Station segmentation of Lisbon bicycle sharing system based on users demand and supply

S a ion Segmen a ion o Lisbon bicycle sha ing sys em based on use s demand and supply Ma isa Ma inho Fe nandes P ojec wo k p esen ed as he pa ial equi emen o ob aining a Mas e 's deg ee in In o ma ion Managemen NOVA In o ma ion Managemen School Ins i u o Supe io de Es a ís ica e Ges ão de In o mação Uni e sidade No a de Lisboa STATION SEGMENTATION OF LISBON BICYCLE SHARING SYSTEM BASED ON USERS DEMAND AND SUPPLY Ma isa Ma inho Fe nandes P ojec Wo k p esen ed as he pa ial equi emen o ob aining a Mas e 's deg ee in In o ma ion Managemen , Specializa ion in Knowledge Managemen and Business In elligence Ad iso : Mau o Cas elli Janua y 2021 iii ACKNOWLEDGEMENTS I would like o hank e e yone ha c ossed my pa h du ing my academic li e and con ibu ed o en ich my li e and o my pe sonal and academic g ow h. A wa m hank you o my amily, in special o my pa en s ha suppo ed me in his jou ney and wo ked ha d all hei li es o make su e ha I had he oppo uni y o educa e mysel and pu sui o a be e and p ospe ous u u e o me. A huge hank you o Mau o Cas elli ha i elessly suppo ed me h oughou my mas e hesis, wi hou him o achie ing his ma k on my li e would ha e been much mo e di icul . All my iends ha kep on o e ing me all he suppo ha I need and kep on eminding me ha I was almos he e, a big hank you ollowed by a big hug, wi hou you his jou ney would ha e been lonelie . A las , bu no leas , an eno mous hank you o mysel o keeping on his p ojec while wo king, o no s opping belie ing ha i was possible hough di icul , o no accep ing he emp ing hough o “I can lea e i o he nex yea ”, o keeping de e minedly ai h ul o my ambi ion. i E e yone hinks o changing he wo ld, bu no one hinks o changing himsel . Leo Tols oy ABSTRACT Bike-sha ing sys ems a e well known in he sus ainable mobili y ield and ha e se e al aspec s ha need op imiza ion and imp o emen . One o he mos ele an aspec s is s a ion segmen a ion based on use demand and supply, and i is he ocus o he hesis. The segmen a ion wo k has an eno mous po en ial o educe complexi y in p edic ing he bicycle demand and supply, hus imp o ing he o e all quali y o se ice. Se e al machine lea ning algo i hms we e used o in es iga e he a o emen ioned segmen a ion ask. This wo k conside s wo popula and well-known clus e ing algo i hms o ex ac and analyze in e es ing pa e ns, like he di e ence be ween a i als and depa u es h oughou ime and s a ions: he DBSCAN (Densi y-Based Spa ial Clus e ing o Applica ions wi h Noise) and he hie a chical clus e ing. The algo i hms a e applied o he speci ic case o GIRA, he bicycle sha ing sys em (BSS) o he ci y o Lisbon. The ob ained esul s sugges ha conside ing he a iables unde analysis, he op imal numbe o clus e s o be used in a second phase o he BSS op imiza ion (demand and supply o ecas ) is he same as he numbe o s a ions in he Lisbon BSS. The esul s a e e y insigh ul and allow u u e wo k o ocus ei he on he demand o ecas o he en ichmen o he a iables unde s udy. KEYWORDS Machine lea ning; Timese ies segmen a ion; Bike-sha ing sys ems; Sus ainable mobili y i Index 1. In oduc ion .................................................................................................................. 1 2. Rela ed wo k ................................................................................................................. 3 3. Da a unde s anding ...................................................................................................... 6 4. P e-p ocessing .............................................................................................................. 8 4.1. Da a cleaning ......................................................................................................... 8 4.2. Da a in eg a ion................................................................................................... 10 4.3. Da a Reduc ion .................................................................................................... 11 4.4. Da a T ans o ma ion ........................................................................................... 12 5. Bike S a ions dimensionali y educ ion ...................................................................... 13 5.1. Unsupe ised lea ning s Supe ised lea ning .................................................... 13 5.1.1. Unsupe ised lea ning .................................................................................. 13 5.1.2. Supe ised lea ning ...................................................................................... 13 5.2. Unsupe ised lea ning applied o ime se ies ..................................................... 13 5.3. Dis ance measu e ................................................................................................ 14 5.4. Algo i hms o unsupe ised lea ning ................................................................. 15 5.4.1. Hie a chical Clus e ing ................................................................................. 15 5.4.2. Densi y-based spa ial clus e ing o applica ions wi h noise (DBSCAN) ....... 16 5.5. Measu ing clus e quali y .................................................................................... 17 5.5.1. In insic e alua ion me hods ........................................................................ 18 6. Resul s, conclusion and u u e wo k .......................................................................... 19 7. Bibliog aphy ................................................................................................................ 22 ii LIST OF TABLES Table 1 - Bicycle s a ion ile - in o ma ion ................................................................................. 6 Table 2 - Bicycle ips ile - in o ma ion ..................................................................................... 6 Table 3 - Incohe ence example 1 ............................................................................................... 9 Table 4 - Incohe ence example 2 ............................................................................................... 9 Table 5 - Incohe ence example 3 ............................................................................................. 10 Table 6 - Incohe ence example 4 ............................................................................................. 10 Table 7 - New ea u es in o ma ion ......................................................................................... 11 Table 8 - Di e ences be ween unsupe ised and supe ised lea ning (Jones, Johns on, & K uge , 2019) .................................................................................................................... 13 Table 9 - Calcula ions o he DTW dis ance be ween ime se ies a and b (Izakian, Ped ycz, & Jamal, 2015) ..................................................................................................................... 15 Table 10 - DBSCAN algo i hm (Chauhan, 2020) ....................................................................... 17 Table 11 - Time se ies clus e ing esul s .................................................................................. 20 iii LIST OF ABBREVIATIONS AND ACRONYMS PCA P incipal Componen Analysis IST Ins i u o Supe io Técnico DTW Dynamic Time Wa ping BSS Bicycle Sha ing Sys ems FFBSS F ee-Floa ing Bicycle Sha ing Sys em SBRP S a ic Bicycle Reposi ioning Sys em DBRP Dynamic Bicycle Reposi ioning Sys em ANN A i icial Neu al Ne wo k DBSCAN Densi y-based spa ial clus e ing o applica ions wi h noise 1 1. INTRODUCTION A bicycle sha ing sys em (BSS) can be de ined as a ne wo k o bicycles sp ead in a ci y, a ailable o use s. A use can ake a bicycle a he s a ing poin , d i e i un il he des ina ion poin and lea e he bicycle whe e he ip inished, momen in which he bicycle will become a ailable o o he use s. Bicycle sha ing sys ems gained popula i y in ecen yea s and became a popula se ice in majo ci ies. The i s BSS wo ld-wide was in oduced in Ams e dam in 1965 (Shaheen, 2012) and he bicycles we e unlocked and placed a ound he ci y. The nex BSSs wen h ough some changes and challenges: some o hem we e paid, and some ha e su e ed om he o e en andalism. Th oughou he yea s, BSSs became mo e popula a ound he wo ld and by he beginning o Ap il o 2020 he e we e 2102 ci ies wi h BSS, wi h app oxima ely 17866900 sel -se ice public use bicycles and elec ic assis ed bicycles. (DeMaio & DesJa dins, s.d.). Ci ies a e cha ac e ized by an agi a ed li e, a ic conges ion, long wai ing imes be ween public anspo s connec ions, and bad ai quali y. BSSs can be seen as a way o coun e ac ing o minimizing some o hese issues. In Albiński and coau ho s (Albiński, Fon aine, & Minne , 2018) wo k, a BSS is p esen ed as a good al e na i e anspo mode wi h espec o he exis en ones ( ain, am, me o and bus). In ac , i he ci y has a well-s uc u ed bicycle in as uc u e, iding a bicycle can be he as es way o go om one place o ano he and, as a consequence, a ime-sa ing al e na i e. Besides ha , i has a posi i e impac on use ’s heal h due o he exe cise done by iding a bike. Mo eo e , he educ ion o g eenhouse gas emissions is also a ac o ha con ibu es o he BSS adop ion and i s inc easing popula i y. Fo ma and coau ho s (Fo ma, Ra i , & Tzu , 2015) and Shui and coau ho s (Shui & Sze o, 2018) poin ed ou ha BSS is an en i onmen ally iendly op ion and i can complemen he public anspo a ion. This s udy uses machine lea ning echniques o clus e docking s a ions wi h simila demand and o e beha io s, aking in o accoun he BSS o Lisbon. The ci y made a ailable a BSS in 2017 wi h he p ojec GIRA, and by Sep embe o 2019 i coun ed wi h 81 s a ions and a ound 600 (bo h casual and elec ic) sha ed bicycles. The e a e wo ypes o BSS: he so-called adi ional BSS, which is cha ac e ized by ha ing he bicycles associa ed o a docking s a ion and he ee- loa ing BSS (FFBSS) in which he e is no a ixed place o each bicycle and he bicycles ee- loa a ound he ci y (Liu, Sze o, & Ho, 2018). The BSS o Lisbon is a adi ional BSS. In he con ex o a adi ional BSS, each jou ney ypically s a s om a speci ic docking-s a ion, inishes in ano he , and he use does no need o e u n o he ini ial s a ion. This ype o beha io con ibu es o emp y and ull s a ions. I is impo an o no e he BSSs a e e icien when s a ions a e balanced (no emp y o ull). The e o e, unbalanced s a ions lead o ine iciency in BSS which also leads o unsa is ied use s and, consequen ly, o a po en ial loss o use s. (Dell'Amico, Io i, No ellani, & Sub amanian, 2018) The unbalanced s a ion is also a p oblem in he con ex o he GIRA p ojec ha will be add essed in his wo k. The e a e wo common app oaches o minimize he p oblem o unbalanced BSS, being he i s use -based and he second uck-based. The use -based app oach is usually less cos ly han he la e , bu i a ely sol es he p oblem by i sel . In pa icula , he use -based app oach gi es a ewa d/incen i e o use s ha s a a ip in s a ions wi h an excess o bicycles and o he use s ha end a ip in s a ions wi h a de ici o bicycles. The uck-based app oach add esses he p oblem by 8 4. PRE-PROCESSING This chap e will explo e one o he mos ime consuming and also one o he mos impo an asks o he success o he algo i hm’s esul s. (Kambe , Han, & Pei, 2011) The app oach aken in his chap e was guided by (Wi en, Pal, Hall, & F ank, 2016). The au ho s o he book spli p e-p ocessing s ep in o 4 majo ca ego ies: 1. Da a cleaning ou ines a e applied o ha e clean he da a. Those ou ines a e pu in p ac ice h ough: illing missing alues; smoo hing noisy da a; emo ing ou lie s and iden i ying and esol ing inconsis encies o incohe ences. 2. Da a In eg a ion is used when he e is he need o he possibili y o ge mo e da a om ano he da a sou ce. Ge ing mo e da a, will e y likely en ich he explanabili y o he phenomena unde analysis. Da a in eg a ion is no all oses, i is common ha wi h i , edundancies, noise and inconsis encies will ise. The e o e, i ’s impo an ha his s ep is explo ed along side wi h da a cleaning. 3. Da a Reduc ion goal is o ha e a da ase wi h less a iables bu wi h he same o almos he same explanabili y o he phenomena. The e a e some echniques ha can be used and all unde da a educ ion s ep, such as: dimensionali y educ ion echniques (e.g., PCA, ac o analysis, o wa d ea u e selec ion, e c.), ea u e subse selec ion (e.g., i ele an o edundan ea u es) o ea u e c ea ion (e.g., c ea ion o new ea u es ha summa ize o he s such as c ea ing he a iable du a ion ins ead o ha ing da e s a and da a end). 4. Da a T ans o ma ion s ep is esponsible o ans o ming da a (i needed) in o a s a e ha will make he modeling p ocess mode e icien . This p ocess includes se e al possible echniques, such as: ea u e cons uc ion (e.g., c ea ion o new ea u es om exis ing ones), agg ega ion (e.g., agg ega e da a by da e ime e e y 10 minu es ins ead o ha ing da a o he second), no maliza ion (e.g., scale ea u es o a smalle ange) o disc e iza ion (e.g., con e o pa i ion con inuous alues in o in e als o in o new ea u es). 4.1. DATA CLEANING This sub-chap e will go deepe in how he i s s ep o p e-p ocessing, he da a cleaning, was applied in he con ex o his s udy. The s eps aken will be desc ibed alongside wi h some speci ic example o a be e unde s anding o he wo k done: Resol e incohe encies 1) As i was men ioned in Da a unde s anding chap e , he columns “id_expl”, “id_planeamen o” and “desig_come cial” ( he numbe s in he beginning) e e ence he same alue, he s a ion numbe . The e o e, hose we e checked agains each o he o make su e ha i s alues we e co ec . In he majo i y o he cases, he alues we e cohe en , in he emaining cases whe e he alues we e no cohe en , he da a was co ec ed ha ing he “desig_come cial” numbe has a decision make . Fo example, as i can be seen in Table 3, he id_expl and 9 id_planeamen o a e he same bu he design_come cial isn’ . As he desig_come cial has p e alence o e he o he s, he eco ds in ques ion we e co ec ed o 103. Table 3 - Incohe ence example 1 Id_expl Id_planeamen o desig_come cial 1 1 103-Ja dim da Água 2) The second case o incohe encies e i ied is he e i ica ion o he “desig_come cial” alues. The s a ions names we e analyzed, and some i egula i ies we e no iced unde he ollowing cases ca ego iza ion: a. The id was he same, bu he name was sligh ly di e en . b. The name was he same, bu he id was di e en ( ypically sequen ial, e.g., 224 and 225). c. The e was no name, only id. In o de o esol e hese cases, he websi e (h ps://www.gi a-bicicle asdelisboa.p /descob e- as-es acoes/ ) whe e esides he o icial map wi h all he s a ions in Gi a’s ne wo k was aken unde conside a ion and obse a ion. Rega ding case a), he s a ion names we e co ec ed o he o icial name ( he name p esen in he o icial websi e). The cases obse ed can be seen in Table 4. Table 4 - Incohe ence example 2 Desig_come cial-1 Desig_come cial-2 Desig_come cial-decision 488 - Rua Fe nando Namo a N35 / Rua An ónio Quad o 488 - Rua Fe nando Namo a n35 / Rua An ónio Quad o 488 – Rua Fe nando Namo a / Rua An ónio Quad os 410 - Rua da Mesqui a / Rua D . Júlio Dan as 410 - Rua da Mesqui a /Uni e sidade No a de Lisboa 410 - Rua da Mesqui a /Uni e sidade No a de Lisboa Rega ding case b), he wo cases iden i ied we e co ec , meaning ha he e we e wo s a ions wi h he same name. The cases obse ed can be seen in Table 5. 10 Table 5 - Incohe ence example 3 Desig_come cial-1 Desig_come cial-2 224 - Ma im Moniz 225 - Ma im Moniz 307 - Ma quês de Pombal Rua D . Júlio Dan as 308 - Ma quês de Pombal Rega ding case c), he decision made was simply assigning he o icial name o he ones ha we e missing i . The example can be seen in Table 6E o ! Re e ence sou ce no ound. Table 6 - Incohe ence example 4 Desig_come cial-1 Desig_come cial-2 Desig_come cial-decision 303 303 - A enida da Libe dade / Rua das P e as 303 - A enida da Libe dade / Rua das P e as Remo e noisy da a Rega ding emo ing o no conside ing ce ain da a, he columns “es ado” speci ies i he s a ion is ac i e, in epai o in s ock. Only he eco ds associa ed wi h he “es ado” in s ock o in epai we e emo ed om he da ase . Tha choice was made, based on he ac ha he phenomena unde analysis only s udies he s a ions ha a e ac i e and by consequen ha e ips associa ed. 4.2. DATA INTEGRATION Da a in eg a ion chap e will go h ough he aken s eps in o de o ge mo e ea u es ha can explain he phenomena unde analysis. Th ough hose s eps, da a om 3 di e en ex e nal sou ces we e used: 1) Po uguese holidays websi e: om his websi e, i was possible o ga he all he o icial Po uguese holidays o he 2018 yea and u he con e hose in o a py hon dic iona y. 2) Ins i u o Supe io Técnico wea he s a ion API: IST has a ee API wi h wea he da a, based on a wea he s a ion loca ed in Alameda. In his case, Alameda was conside ed ep esen a i e o he ci y o Lisbon has a wea he p oxy. The da a collec ed om his API con ains hou ly da a. 3) Sun ise and sunse API: In o de o ha e he da a needed o u he unde s and when i was dayligh o no , da a ega ding he sunse and sun ise ime in he ci y o Lisbon was collec ed. The da a is a da e ime wi h de ail un il he second. 11 Table 7 - New ea u es in o ma ion Va iable Desc ip ion Sou ce Sunse ime Con aining he da e ime (un il seconds) o sunse and sun ise o each day h ps://sun ise-sunse .o g/api Sun ise ime Po uguese holidays Con ains all o icial holidays. h ps://www.calenda .com/po ugal/calenda io- 2018/ To al p ecipi a ion How many millime e s o ain h p://me eo2-ciis .is .u l.p :8080/api A mosphe ic p essu e A mosphe ic p essu e in miliba s Sola adia ion Sola adia ion in wa s pe squa e Rela i e humidi y Pe cen age o humidi y Tempe a u e Tempe a u e in Celsius deg ees Wind di ec ion Deg ees o wind di ec ion Wind gus How s ong is he wind gus in me e s pe second Wind speed The wind speed in me e s pe second 4.3. DATA REDUCTION This chap e will explain wha was done in e ms o da a educ ion. As i was explained in P e- p ocessing, he e a e h ee majo se o ac ions ha usually a e pe o med, om which only wo we e used: 1) Fea u e subse selec ion: Some ea u es we e no longe conside ed due o he ac ha ei he hey didn’ add in o ma ion ha wasn’ al eady in o he a iables, o hey didn’ ha e comple e in o ma ion in o de o be used. The cases we e: a. “id_expl” and “id_planeamen o” since hei in o ma ion is al eady in “desig_come cial” b. “es ado” because he da ase will only ha e eco ds wi h “es ado” o ac i e, so i wouldn’ add new in o ma ion. 12 c. “ ipo_se ico_ni eis” because in he ile ha has in o ma ion om s a ions, his column has incomple e in o ma ion, o in o he wo ds, he da a in his column is no su icien o conclusi e abou how many elec ical bicycles o no mal ones a e in he s a ion a each ime. The e o e, o assu e quali y o he da a, i can’ be used. d. “bike_ id”, “geom”, “num_ e ices” a e geog aphical a iables. Since in his s udy, he geog aphical dimension won’ be conside ed, hese a iables won’ apply. e. “id”, since i is only a unique numbe o each ip and won’ add ele an in o ma ion. . “dis ance”, his ea u e is also incomple e, mo e han 49% o he da ase has null alues. Since i ’s no a good app oach o in e pola e 49% o he da a, he ea u e was emo ed om he analysis. 2) Fea u e c ea ion a. A a iable called “du acao_min” was c ea ed, which is a p oduc o he di e ence be ween he da e s a and he da e end. Ins ead o 2 ea u es we now ha e 1 wi h he same in o ma ion. 4.4. DATA TRANSFORMATION In his chap e all he ans o ma ions in he da a will be explained. The ans o ma ions we e made in o h ee majo ypes: a) Bina y ans o ma ion was used in he case o he holidays and dayligh a iables. In he holidays case, now ha a iable has alue 1 i i was holiday in Po ugal and 0 i i wasn’ . In he dayligh case, om he sunse and sun ise da e imes, now he a iable has also bina y alues, 1 i i was dayligh and 0 i i wasn’ . b) Agg ega ion was used o he ime dimension. The decision o agg ega ing he ime dimension in o bins o 20 minu es was made because o 2 easons, i s he pe iodici y o he da a was inconsis en (1 second, 2 minu es, 5 minu es, e c.), second in e ms o he s udy scope, he bike sha ing ebalancing p oposal won’ be made e e y second, so he decision o 20 minu es pe iodici y was made based on he al eady men ioned pape . (Regue & Recke , 2014) c) New ea u es c ea ed all in o wo ypes: ime ela ed and numbe o bikes ela ed. The ime ela ed ones a e a iables elling ( ip wise) he hou , minu e and i i was a weekday o no . The numbe o bikes ela ed ones, a e he numbe o bicycles p esen in he s a ion 1, 24 and 168 hou s be o e (1 hou , 1 day and 1 week, espec i ely). 13 5. BIKE STATIONS DIMENSIONALITY REDUCTION 5.1. UNSUPERVISED LEARNING VS SUPERVISED LEARNING Supe ised lea ning and unsupe ised lea ning a e wo machine lea ning asks ha a e commonly employed o add essing di e en kinds o p oblems and ha e some main di e ences (Jones, Johns on, & K uge , 2019) Table 8 - Di e ences be ween unsupe ised and supe ised lea ning (Jones, Johns on, & K uge , 2019) Unsupe ised lea ning Supe ised lea ning No labels p o ided Labels p o ided Finds s uc u e in unlabeled da a Finds pa e ns in exis ing s uc u e Uses echniques such as clus e ing o dimensionali y educ ion Uses echniques such as eg ession o classi ica ion 5.1.1. Unsupe ised lea ning Unsupe ised lea ning is used when he a ge alue o each obse a ion is unknown and he inpu da a is he only a ailable in o ma ion. This ype o lea ning ask is commonly used o iden i ying g oups o simila obse a ions: his p ocess is pa icula ly help ul when ying o ind he meaning in he da a, assign he obse a ions o simila g oups o educe dimensionali y. 5.1.2. Supe ised lea ning Supe ised lea ning is used o sol e p oblems whe e he a ge alue o each obse a ion is known, so his in o ma ion can be used o ei he classi y (e.g. p edic ing i a pe son will has endency o be an alcoholic o no based on hei s b ain cells ac i i y) o i a eg ession (e.g. p edic ing he p ice o a pe sonal compu e based on how much memo y and p ocessing capaci y i has). 5.2. UNSUPERVISED LEARNING APPLIED TO TIME SERIES As ou lined in he wo k o Reddy and Agga wal, ime-se ies segmen a ion can ha e wo main o mula ions, which s ongly depend on he p oblem aken in o accoun (Reddy & Agga wal, 2013). I he p oblem consis s o inding se s o ime se ies wi h simila ends, we ha e a co ela ion-based online clus e ing p oblem. On he o he hand, i he p oblem consis s o ime se ies wi h simila shapes, we ha e a shape-based o -line clus e ing p oblem. Co ela ion-based online clus e ing: This o mula ion is commonly used in cases o inancial ma ke s domain o iden i ying g oups o s ocks ha ha e simila ends o co ela ed ends. Shape-based o -line clus e ing: Con e sely o he p e ious explained o mula ion, in he shape-based o mula ion, he ime se ies a e e alua ed and clus e ed o -line. This o mula ion is used in he cases in which he objec i e is o ind ime se ies wi h simila shapes. The bigges challenge and mos 14 de e mina e aspec o g ouping based on shapes is he de ini ion o how o measu e simila i y in he shapes. Depending on he p oblem being sol ed, he e a e se e al good simila i y unc ions, such as Euclidean unc ion o dynamic ime w apping. Ha ing bo h o mula ion ypes o ime-se ies segmen a ion and knowing ha he goal wi h he segmen a ion wi h his wo k is o ind g oups o ime se ies (s a ions) ha ha e simila beha io s, he mos sui able o mula ion is he shape-based o -line clus e ing. 5.3. DISTANCE MEASURE As explained in he wo k o Reddy and Agga wal, when he clus e ing p oblem is a imese ies p oblem he simila i y concep and how i is measu ed is e y impo an o ha e in conside a ion. In his sec ion we will go h ough simila i y/dis ance me ics. As i was men ioned in Sec ion 3.2 and as s a ed by Izakian and coau ho s, “Selec ing a dis ance unc ion o e alua e simila i ies/dissimila i ies o ime se ies has a signi ican impac on he clus e ing algo i hms and hei inal esul s p oduced by hem” (Izakian, Ped ycz, & Jamal, 2015). Due o his signi ican impac , some well-known and commonly used dis ance unc ions will be explained and conside ed: • Euclidean dis ance: Conside ing ha he da apoin s ha e n dimensions, his me ic ha akes he di e ence o he coo dina es be ween wo da a poin s p and q, squa es i and sums i . The dis ance be ween he wo poin s is gi en by he squa e o ha sum. 𝑑(𝑝,𝑞)= √(𝑞1−𝑝1)2+(𝑞2−𝑝2 )2 +⋯+(𝑞𝑛−𝑝𝑛)2 • Manha han dis ance: Conside ing ha he da apoin s ha e n dimensions, his me ic e u ns sum o he absolu e di e ence among he n coo dina es o he da a poin s p and q. The Manha han dis ance be ween wo da a p and q is o malized as ollows: 𝑑(𝑝,𝑞)= ∑|𝑝𝑖−𝑞𝑖 | 𝑛 𝑖=1 Besides he dis ance me ics jus men ioned abo e, he e is an impo an aspec o his s udy ha will a ec he choice o he me ic, he ac ha he ype o obse a ions ha compose ou da ase a e ime se ies. Wo king wi h ime se ies b ings some conce ns wi h espec o hei compa ison. Fo example, wo ime se ies can be exac ly equal bu wi h a ime shi o 2 hou s, and i he Euclidean dis ance is used, he wo ime-se ies will appea di e en o each o he , which is no in ac ue i we conside he ime shi o 2 hou s. To add ess ha impo an aspec and commonly aced p oblem, dynamic ime w apping is he bes dis ance o deal wi h ha . This measu e “de e mines an op imal ma ch be ween wo ime se ies by s e ching o comp essing some segmen s o he se ies. As a esul , pa e ns occu ing a di e en ime ins ances o ime se ies a e conside ed as simila ”. (Izakian, Ped ycz, & Jamal, 2015) 15 DTW acul y o add ess his p oblem has a lo o do wi h he abili y o conside ime si s by compa ing each poin belonging o ime se ies a wi h any poin om ime se ies b. (Izakian, Ped ycz, & Jamal, 2015) DTW algo i hm pseudo code can be consul ed in Table 9. Table 9 - Calcula ions o he DTW dis ance be ween ime se ies a and b (Izakian, Ped ycz, & Jamal, 2015) Calcula ions o he DTW dis ance be ween ime se ies a and b Gi en: a = 𝑎1,𝑎2,…𝑎𝑛, he i s ime se ies wi h leng h n b = b1,𝑏2,…𝑏𝑚, he second ime se ies wi h leng h m Ou pu : cos : a ma ix o size 𝑛×𝑚 con aining he cos alues cos n,m is he DTW dis ance be ween a and b pa h: a ma ix o size 𝑛×𝑚 con aining a wa ping pa h DTW(a, b): Le δbe a dis ance be ween coo dina es o sequences cos 1,1 = δ(a1; b1); pa h1,1 = (0,0); o i = 2,3,…, n do cos i,1 = cos i-1,1 + δ(ai , b1) end o j = 2,3,…, m do cos 1,j = cos 1,j-1 + δ(a1 , bj) end o I = 2,3,…, n do o j = 2,3,…, m do cos i,j = min (cos i-1,j , cos i,j-1 , cos i-1,j-1 ) + δ(ai ,bj ) pa hi,j = min _index(( i – 1, j),( i , j – 1),( i -1 , j – 1)); end end 5.4. ALGORITHMS FOR UNSUPERVISED LEARNING In his chap e , we explo e he echniques and some pa ame e s used o sol e he bicycle s a ions clus e ing p oblem. 5.4.1. Hie a chical Clus e ing Hie a chical clus e ing algo i hm has wo speci ica ions: The Agglome a i e and he di isi e. Bo h ollow di e en app oaches o achie e he clus e s o ma ion. The usage o one o he o he depends 16 on he ollowed app oach. Ei he he clus e s a e eached by a bo om-up (me ging) o by a op-down (spli ing) app oach. The in e es ed eade is e e ed o he wo ks o Reddy and coau ho s (Reddy & Agga wal, 2013) and Kambe and coau ho s (Kambe , Han, & Pei, 2011) o a comp ehensi e o e iew on hese clus e ing echniques. Agglome a i e hie a chical clus e ing app oach: This app oach uses a bo om-up s a egy, which means ha he algo i hm s a s by conside ing as many clus e s as obse a ions and i e a i ely me ges he close wo clus e s (based on a simila i y /dis ance measu e). This p ocess is i e a ed un il he algo i hm eaches one clus e con aining all he obse a ions o un il some s opping c i e ia ( ypically he numbe o clus e s ob ained) is me . Di isi e hie a chical clus e ing app oach: This app oach uses a op-down s a egy, which s a s by assigning all he obse a ions o one clus e and i e a i ely di ides he clus e s in o smalle ones. This p ocess is i e a ed un il he algo i hm eaches a numbe o clus e s equal o he numbe o obse a ions o un il some s opping c i e ia ( ypically he numbe o clus e s ob ained) is me . How agglome a i e hie a chical clus e ing measu es he closes wo clus e s o me ge a e explained below: Single linkage: The single linkage dis ance be ween clus e a and b is he minimum o all dis ances be ween poin s o clus e a and clus e b. Comple e linkage: The comple e linkage dis ance be ween clus e a and b is he maximum o all dis ances be ween poin s o clus e a and clus e b. A e age linkage: The a e age linkage dis ance be ween clus e a and b is he a e age o all dis ances be ween poin s o clus e a and clus e b. 5.4.2. Densi y-based spa ial clus e ing o applica ions wi h noise (DBSCAN) DBSCAN is a clus e ing algo i hm ha ies o iden i y clus e s o obse a ions using he ac ha he in e -clus e densi y is highe han he densi y among he obse a ions ha do no belong o he same clus e (Kambe , Han, & Pei, 2011). DBSCAN ecei es wo pa ame e s: 1) Eps: This pa ame e speci ies he maximum dis ance be ween i sel (poin A) and i s neighbo hood. I he dis ance be ween i sel and a poin B is smalle han eps, poin B is conside ed o be a neighbo o poin A. 2) minP s: The minimum numbe o poin s ha cons i u e a clus e . Fo example, i minP s is wo, means ha o a clus e o be o med needs o ha e a leas wo poin s. DBSCAN ca ego izes obse a ions in o 3 di e en classes: 1) Co e poin s: a e he poin s ha ha e in hei neighbo hood (eps) a leas he minimum numbe o poin s a clus e needs o ha e (minP s), i sel included. 2) No co e poin s/bo de poin s: a e he poin s ha do no comply wi h he ules o he co e poin s. Howe e , hey include inside hei neighbo hood a leas 1 co e poin . 17 3) Noise/Ou lie : hese a e he poin s ha do no comply wi h ei he ule. In o he wo ds, hey a e a away om any o he co e poin . The e o e, hey a e conside ed ou lie s o noise. In he ollowing sequence o s eps is explained how he algo i hm pe o ms in o de o iden i y he clus e s: 1. The pa ame e s a e de e mined (eps and minP s) 2. A andom poin A is selec ed a. The neighbo hood o poin A is calcula ed using eps. b. I he e a e a leas minP s numbe o poin s in i s neighbo hood, poin A is ca ego ized as a co e poin and a clus e is o med wi h poin A and i s neighbo s. I no , poin A is ca ego ized as noise. Table 10 - DBSCAN algo i hm (Chauhan, 2020) DBSCAN (D, Eps, MinP s) //All objec s in D a e un isi ed Begin Fo all objec s in D, selec A: I A is un isi ed: Neigh = Calcula e A’s neighbo hood N = numbe o poin s in Neigh I N +1 >= eps: Classi y A as co e poin Conside all o his poin s o be pa o he same clus e Else: Classi y A as noise END 5.5. MEASURING CLUSTER QUALITY The e comes a poin in which se e al models mus be compa ed so ha he bes model o he p oblem unde exam is selec ed. To selec he bes pe o me among he exis ing models, i is necessa y o measu e hei quali y and, subsequen ly, o compa e hem. The e a e se e al me hods o assess clus e ing quali y, ha all in wo ca ego ies: 1) Ex insic me hods: To use his me hod, he ac ual label o each obse a ion mus be a ailable. The ex insic me hods compa e he labels a ibu ed by he clus e ing model wi h he ac ual labels and measu e how accu a e he classi ica ion was. 2) In insic me hods: The e is no he need o ha e he ac ual label o each obse a ion o use in insic me hods. This ca ego y o me hods measu es how well he clus e s a e sepa a ed. In he p oblem conside ed in his wo k, he ac ual label o each obse a ion is no known. Thus, only he in insic me hods we e used o add ess his p oblem. 24