op ion o no malize he simila i y ma ix o he books is no se , as gene al di e ences in he a ings a e al eady aken in o accoun when calcula ing he simila i ies o he books (see Sec .3.1). Fo an o e iew o he se ings see Table 7. 4.2.4 Ma ix Fac o iza ion Algo i hm Using he S ochas ic G adien Descen Me hod Fo he a ian s o he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod, he numbe o la en ac o s is a ied om 5 o 15 la en ac o s. Funk [40], as he ounde o he me hod, s a ed in his blog en y 25 and 40 as alues o a easonable numbe o la en ac o s o he Ne lix da a se , whe e he use -i em ma ix has a size o 8.5 billion en ies. Ko en e al. [24] men ioned a numbe o 20 o 100 la en ac o s o he same da a se . Since he modi ied Book-C ossing da a se has app oxima ely 3.8 million en ies, alues be ween 5 and 15 a e chosen o he numbe o la en ac o s. Fo no maliza ion, he z-sco e is used, as o he a ian s o he book-based knn- algo i hm. The z-sco e is chosen, since he common app oach o conside ing he bias bu, he bias bi, and he mean o all known a ings μin he p edic ion o he a ings could no be selec ed, see Sec .3.2. The o he pa ame e s (see Table 8) a e le a he de aul alues [27,40]. 4.3 Resul s In his sec ion, he esul s om all a ian s o bo h AI algo i hms a e p esen ed o he p edic ion accu acy me ics RMSE, MSE, and MAE as well as he classi ica ion accu acy me ics P ecision and Recall. In o de o addi ionally check he quali y o heseAIalgo i hmsc i ically, heya e also compa ed wi h he esul s o he wocon ol 123 Annals o Da a Science (2024) 11(5):1705–1739 1723 Table 9 Compa ison o he alues o he bes a ian s o bo h AI algo i hms o RMSE, MSE, and MAE wi h he alues o he con ol algo i hms RMSE MSE MAE Random_1 2.092 4.383 1.563 Popula _1 1.562 2.443 1.178 SVDF_15 1.555 2.420 1.148 kNN_24 2.040 4.180 1.396 kNN_50 2.036 4.157 1.407 algo i hms“popula ” and “ andom”. The esul s a e ounded o he hi ddecimalplace. The alues o he e alua ion me ics o all a ian s o bo h AI algo i hms (see Tables 12–16) and he wo con ol algo i hms “popula ” and “ andom” (see Tables 17–18) can be ound in Appendix B. Fo he ma ix ac o iza ion algo i hm, he a ian wi h 15 la en ac o s ecei ed he lowes alues (RMSE =1.555, MSE =2.420, MAE =1.148, see Table 9) and he a ian wi h 5 la en ac o s he highes alues (RMSE =1.560, MSE =2.437, MAE =1.159, see Table 12) o all h ee p edic i e accu acy me ics. In each case, he inc ease in a la en ac o sligh ly imp o ed he p edic i e accu acy me ics. The e o e, he di e ence be ween he wo s and he bes a ian is abou 0.005 o RMSE, abou 0.017 o MSE, and abou 0.011 o MAE. Fo he book-based knn algo i hm, he a ian wi h 24 nea es neighbo s ecei ed he bes alue o he p edic ion accu acy me ic MAE wi h a alue o 1.396. The a ian wi h 50 nea es neighbo s pe o med he bes o he p edic i e accu acy me ics RMSE (2.036) and MSE (4.157) (see Table 9). Table 9and Fig. 3show he a ian s o bo h AI algo i hms wi h he bes alues o RMSE, MSE and MAE and he alues o he con ol algo i hms. The ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod achie ed o all a ian s lowe alues in he p edic ion accu acy me ics compa ed o all a ian s o he book-based knn algo i hm and han he con ol algo i hms. All a ian s o he book-based knn algo i hm had lowe sco es on he h ee p edic i e accu acy me ics han he con ol algo i hm “ andom”. Compa ed o he con ol algo- i hm “popula ”, all a ian s o he book-based knn algo i hm had highe alues. The minimum di e ence be ween he p edic ion accu acy me ics o bo h AI algo i hms is 0.476 o RMSE, 1.72 o MSE, and 0.248 o MAE. The maximum di e ence is 0.506 o RMSE, 1.854 o MSE, and 0.262 o MAE (see Tables 12 and 14). In he ollowing, he esul s o P ecision and Recall a e discussed o bo h a lis o 10 and 20 ecommended books. As o he book-based knn algo i hm, o he lis wi h 10 ecommended books, he a ian wi h 29 nea es neighbo s achie ed he bes alues o P ecision (0.006) and Recall (0.017). In con as , o he lis o 20 ecommended books, he a ian wi h 22 nea es neighbo s ecei ed he highes alue o P ecision (0.006), and he a ian wi h 26 nea es neighbo s ecei ed he highes alue o Recall (0.024) (see Tables 10–11). Fo he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod, he a ian wi h 5 la en ac o s ob ained he highes alues o P ecision (0.016) and Recall (0.035) o he lis o 10 ecommended books. Fo he lis o 20 ecommended books, he a ian wi h 5 la en ac o s a P ecision (0.013) and he a ian wi h 9 la en ac o s a Recall (0.060) pe o med bes (see Tables 10–11). 123 1724 Annals o Da a Science (2024) 11(5):1705–1739 Fig. 3 G aphical compa ison o he alues o he bes a ian s o bo h AI algo i hms o RMSE, MSE, and MAE wi h he alues o he con ol algo i hms Table 10 Compa ison o he alues o he bes a ian s o bo h algo i hms o P ecision and Recall a he op 10 lis wi h he alues o he con ol algo i hms TP FP FN TN NP ecision Recall Random_1 0.020 9.980 5.740 2040.260 2056 0.002 0.003 Popula _1 0.249 9.751 5.511 2040.489 2056 0.025 0.059 SVDF_5 0.158 9.842 5.603 2040.397 2056 0.016 0.035 kNN_29 0.061 9.751 5.699 2040.489 2056 0.006 0.017 Table 11 Compa ison o he alues o P ecision and Recall o he bes a ian s o bo h AI algo i hms a he op 20 lis wi h he alues o he con ol algo i hms TP FP FN TN NP ecision Recall Random_1 0.054 19.946 5.706 2030.294 2056 0.003 0.010 Popula _1 0.360 19.640 5.400 2030.600 2056 0.018 0.082 SVDF_5 0.264 19.736 5.496 2030.504 2056 0.013 0.057 SVDF_9 0.264 19.736 5.496 2030.504 2056 0.013 0.060 kNN_22 0.111 19.511 5.649 2030.729 2056 0.006 0.023 kNN_26 0.104 19.519 5.656 2030.720 2056 0.005 0.024 All a ian s o he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod had highe alues o P ecision and Recall han all a ian s o he book-based knn algo i hm. Addi ionally, all a ian s o bo h AI algo i hms had highe alues o P ecision and Recall han he con ol algo i hm andom (see Tables 10–11). Fo he lis o 10 ecommended books, he minimum di e ence be ween bo h AI algo i hms o P ecision is 0.007, while he minimum di e ence o Recall is 0.012. The maximum di e ence is 0.011 o P ecision and 0.021 o Recall. Fo he lis o 20 ecommended books, he minimum di e ence be ween he AI algo i hms is 0.006 o P ecision and 0.029 o Recall. The maximum di e ence is 0.008 o P ecision and 0.038 is Recall (see Tables 13,15,16). 123 Annals o Da a Science (2024) 11(5):1705–1739 1725 Fig. 4 G aphical compa ison o he alues o he bes a ian s o bo h AI algo i hms o P ecision and Recall Fo bo h AI algo i hms, a highe alue o Recall is obse ed o all a ian s o he lis o 20 ecommended books. The alue o P ecision is highe o all a ian s in he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod o he lis wi h 10 ecommended books. Fo he book-based knn algo i hm, his is ue o mos a ian s, al hough he di e ence is much smalle he e. Figu e 4shows his endency by looking a he a ian s o he AI algo i hms ha sco ed he highes o Recall o P ecision. 4.4 Discussion Fo he chosen se ings o bo h AI algo i hms, all a ian s o he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod show supe io pe o mance compa ed o all conside ed a ian s o he book-based knn algo i hm. The ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod led o be e esul s o he p edic ion accu acy me ics compa ed o bo h con ol algo- i hms. As o P ecision and Recall, he ma ix ac o iza ion algo i hm showed a be e pe o mance han he “ andom” algo i hm and a wo se pe o mance han he “popu- la ” algo i hm. Thus, he quali y o he ma ix ac o iza ion algo i hm applied o he modi ied Book-C ossing da a se can be conside ed as good. The a ian s o he knn algo i hm led o be e sco es han he con ol algo i hm “ andom” and wo se sco es han he con ol algo i hm “popula ” on he p edic ion accu acy and classi ica ion accu acy me ics. One eason o he poo pe o mance o he book-based knn algo- i hm could be a possibly low co e age o he books o he modi ied Book-C ossing da a se [34]: he co e age o a book is he p opo ion o use s who ha e no a ed a book and a he same ime ha e a ed one o he knea es neighbo s o he book (see 123 1726 Annals o Da a Science (2024) 11(5):1705–1739 Sec .2.3). Low co e age means a high p obabili y ha i a use has no a ed a book, he use has a ed only a e y small ac ion o he knea es neighbo s, o in ex eme cases, none o he knea es neighbo s o he book. In he i s case, he p oblem o o e i ing he p edic ed a ing o he use ’s a ing a he ew knea es neighbo s may occu [28]. In he second case, no p edic ion can be made o he a ing. The good esul s o he con ol algo i hm “popula ” on he classi ica ion accu acy me ics ecall and p ecision and on he p edic ion accu acy me ics migh be ela ed o he ac ha use s migh like books ha ha e been a ed by many use s. Based on Fig.4, whe e he bes alues o bo h AI algo i hms o he lis s o 10 and 20 ecommended books a e plo ed, he ade-o be ween a high alue o Recall and a high alue o P ecision desc ibed in Sec .2.3 can be seen. Mo eo e , he compu a ion o P ecision and Recall in he Recommende lab package can be conside ed o be c i ical: when c ea ing he lis o ecommended books o a es use , he 10 o 20 books wi h he highes p edic ed a ings we e ecommended. This in ol es p edic ing a ings o books wi h a a ing o be alida ed and a ings o books whe e he ue a ing is unknown. He e, an AI algo i hm lead o a high alue o Recall i a la ge p opo ion o he books a e ecommended wi h a ele an a ing o alida e and a high alue o P ecision i a la ge p opo ion o he ecommended books a e books wi h a ele an a ing o alida e (see Sec .4.2). He e, i is no possible o s a e wi h ce ain y, whe he he use migh ind he ecommended books wi h he p edic ed a ing mo e in e es ing han he a ings o be alida ed o he books o which he use has gi en a a ing o 9 o 10. The alues o Recall and P ecision we e he e o e calcula ed bu should only be in e p e ed wi h cau ion. 5 Conclusions In his pape , we in es iga ed he pe o mance o wo popula AI algo i hms o col- labo a i e book ecommende sys ems using he Book-C ossing benchma k da a se . We implemen ed di e en a ian s o he book-based knn algo i hm and he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod based on selec ed p edic ion and classi ica ion accu acy me ics as well as using wo con ol algo i hms. These a ian s a e cha ac e ized by a ia ions in he numbe o knea es neighbo s in he book-based knn algo i hm and in he numbe o jla en ac o s in he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod. We pe o med a comp ehensi ecase s udy o analyze he quali yo bo hAIalgo i hms o collabo a i e book ecommende sys ems o ecommend books om he modi ied Book-C ossing da a se . Fo he in es iga ed a ian s o bo h AI algo i hms, he a ian s o he ma ix ac- o iza ion algo i hm using he s ochas ic g adien descen me hod showed supe io pe o mance. In con as , he book-based a ian s pe o med wo se han he a ian s o he ma ix ac o iza ion algo i hm using he s ochas ic g adien descen me hod and han he con ol algo i hm “popula ”. I seems ha he poo pe o mance o he book-based knn algo i hm migh be ela ed o he p oblem o poo co e age o he book-based knn algo i hm. 123 Annals o Da a Science (2024) 11(5):1705–1739 1727 This pape conside ed use s who ha e al eady a ed books and books ha ha e al eady ecei ed a ings. Fo AI algo i hms, he e is also he ques ion o how o deal wi h new use s who ha e no ye submi ed a ings and new books ha ha e no ye ecei ed a ings. This p oblem is known as he cold s a p oblem. I deals wi h he ques ion o which books a e sugges ed o a new use and o which use s a new book is sugges ed. Ano he in e es ing ques ion is how AI algo i hms deal wi h he g ey sheep p oblem. This p oblem deals wi h use s whose a ing beha io is di icul o explain by any pa e ns, which makes i e y di icul o AI algo i hms o ecommend sui able books o hem. In addi ion o hese aspec s, u u e esea ch could ocus on he pe o mance o bo h algo i hms when es ed on o he ecen book da a se s such as he Goodbooks-10k da a se [45] and he Good eads da a se [46,47], which a e also equen ly used in esea ch abou book ecommende sys ems [6,21].1 Acknowledgemen s The au ho s hank bo h anonymous e iewe s o hei aluable eedback and sugges- ions, which we e impo an and help ul o imp o e he pape . Au ho con ibu ions ClemensTege meie :Concep ualiza ion, Me hodology, So wa e, Valida ion, Fo mal analysis, In es iga ion, W i ing - O iginal D a , Visualiza ion A ne Johannssen: Valida ion, Fo mal analy- sis, In es iga ion, W i ing - O iginal D a , W i ing - Re iew & Edi ing, Supe ision, P ojec adminis a ion Na aliya Chukh o a: Valida ion, Fo mal analysis, In es iga ion, W i ing - Re iew & Edi ing, Supe ision. Funding Open Access unding enabled and o ganized by P ojek DEAL. Da a a ailibili y The da a ha suppo he indings o his s udy a e a ailable om he espec i e e e ences as men ioned in he main ex . Code A ailabili y The code is a ailable om he au ho s upon eques . Decla a ions Compliance wi h E hical S anda ds This a icle does no con ain any s udies wi h human pa icipan s o animals pe o med by he au ho s. Con lic o in e es The au ho s decla e ha hey ha e no known compe ing inancial in e es s o pe sonal ela ionships ha could ha e appea ed o in luence he wo k epo ed in his pape . Disclosu e o po en ial con lic s o in e es (i) This manusc ip is he au ho s’ o iginal wo k, which has no been published no submi ed simul aneously elsewhe e; (ii) all au ho s ha e checked he manusc ip and ag eed o he submission, and (iii) he e is no con lic o in e es . Open Access Thisa icleislicensedunde aC ea i eCommonsA ibu ion4.0In e na ionalLicense,which pe mi s use, sha ing, adap a ion, dis ibu ion and ep oduc ion in any medium o o ma , as long as you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e Commons licence, and indica e i changes we e made. The images o o he hi d pa y ma e ial in his a icle a e included in he a icle’s C ea i e Commons licence, unless indica ed o he wise in a c edi line o he ma e ial. I ma e ial is no included in he a icle’s C ea i e Commons licence and you in ended use is no pe mi ed by s a u o y egula ion o exceeds he pe mi ed use, you will need o ob ain pe mission di ec ly om he copy igh holde . To iew a copy o his licence, isi h p://c ea i ecommons.o g/licenses/by/4.0/. 1The da a se s a e a ailable a h p:// as ml.com/goodbooks-10k-a-new-da ase - o -book- ecommenda ions/ and h ps://si es.google.com/eng.ucsd.edu/ucsdbookg aph/home?pli=1. 123 1728 Annals o Da a Science (2024) 11(5):1705–1739 Appendix A See Figs. 5,6,7,8,9,10,11 and 12. Fig. 5 F equencies o he numbe o a ings pe use in he modi ied Book-C ossing da a se ( he use wi h 964 submi ed a ings is no included in his igu e) Fig. 6 F equencies o he numbe o a ings pe book in he modi ied Book-C ossing da a se 123 Annals o Da a Science (2024) 11(5):1705–1739 1729 Fig. 7 F equencies o he medians o one use ’s a ings in he modi ied Book-C ossing da a se Fig. 8 F equencies o he medians o one book’s a ings in he modi ied Book-C ossing da a se 123 1736 Annals o Da a Science (2024) 11(5):1705–1739 Table 16 Values o P ecision and Recall o he book-based knn-algo i hm o 36–50 neighbo s TP FP FN TN NP ecision Recall n kNN_36 0.054 9.758 5.706 2040.482 2056 0.005 0.014 10 kNN_36 0.099 19.524 5.661 2030.716 2056 0.005 0.022 20 kNN_37 0.054 9.758 5.706 2040.482 2056 0.006 0.014 10 kNN_37 0.101 19.523 5.660 2030.717 2056 0.005 0.022 20 kNN_38 0.052 9.760 5.708 2040.480 2056 0.005 0.014 10 kNN_38 0.098 19.525 5.662 2030.715 2056 0.005 0.022 20 kNN_39 0.051 9.761 5.709 2040.479 2056 0.005 0.014 10 kNN_39 0.099 19.525 5.661 2030.715 2056 0.005 0.022 20 kNN_40 0.052 9.760 5.708 2040.480 2056 0.005 0.014 10 kNN_40 0.097 19.527 5.663 2030.713 2056 0.005 0.022 20 kNN_41 0.053 9.759 5.707 2040.481 2056 0.005 0.015 10 kNN_41 0.098 19.526 5.662 2030.714 2056 0.005 0.023 20 kNN_42 0.056 9.755 5.704 2040.484 2056 0.006 0.016 10 kNN_42 0.099 19.524 5.661 2030.716 2056 0.005 0.023 20 kNN_43 0.058 9.754 5.703 2040.485 2056 0.006 0.016 10 kNN_43 0.101 19.523 5.660 2030.717 2056 0.005 0.024 20 kNN_44 0.058 9.754 5.702 2040.486 2056 0.006 0.016 10 kNN_44 0.099 19.524 5.661 2030.716 2056 0.005 0.023 20 kNN_45 0.059 9.753 5.702 2040.487 2056 0.006 0.016 10 kNN_45 0.101 19.523 5.660 2030.717 2056 0.005 0.023 20 kNN_46 0.060 9.752 5.700 2040.488 2056 0.006 0.016 10 kNN_46 0.102 19.522 5.658 2030.718 2056 0.005 0.024 20 kNN_47 0.058 9.754 5.703 2040.485 2056 0.006 0.016 10 kNN_47 0.103 19.521 5.658 2030.719 2056 0.005 0.024 20 kNN_48 0.059 9.753 5.702 2040.487 2056 0.006 0.015 10 kNN_48 0.104 19.520 5.656 2030.720 2056 0.005 0.024 20 kNN_49 0.059 9.753 5.702 2040.487 2056 0.006 0.015 10 kNN_49 0.103 19.521 5.658 2030.719 2056 0.005 0.023 20 kNN_50 0.057 9.755 5.703 2040.485 2056 0.006 0.015 10 kNN_50 0.101 19.523 5.659 2030.717 2056 0.005 0.023 20 123 Annals o Da a Science (2024) 11(5):1705–1739 1737 Table 17 Values o RMSE, MSE, and MAE o he con ol algo i hms “ andom” and “popula ” RMSE MSE MAE Random_1 2.092 4.383 1.563 Popula _1 1.562 2.443 1.178 Table 18 Values o P ecision and Recall o he con ol algo i hms “ andom” and “popula ” TP FP FN TN NP ecision Recall n Random_2 0.020 9.980 5.740 2040.260 2056 0.002 0.003 10 Random_2 0.054 19.946 5.706 2030.294 2056 0.003 0.010 20 Popula _2 0.249 9.751 5.511 2040.489 2056 0.025 0.059 10 Popula _2 0.360 19.640 5.400 2030.600 2056 0.018 0.082 20 Re e ences 1. 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