Person Movement Prediction Using Hidden Markov Models

Transcription

1 Person Movemen Predcon Usng dden Mrkov Models Arpd Geller Lucn Vnn Compuer Scence Deprmen Lucn Blg Unversy of Su E Corn Sr o 4 Su-5525 omn {rpdgeller lucnvnn}@ulsuro Asrc: Uquous sysems use conex nformon o dp pplnce ehvor o humn needs Even more convenence s reched f he pplnce foresees he user s desres nd cs procvely hs pper nroduces dden Mrkov Models n order o ncpe he nex movemen of some persons he opml confguron of he model s deermned y evlung some movemen sequences of rel persons whn n offce uldng he smulon resuls show ccurcy n nex locon predcon rechng up o 92% Keywords: Uquous Compung Conex Predcon Mehods dden Mrkov Models eurl eworks Professor Lucn Vnţn PhD Lucn Blg Unversy of Su s n cve resercher n Advnced Compuer Archecure Conex Predcon n Uquous Compung Sysems Prllel nd Dsrued Sysems e s memer of Acdemy of echncl Scences from omn Europen Commsson Exper n Compuer Scence Vsng esercher Fellow Unversy of erfordshre UK Professor Vnţn pulshed 8 ooks nd over scenfc ppers omn USA Ily UK Porugl ungry Ausr Germny Polnd ec e nroduced some well-known orgnl rchecurl conceps n Compuer Archecure domn Dynmc eurl Brnch Predcon Pre-Compued Brnches Vlue Predcon focused on CPU's Conex ec recognzed ced nd deed hrough over 5 ppers pulshed n mny presgous nernonl conferences nd scenfc revews ACM IEEE IEE ec Arpd Geller MSc s workng s echng sssn Compuer Scence Deprmen from Lucn Blg Unversy of Su omn e receved he Mser of Scence degree n Compuer Scence he sme unversy n 23 Arpd Geller s currenly PhD suden n Compuer Scence workng on hess enled Advnced Predcon Mehods Inegred no Speculve Compuer Archecures hvng s supervsor professor dr Lucn Vnţn nd co-supervsor professor dr heo Ungerer from Unversy of Augsurg Germny e s n cve resercher n Advnced Compuer Archecure Conex Predcon n Uquous Compung Sysems nd he pulshed over scenfc ppers n some pprece revews IEE Proc Compuer nd Dgl echnques nd nernonl conferences UK Germny Belgum nd omn Inroducon Uquous sysems srve for dpon o user needs y ulzng nformon ou he curren conex n whch user s pplnce works A new quly of uquous sysems my e reched f conex wreness s enhnced y predcons of fuure conexs sed on curren nd prevous conex nformon Such predcon enles he sysem o procvely ne cons h enhnce he convenence of he user or h led o n mproved overll sysem umns ypclly c n cern hul pern however hey somemes nerrup her ehvor pern nd hey somemes compleely chnge he pern ur m s o releve people of cons h re done hully whou deermnng person s con he sysem should lern hs uomclly nd reverse ssumpons f h chnges he predcor nformon should herefore e sed on prevous ehvor perns nd ppled o specule on he fuure ehvor of person If he speculon fls he flng mus e recognzed nd he predcor mus e upded o mprove fuure predcon ccurcy [4 5] For our pplcon domn we chose nex locon predcon nsed of generl conex predcon he lgorhms my lso e pplcle for oher more generl conex domns; however here lredy exs numerous scenros whn our pplcon s domn Some smple scenros my e he followng [4]: Smr doorples h re le o drec vsors o he curren locon of n offce owner sed on locon-rckng sysem nd predc f he offce owner s soon comng ck hs scenro s currenly developed Augsurg Unversy nd we re nvolved n he conex predcon pproch Elevor predcon could ncpe whch floor n elevor wll e needed nex oung predcon for cellulr phone sysems my predc he nex rdo cell cellulr phone owner wll ener sed on hs prevous movemen ehvor Sudes n Informcs nd Conrol Vol 5 o Mrch26 7

2 o predc or ncpe fuure suon lernng echnques s eg Mrkov Chns dden Mrkov Models Byesn eworks me Seres or eurl eworks re ovous cnddes he chllenge s o rnsfer hese lgorhms o work wh conex nformon Pezold e l n her work [4] rnsformed some predcon lgorhms used n rnch predcon echnques of curren hgh-performnce mcroprocessors o hndle conex predcon hey evlued he one-level onese wo-se nd mulple-se predcors nd he wo-level wo-se predcors wh locl nd glol frslevel hsores he evluon ws performed y smulng he predcors wh ehvor perns of people wlkng hrough uldng s worklod her smulon resuls show h he conex predcors perform well u exh dfferences n rnng nd rernng speed nd n her ly o lern complex perns In noher work [5] Pezold e l nroduced conex predcon echnques sed on prevous ehvor perns n order o ncpe person s nex movemen hey nlyzed he wo-level predcors wh glol frs-level hsores nd he wo-se predcors nd hey compred hese predcors wh he Predcon y Prl Mchng PPM mehod hey evlued he predcors y some movemen sequences of rel persons whn n offce uldng rechng up o 59% ccurcy n nex locon predcon whou pre-rnng nd respecvely up o 98% wh pre-rnng ner n hs work [7] shows how MMs cn e ppled o seleced prolems n speech recognon s pper presens he heory of MMs from he smples conceps dscree Mrkov chns o he mos sophsced models vrle duron connuous densy models ec e lso llusred some pplcons of he heory of MMs o smple prolems n speech recognon nd poned ou how he echnques hve een ppled o more dvnced speech recognon prolems Lu e l n her work [3] descre MM sed frmework for hnd gesure deecon nd recognon he gol of gesure nerpreon s o mprove humn-mchne communcon nd o rng humnmchne nercon closer o humn-humn nercon mkng possle new pplcons such s sgn lnguge rnslon hey presen n effcen mehod for exrcng he oservon sequence usng he feure model nd Vecor Qunzon nd demonsre h compred o he clssc emple-sed mehods he MM-sed pproch offers more flexle frmework for recognon Gl e l n her work [2] presen novel pproch for uomclly cqurng sochsc models of he hgh-level srucure of humn cvy whou he ssumpon of ny pror knowledge he process nvolves emporl segmenon no plusle omc ehvour componens nd he use of vrle lengh Mrkov models for he effcen represenon of ehvours her expermenl resuls demonsre h he use of vrle lengh Mrkov models provdes n effcen mechnsm for lernng complex ehvorl dependences nd consrns Mchne Lernng echnques sed on MMs hs een lso ppled o prolems n compuonl ology nd hey cn e used s mhemcl models of moleculr processes nd ologcl sequences he gol of compuonl ology s o elucde ddonl nformon requred for drug desgn medcl dgnoss nd medcl remen he mory of moleculr d used n compuonl ology consss n sequences of nucleodes correspondng o he prmry srucure of DA nd A or sequences of mno cds correspondng o he prmry srucure of proens Brney n hs work [] revews gene-predcon MMs nd proen fmly MMs he role of gene-predcon n DA s o dscover he locon of genes on he genome MMs hve lso een used n proen proflng o dscrmne eween dfferen proen fmles nd predc new proen-fmly or sufmly Yoon e l n her work [] proposed new mehod sed on conexsensve MMs whch cn e used for predcng A secondry srucure he A secondry srucure resuls from he se prs formed y he nucleodes of A he conex-sensve MM cn e vewed s n exenson of he rdonl MM where some of he ses re equpped wh uxlry memory Symols h re emed cern ses re sored n he memory nd hey serve s he conex h ffecs he emsson nd rnson proles of he model hey demonsred h he proposed model predcs he secondry srucure very ccurely low compuonl cos hs pper focuses on dden Mrkov Model MM pproch nroducng he MM-sed predcors nd comprng hem wh smple Mrkov nd respecvely neurl predcors ur pplcon predcs he nex room sed on he hsory of rooms vsed y cern person movng whn n offce uldng We evlue hese predcors y some movemen sequences of rel persons cqured from he Smr Doorples proec developed Augsurg Unversy [4 5 6] he nex secons descre he proposed dden Mrkov Models nd presen he smulon resuls 8 Sudes n Informcs nd Conrol Vol 5 o Mrch26

3 2 dden Mrkov Models of order 2 Elemens of MM of rder - he numer of hdden ses wh S {S S S - } he se of hdden ses nd q he hdden se me wll e vred n order o on he opml vlue 2 M - he numer of oservle ses wh V {V V V M- } he se of oservle ses symols nd he oservle se me 3 A { } - he rnson proles eween he hdden ses S nd S where P[ q S q S ] 4 B { k} - he proles of he oservle ses V k n hdden ses S where k P[ V q S ] k M k 5 π {π } - he nl hdden se proles where π P[ q S ] here re lso defned he followng vrles: P 2 q λ - he forwrd vrle [7] represenng he proly of he prl oservon sequence unl me nd hdden se S me gven he model λ A π P 2 q λ - he ckwrd vrle [7] represenng he proly of he prl oservon sequence from o he end gven hdden se S me nd he model λ A π ξ P q q S 2 λ - he proly of eng n hdden se S me nd hdden se S me gven he model λ A π nd he oservon sequence γ P q 2 λ - he proly of eng n hdden se S me gven he model λ A π nd he oservon sequence - he hsory he numer of oservons used n he predcon process In [7] nd [8] he enre oservon sequence s used n he predcon process u n some prccl pplcons he oservon sequence ncreses connuously herefore s necessry s lmon hus he ls oservons cn e sored n lef shf regser I - he mxmum numer of erons n he dusmen process Usully he dusmen process ends when he proly of he oservon sequence doesn ncrese nymore u for fser dusmen s lmed he numer of erons 22 Adusmen Process of MM of rder IIIALIZE λ A π ; 2 CMPUE ξ γ ; 3 ADJUS E MDEL λ A π ; 4 IF P ICEASES G 2 λ 23 Inlzon of he Model of rder he rnson proles eween he hdden ses AX {} re rndomly nlzed o pproxmely / ech row summng o he proles of he oservle ses BXM {k} re rndomly nlzed o pproxmely /M ech row summng o he nl hdden se proles πx {π} re rndomly se o pproxmely / her sum eng Sudes n Informcs nd Conrol Vol 5 o Mrch26 9

4 24 Predcon Algorhm Usng MM of rder s he lengh of he oservon sequence; 2 ; f < go o 2 3 c c s he numer of curren eron s mxmum vlue s gven y I; 4 he model λ A π s repeedly dused sed on he ls oservons 2 he enre oservon sequence f n order o ncrese he proly of he oservon sequence P 2 λ In 4 42 nd 43 seps he denomnors re used n order o on proly mesure nd o vod underflow As Smp showed n [8] underflow s nevle whou sclng snce he proles end o exponenlly s ncreses 4 Compue he forwrd vrle n recursve mnner: π where s he π proly of oservon symol - nd nl hdden se S gven he model λ A π ; 2 where s he proly of he prl oservon sequence unl me - nd hdden se S me gven he model λ A π Snce y defnon P 2 q S λ he sum of he ermnl forwrd vrles gves he proly of he oservon sequence: P 2 λ 42 Compue he ckwrd vrle n recursve mnner: ; where s he proly of he prl oservon sequence from o he end 2 gven hdden se S me nd he model λ A π 43 Compue ξ : 2 Sudes n Informcs nd Conrol Vol 5 o Mrch26

5 ξ where ξ s he proly of eng n hdden se S me nd respecvely S me gven he oservon sequence 2 nd he model λ A π 44 Compue γ : γ ξ where γ s he proly of eng n he hdden se S me gven he model λ A π nd he oservon sequence 2 45 Adus π: π γ - represens he expeced numer of mes he hdden se s S he nl me 46 Adus A: ξ γ - represens he proly of rnson from hdden se S o S he numeror s he expeced numer of rnsons from se S o S whle he denomnor s he expeced numer of rnsons from se S o ny se 47 Adus B: Vk k γ - he proly of oservon symol V k gven h he model s n γ hdden se S he numeror s he expeced numer of mes he model s n hdden se S nd he oservon symol s V k whle he denomnor s he expeced numer of mes he model s n hdden se S 48 cc; f log[ P λ] > log[ P λ] nd c<i hen go o 4 Snce P would e ou of he dynmc rnge of he mchne [7] we compue he log of P usng he followng formul [8]: log[ P λ] log log 2 π A curren me s predced he nex oservon symol usng he dused model λ A π : - choose hdden se S me - mxmzng ; - choose nex hdden se S me - mxmzng ; - predc nex symol V k me k M- mxmzng k If he process connues hen nd go o 3 Sudes n Informcs nd Conrol Vol 5 o Mrch26 2

6 3 A Possle Generlzon: dden Mrkov Models of rder In hs prgrph we ry o develop dden Mrkov Model of order here re mulple possles for dong hs u we presen here only one we consdered he mos ppropre he key of our proposed model s represened y he so-clled hdden super-ses comnon of prmve hdden ses herefore he mn dfference comprng wh n order MM consss n he fc h he sochsc hdden Mrkov model s of order nsed of order one hs new model s usfed ecuse we suppose h n some specfc pplcons here re longer correlons whn he hdden se model In oher words we suppose h he nex hdden se s eer deermned y he curren super-se rher hn y he curren prmve se As cn e furher seen he new proposed model s smlr wh he well-known MM of order one excepng h he generc prmve hdden se ecomes now generc super-se 3 Elemens of MM of rder - he order of MM comnon of prmve hdden ses form so clled super-se 2 - he numer of prmve hdden ses elongng o MM of order wh S { S S S } eng he se of hdden super-ses nd q S he hdden superse me he curren super-se deermnes he rnson no he nex one sed on super-se rnson mrx wh resrcons hs rnson mrx nvolve non-ergodc model see exmple of le wll e vred n order o on he opml vlue 3 M - he numer of oservle ses wh V {V V V M- } he se of oservle ses symols nd he oservle se me 4 A { } - he rnson proles eween he hdden super-ses S nd S where P[ q S q S ] 5 B { k} - he proles of he oservle ses V k consderng he curren hdden superse S where k P[ V q S ] k M k 6 π {π } - he nl hdden super-se proles where π P[ q S ] In order o smplfy he ermnology n he res of he pper we ll refer o he hdden super-ses s smply hdden ses elongng o he MM of order We lso defne he followng vrles: P 2 q λ - he forwrd vrle [7] represenng he proly of he prl oservon sequence unl me nd hdden se S me gven he model λ A π P 2 q λ - he ckwrd vrle [7] represenng he proly of he prl oservon sequence from o he end gven hdden se S me nd he model λ A π ξ P q q S 2 λ - he proly of eng n hdden se S me nd hdden se S me gven he model λ A π nd he oservon sequence γ P q 2 λ - he proly of eng n hdden se S me gven he model λ A π nd he oservon sequence - he hsory he numer of oservons used n he predcon process In [7] nd [8] he enre oservon sequence s used n he predcon process u n some prccl pplcons he oservon sequence ncreses connuously herefore s necessry s lmon hus he ls oservons cn e sored n lef shf regser hvng cern lengh 22 Sudes n Informcs nd Conrol Vol 5 o Mrch26

7 I - he mxmum numer of erons n he dusmen process Usully he dusmen process ends when he proly of he ls oservons doesn ncrese nymore u for fser dusmen s lmed he numer of erons For MM of order wh hdden ses he rnson proles eween he hdden ses A X { } re sored n le wh rows nd columns u no ll cells of he le re used; here re only conssen possle rnsons from ech se nvolvng non-ergodc model he followng le for exmple corresponds o MM of order 3 3 wh 2 prmve hdden ses 2: AAA ABA ABB BAA BAB BBA BBB AAB AAA X X AAB X X 2 ABA X X 3 ABB X X 4 BAA X X 5 BAB X X 6 BBA X X 7 BBB X X le Conssen rnsons for MM of rder 3 3 wh 2 dden Ses 2 here re used only he conssen cells mrked wh X ecuse rnsons re possle only eween ses whch end nd respecvely sr wh he sme - prmve hdden ses he conssen cells of he rnson le re gven y he followng formuls: For nex hdden ses columns re conssen only he curren hdden ses rows ; For curren hdden ses rows re conssen only he nex hdden ses columns mod mod 32 Adusmen Process of MM of rder Inlze λ A π ; 2 Compue ξ γ ; 3 Adus he model λ A π ; 4 If P λ ncreses go o 2 33 Inlzon of he Model of rder he rnson proles eween he hdden ses A X { } re rndomly nlzed o pproxmely /; he sum of ech row s elemens mus e he hdden se rnson proles re nlzed for nd mod mod 2 he proles of he oservle ses B XM { k} re rndomly nlzed o pproxmely /M; he sum of ech row s elemens mus e 3 he nl hdden se proles πx {π } re rndomly se o pproxmely / her sum eng Sudes n Informcs nd Conrol Vol 5 o Mrch26 23

8 24 Sudes n Informcs nd Conrol Vol 5 o Mrch26 34 Predcon Algorhm Usng MM of rder s he lengh of he oservon sequence; 2 ; f < go o 2 3 c c s he numer of curren eron s mxmum vlue s gven y I; 4 he model π λ B A s repeedly dused sed on he ls oservons 2 he enre oservon sequence f n order o ncrese he proly of he oservon sequence 2 λ P In 4 42 nd 43 he denomnors re used n order o on proly mesure nd o vod underflow As Smp showed n [8] underflow s nevle whou sclng snce he proles end o exponenlly s ncreses 4 Compue he forwrd vrle n recursve mnner: π π where s he proly of oservon symol - nd nl hdden se S gven he model π λ B A ; 2 where s he proly of he prl oservon sequence unl me - nd hdden se S me gven he model π λ B A Snce y defnon 2 λ S q P he sum of he ermnl forwrd vrles gves he proly of he oservon sequence: 2 P λ 42 Compue he ckwrd vrle n recursve mnner: ; mod mod mod mod

9 where s he proly of he prl oservon sequence from o he end 2 gven hdden se S me nd he model λ A π 43 Compue ξ : ξ mod mod mod mod where ξ s he proly of eng n hdden se S me nd respecvely S me gven he oservon sequence 2 nd he model λ A π 44 Compue γ : mod mod γ ξ where γ s he proly of eng n hdden se S me gven he model λ A π nd he oservon sequence 2 45 Adus π: π γ - represens he expeced numer of mes he hdden se s S he nl me 46 Adus A: ξ γ - he proly of rnson from hdden se S o S where nd mod mod he numeror s he expeced numer of rnsons from se S o S whle he denomnor s he expeced numer of rnsons from se S o ny se 47 Adus B: Vk k γ - he proly of oservon symol V k k M gven γ h he model s n hdden se S he numeror s he expeced numer of mes he model s n hdden se S nd he oservon symol s V k whle he denomnor s he expeced numer of mes he model s n hdden se S 48 cc; f log[ P λ] > log[ P λ] nd c<i hen go o 4 Snce P would e ou of he dynmc rnge of he mchne [7] we compue he log of P usng he followng formul [8]: Sudes n Informcs nd Conrol Vol 5 o Mrch26 25

10 log[ P λ] log π 2 log A me s predced he nex oservon symol usng he dused model λ A π : - choose hdden se S me mxmzng ; - choose nex hdden se S me mod mod mxmzng ; - predc nex symol V k me k M mxmzng k If he process connues hen nd go o 3 4 Expermenl esuls ur pplcon predcs he nex room sed on he hsory of rooms vsed y cern person movng whn n offce uldng We evlue hese MM predcors y some movemen sequences of rel persons developed y he reserch group he Unversy of Augsurg [6] In hs work we re neresed n predcng he nex room from ll rooms excep for he own offce Ech lne from he orgnl enchmrks [6] represens person s movemen hs/her enry n room I conns he movemen s de nd hour he room s nme he person s nme nd mesmp In he codfcon process we elmned from he enchmrk he common corrdor ecuse could ehve s nose le 2 shows how looks he enchmrk efore nd fer he room codfcon process rgnl enchmrk Benchmrk fer room codfcon 2377 :3:45; 42; Employee2; :2:4; corrdor; Employee2; :2:45; 4; Employee2; :2:48; corrdor; Employee2; :2:54; 42; Employee2; le 2 he Frs Lnes From Cern Benchmrk Wh Movemen Sequence of Employee 2 Before nd Afer he oom Codfcon Process Afer he codfcon process he enchmrks conn only he room codes 3 ecuse n hs srng sge of our work only hs nformon s used n he predcon process We used wo enchmrk ypes: some shor enchmrks connng ou 3-4 movemens nd some long enchmrks connng ou movemens We used he shor enchmrks o pre-rn he MM predcors nd he long enchmrks for evluons We sred wh MM of order wh 2 hdden ses 2 nd we esed on he fll enchmrks developed Augsurg Unversy [6] whou corrdor he followng smulon mehodology ws used n order o predc ech room from cern enchmrk: we predced he nex room me sed on he enre room sequence from h enchmrk unl me - We compred MM whou ched confdence uom wh MMs usng dfferen confdence uom We denoed s n rooms m ses conf n m-se confdence couner ssoced o ech sequence of he ls n rooms vsed y he person he 4-se uom hve 2 predcle ses whle he 2-se uom hve only predcle se In he cse of usng 4-se uom predcon s genered n ech of he wo predcle ses [9] le 3 shows h he es verge predcon ccurcy AM s oned when usng 4-se confdence for ech sequence of 2 rooms: 26 Sudes n Informcs nd Conrol Vol 5 o Mrch26

11 Benchmrk no conf 2 rooms 4 ses conf 2 rooms 2 ses conf room 4 ses conf Employee Employee Employee Boss AM le 3 Comprng MM Whou Confdence wh MMs Usng Dfferen ypes of Confdence We connued our smulons vryng he numer of hdden ses We used gn he fll enchmrks [6] nd MM of order wh 4-se confdence uom ssoced o ech sequence of wo rooms le 4 shows how s ffeced he predcon ccurcy of MM y he numer of hdden ses: Benchmrk Employee Employee Employee Boss AM le 4 Sudy of he umer of dden Ses Usng MM wh 4-Se Confdence Auom I cn e oserved n le 4 h for MM of order he opml numer of hdden ses s 5 ur scenfc hypohess s h he hdden ses re he fve workng dys of week We vred gn he numer of hdden ses whou usng he confdence uom le 5 shows h n hs cse he opml numer of hdden ses s Benchmrk Employee Employee Employee Boss AM le 5 Sudy of he umer of dden Ses Usng MM Whou Confdence Auom We compre now he es MM of order wh dfferen confgurons of some equvlen s eurl eworks developed n our prevous work [9] nd respecvely smple Mrkov predcors Equvlen mens n hs cse h we compre ll hese dfferen predcors consderng h hey hve however he sme npus We used he MM of order wh 5 hdden ses consderng n ched 4-se confdence uom We compred wh sclly pre-rned wh room hsory lengh of of order nd 2 of order 2 lernng re of 2 nd hreshold of 3 hvng he sme confdence uom We lso compred he MM wh some smple Mrkov predcors of order nd 2 hvng he sme confdence uom he ws sclly rned on he summer enchmrks [6] nd ech predcor ws esed on he longer fll enchmrks [6] le 6 presens he predcon ccurces oned wh he MM nd Mrkov predcors ll wh 4-se confdence uom ssoced o ech sequence of wo rooms: Benchmrk MM of order of order of order 2 Mrkov of order Mrkov of order 2 5 Employee Employee Employee Boss AM le 6 Comprng MM of rder wh nd Mrkov Predcors Usng 4-Se Confdence Auom Employee 2 hsn go ehvor correled wh dys of week see le 4 nd lso le 6 I cn e seen n le 6 oo ecuse he Mrkov predcor of order ouperforms he MM of order s re eer hn MM on Employee 2 u we suspec h hese resuls re oo opmsc due o he s prernng frs cse nd respecvely due o he s order 2 second cse Sudes n Informcs nd Conrol Vol 5 o Mrch26 27

12 le 7 presens he predcon ccurces oned wh he MM nd smple Mrkov predcors he sme confguron whou confdence uom: Benchmrk MM of order of order of order 2 Mrkov of order Mrkov of order 2 Employee Employee Employee Boss AM le 7 Comprng MM of order wh nd smple Mrkov predcors whou confdence uom In order o confrm or nfrm our scenfc hypohess h n he cse of MM wh 4-se confdence uom he fve hdden ses mgh e he workng dys of he week we mplemened predcor whch consss of fve smple Mrkov predcors Ech Mrkov predcor s ssoced o one of he 5 dys Mondy uesdy Frdy le 8 compres hs predcor connng 5 smple Mrkov predcors wh MMs nd smple Mrkov predcors usng he 4-se confdence uom nd shows h only on one person Boss s confrmed our hypohess Benchmrk MM of order 5 Mrkov of order 5 Mrkov predcors of order Employee Employee Employee Boss AM le 8 Comprng MM of order wh Mrkov of order nd predcor conssng n 5 Mrkov predcors usng 4-se confdence uom le 9 compres he sme predcors MM Mrkov 5 Mrkovs whou usng he confdence uom In hs cse however he es numer of hdden ses ws We oned for ll enchmrks lower predcon ccurces when we used 5 smple Mrkov predcors even reled o he smple Mrkov predcor Benchmrk MM of order Mrkov of order 5 Mrkov predcors of order Employee Employee Employee Boss AM le 9 Comprng MM of order wh Mrkov of order nd predcor conssng n 5 Mrkov predcors whou usng confdence uom In order o decrese predcon lency we pre-rned MMs on he summer enchmrks [6] nd fer h we esed hem on he longer fll enchmrks [6] le presens comprvely he oned resuls when we used MM wh 5 hdden ses nd 4-se confdence uom: MM of order 5 Pre-rned MM of order 5 Benchmrk Predcon ccurcy [%] ol me Predcon me of he ls room Predcon ccurcy [%] ol me Predcon me of he ls room Employee Employee Employee Boss AM le Comprng smple MMs wh pre-rned MMs oh wh 4-se confdence uom n erms of predcon lency 28 Sudes n Informcs nd Conrol Vol 5 o Mrch26

13 As cn e oserved wh pre-rned MMs we oned eer predcon lences ou 85 ms u for Employee 3 nd Boss we oned lower predcon ccurces he sme predcon ccurces were oned usng he unrned MM wh only hdden se see le 4 hus n our opnon hrough pre-rnng he MM wh 5 hdden ses uses only of he hdden ses We repeed he sme smulons whou usng he confdence uom le presens he resuls for MM wh 5 hdden ses nd le 2 presens he resuls for MM wh hdden se: MM of order 5 Pre-rned MM of order 5 Benchmrk Predcon ccurcy [%] ol me Predcon me of he ls room Predcon ccurcy [%] ol me Predcon me of he ls room Employee Employee Employee Boss AM le Comprng smple MMs wh pre-rned MMs oh whou confdence uom n erms of predcon lency 5 MM of order Pre-rned MM of order Benchmrk Predcon ccurcy [%] ol me Predcon me of he ls room Predcon ccurcy [%] ol me Predcon me of he ls room Employee Employee Employee Boss AM le 2 Comprng smple MMs wh pre-rned MMs oh whou confdence uom n erms of predcon lency As cn e seen n le for MM wh 5 hdden ses hrough pre-rnng here re oned eer predcon lences nd eer predcon ccurces I s neresng h we oned he sme predcon ccurces usng he unrned MM wh hdden se see le 7 And s more neresng h for MM wh hdden se fer pre-rnng he predcon ccurcy s he sme gn hese resuls encourge our prevous concluson h he es numer of hdden ses s when we don use confdence uom hrough pre-rnng he MM wh 5 hdden ses nd whou confdence uom uses only of he hdden ses he nex prmeer we vred ws he order of MM We suded MMs of dfferen orders nd he sme numer of hdden ses 2 As cn e oserved n le 3 wh frs order MM were oned he es predcon ccurces: BECMAK Wh 4-se confdence Whou confdence EMPLYEE EMPLYEE EMPLYEE BSS AM le 3 Sudyng MMs of dfferen orders Sudes n Informcs nd Conrol Vol 5 o Mrch26 29

14 5 Conclusons nd Furher Work hs pper nlyzed mchne lernng echnques sed on MMs used n uquous compung pplcon ur gol ws o predc ccurely he movemens of persons whn n offce uldng wo predcor ypes were nlyzed: MMs wh confdence uom nd respecvely whou confdence uom he expermenl resuls show h MMs ouperform oher mplemened predcon echnques such s eurl ework nd respecvely Mrkov predcors he evluons show h he smples confguron of MM nd equvlen wh smple Mrkov model of order s he mos ccure for hs specfc pplcon We connued our sudy mplemenng sclly pre-rned MM nd we oned lower predcon lences Predcng from ll rooms excep own room nd usng MM wh 4-se confdence uom we oned n verge predcon ccurcy of 848% u he predcon ccurcy mesured on some locl predcors grew up o over hn 92% As furher work we nend o use our nd MM developed predcors n oher conex predcon n uquous compung pplcons eg nex cell movemens n GSM communcons sed on ok s enchmrks Acknowledgmens hs work ws suppored n pr y he omnn onl Councl of Acdemc eserch CCSIS hrough he grn CCSIS 7 / Also our grude o Professor heo Ungerer from he Unversy of Augsurg Germny for provdng us he used enchmrks for persons movemens nd for supporng he second uhor durng wo monhs reserch sge Augsurg n 23 EFEECES BIEY E dden Mrkov Models n Bologcl Sequence Anlyss IBM Journl of eserch nd Developmen Volume 45 umers 3/4 2 2 GALAA A JS GG D Lernng Behvour Models of umn Acves Proceedngs of Brsh Mchne Vson Conference pges 2-22 onghm UK Sepemer LIU LVELL B C Gesure Clssfcon Usng dden Mrkov Models nd Ver Ph Counng Proceedngs of he Sevenh Inernonl Conference on Dgl Imge Compung: echnques nd Applcons pges Sydney Ausrl Decemer 23 4 PEZLD J BAGCI F UMLE W UGEE Conex Predcon Bsed on Brnch Predcon Mehods echncl epor Unversy of Augsurg Germny 23 5 PEZLD J BAGCI F UMLE W UGEE VIA L Glol Se Conex Predcon echnques Appled o Smr ffce Buldng Communcon eworks nd Dsrued Sysems Modelng nd Smulon Conference Sn Dego Clforn SUA Jnury PEZLD J Augsurg Indoor Locon rckng Benchmrks echncl epor 24-9 Insue of Compuer Scence Unversy of Augsurg Germny 24 hp://wwwnformkunugsurgde/skrps/echrepors/ 7 ABIE L A uorl on dden Mrkov Models nd Seleced Applcons n Speech ecognon Proceedngs of he IEEE Vol 77 o 2 Ferury SAMP M A evelng Inroducon o dden Mrkov Models Jnury 24 hp://wwwcsssuedu/fculy/smp/ua/mmpdf 9 VIA L GELLE A PEZLD J UGEE Person Movemen Predcon Usng eurl eworks Proceedngs of he KI24 Inernonl Workshop on Modelng nd erevl of Conex MC 24 Vol-4 ISS Ulm Germny Sepemer 24 Y VAIDYAA P P A Secondry Srucure Predcon Usng Conex-Sensve dden Mrkov Models Proceedngs of Inernonl Workshop on Bomedcl Crcus nd Sysems Sngpore Decemer 24 3 Sudes n Informcs nd Conrol Vol 5 o Mrch26