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1 !"#$%&'()&*'+(',-.')/)) ))))))-%%(0+12) )53+&%,)6%5'(#() 7) Méhodes d ensemble!"#$%"&'($)"*+,$-.'!"#$%&#'()*+,- Boosing 2 Moivaion Illuraion! /'8$')94(&%,)%6):5%9&)0' 1234&.'5*)$6%&78%9':;;<=' >?.@43@$"'A*'B$%A.'AC*"'B3"%&)'A3".'*"'43)7D+'' EFE'B3)@7%B3"#.'' G H&'4&%--&*)'I'B-*.'AC*"'7&"@J4&'AC&))&*)' G K$L&""&'M'4$%".'AC*"'4%--%J4&'AC&))&*)' '1N)3"7%.'O3-#$" P 9'PQ;R'SFT'3".U=' P '3"#D)$B$-$V*&9'&WB-$)3#&*)9'V+$V)3BD&9'%"X&"#&*)9'4+#+$)$-$V*&9'B)$#$YV+"+@7%&"9'' '''B.L7D$4+#)%7%&"'&#'.#3@.@7%&"' Boosing 3 Boosing 4

2 Illusraion Types d expers!!"#$%&'#%()%*+'.*)'-c%"$%,-'%#.%#x'''!!"#%()%*+#b3)'$/&$0*123/"$#.%#x's&zvz'3)[)&.'a&'a+7%.%$".u'! 4'&$3%&*$#%()%*+$9'#$*.'.*)'-C%"$%,-'%#.%#X''! 4'&$3%&*$#%()%*+$'.B+7%3-%.+.'.*)'A&.'$/&$0*123/"$#.%#X## Boosing 5 Boosing 6 Types d expers Schéma général : apprenissage!!"#$%&'#%()%*+'.*)'-c%"$%,-'%#.%#x'''!!"#%()%*+#b3)'$/&$0*123/"$#.%#x's&zvz'3)[)&.'a&'a+7%.%$".u'! 4'&$3%&*$#%()%*+$9'#$*.'.*)'-C%"$%,-'%#.%#X''! 4'&$3%&*$#%()%*+$'.B+7%3-%.+.'.*)'A&.'$/&$0*123/"$#.%#X## Boosing 7 Boosing 8

3 Jusificaions inuiives Succès applicaifs! 56607&)# > C'#9%5<)4+#5>(4%+)&'#':0%+)DEFFFG)H),%.':>.35)-4%3:0I4#B)J)=5%#'4+).%:3.') =5'&4:0%+)DKLLEG)H)D7G)=>.,%+35B)',-%.4(,')&'#':0%+)DKLLMG)H):>(#%,'5) 5'.30%+($4=),3+31','+#)DKLLFG)H)'&>:30%+3.)&3#3),4+4+1)DKLELG)H),>(4:) 5':%,,3+&30%+)DKLEEG)H)7)) > ^$*.'-&.'P &) 'B)%W'&#': J4& 'B)%W'B$*)'-&.',1+8/.%$#.9%"$%,-'%'S:;;QY:;PP' Y'aaaU'! :%;'3(#)*3<%# > N,=5%I')3::>53:B)3-%>#)$%9),>:$)(%,'%+')4()1%4+1)#%)'+O%B)3),%I4') -3('&)%+)#$'45)=5'6'5'+:') > P';;;';;;'b'c$)'3'"&6'3-V$)%#D4'%4B)$X%"V'$"'d&e-%WC$"&'[L'4$)&'#D3"'P;f' Boosing 9 > g%""&)'%"':;;q'c$)'3"'%"$%,-'%#,%+8/.# Boosing 10 Illusraion Illusraion! 5$%#'X'*"'&.B37&'AC&"#)+&'h'=>#.3,%"$3/"$#! H&.'3])%[*#.'.$"#'%"A+B&"A3"#.'&#'A&'A%.#)%[*@$"'V3*..%&""&'! H&'?/"?%)+#?3-'%'&.#'A+i"%'B3)'M' u = 2 $ 1 si " j=1,10 x % j & #1 sinon >! 2 10 (0,5) 0,5 0,4 0,3 Arbre à un noeud Arbre à 400 noeuds avec :! 2 10 (0, 5) = 9, 34 0,2! :;;;''P',=.'()&*3==5'+0((31''SP;;;jkP;;;YU'! P;;;;''P',=.'()&')#'(#)!!BB)&"@..3V&'AC@*-*%$#.%#.1?3$3/"# 0,1 0,0 Arbres à un nœud avec boosing Boosing 11 Boosing 12

4 Performances du boosing Exemple simple! Quel es le meilleur séparaeur linéaire? Boosing 13 Boosing 14 Exemple simple Exemple simple! Taux d erreur = 5/20 = 0.25! Taux d erreur (h 1 ) = 5/20 = 0.25 E si je pouvais combiner avec un aure séparaeur linéaire? Ou même plusieurs aures! Boosing 15 Boosing 16

5 Exemple simple Exemple simple E si je pouvais combiner avec un aure séparaeur linéaire? Ou même plusieurs aures! Par exemple en uilisan un voe pondéré : H(x) = sign{ h 1 (x) h 2 (x) h 3 (x) h 4 (x) h 5 (x) } Boosing 17 Boosing 18 Exemple simple H(x) =sign{ h 1 (x) h 2 (x) h 3 (x) h 4 (x) h 5 (x) } Le boosing! Commen arriver à ce genre de combinaison? Algorihme du boosing Boosing 19 Boosing 20

6 Une quesion > X '.*)'X9'&#'B$*)'#$*#&'c$"7@$"'6' &.#'#&-'m*&'m'' Commen engendrer les apprenans! l"&')&7&]&'d%.#$)%m*&'!!bb)&"@..3v&'/'a@3-'%'0' > l"&'7-3..&'a&'c$"7@$".'f'&.#'3bb)&"3[-&'s3*'.&".'c3%[-&u'.%9'b$*)'!'n';9'%-'&w%.#&' *"'3-V$)%#D4&'AC3BB)&"@..3V&'A'm*%'B$*)'#$*#&'A%.#)%[*@$"'D X '.*)'X9'&#'B$*)' #$*#&'c$"7@$"'6'&.#'#&-'m*&'m''! 5$"#Y%-.'A&'"3#*)&'A%o+)&"#&'a' Boosing 21 Boosing 22 Commen engendrer les apprenans Commen engendrer les apprenans! l"&')&7&]&'d%.#$)%m*&'! l"&')&7&]&'d%.#$)%m*&' Boosing 23 Boosing 24

7 Quesions Commen engendrer les apprenans (suie)! > Q+).'/'01&02-.*4,=%5#3+:')&'()'P',=.'()3'*0-:.3(("() > Q+)&1"/*02&02-RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR)/&4-RRRRRRRR' > \&'7$4[%&"'a' Boosing 25 Boosing 26 Boosing Schéma général : apprenissage Boosing 27 Boosing 28

8 Quesions! ($44&"#'7D$%.%)'-&.'7$*).&.'h'7D3m*&'+#3B&a'! 5&'7$"7&"#)&)'.*)'-&.'7$*).&.'-&.'B-*.'pA%q7%-&.r' B&)c$)43"#&.U'! _)&"A)&'*"&'X$#&'SB$"A+)+U'43,$)%#3%)&'A&'7&.')JV-&.' Boosing : vue formelle! s#3"#'a$""+'-c+7d3"@--$"'ac3bb)&"@..3v&'s I'SP P 2B P U272SP, 2B, Uu'! B 4 " 1,+1u'+@m*&]&'A&''-C&W&4B-&'P 4 "'S'! _$*)'#)S)P2728M' ($".#)*%)&'-3'A%.#)%[*@$"'T # '.*)'P9v9,u' ^)$*X&)'-CDLB$#DJ.&'c3%[-&'SpD&*)%.@m*&rU' '''''' '$ # 'M'S'#' 1,+1u' ' '3X&7'&))&*)'B&@#&'! #).*)'T # M' " = PrD [ h ( xi )! y ] i! w&#$*)"&)'-cdlb$#dj.&'i"3-&'$ i"3- ' Boosing 29 Boosing 30 Schéma général : prédicion Le principe général D T X h T D 2 D 1 D 0 X h 2 X h 1 X h 0 # H finale (x) = sgn $ % T " = 0 &!. h (x) '(! 7/,,%"+#)@$$%*#.%#D 2 #B#D 2C= #D# Boosing 31! 7/,,%"+#?@'?&'%*#'@#)/".1*@E/"#$ 2 #D# Boosing 32

9 Boosing 33 AdaBoos [Freund&Schapire 97]! 7$".#)*%)&'T # M' s#3"#'a$""+&'t #) &#'$ # M' ' ' '$xm'u #) I'7$".#3"#&'A&'"$)43-%.3@$"'! ylb$#dj.&'i"3-&'m' )) ( exp( i i x h y Z D!! "! = #! " # $ = % = & + ) ( if ) ( if 1 i i i i x h y e x h y e Z D D ' ' m i D 1 ) ( 1 = 0 1 ln 2 1 >!! " # $ $ % & ' = ( ( )! " # $ % & = ' x h x H ) ( sgn ) ( final ( Boosing 34 AdaBoos en plus gros! " # $ = % = & + ) ( if ) ( if 1 i i i i x h y e x h y e Z D D ' ' 0 1 ln 2 1 >!! " # $ $ % & ' = ( ( )! " # $ % & = ' x h x H ) ( sgn ) ( final ( Boosing 35 Exemple simple! Taux d erreur = 5/20 = 0.25 Boosing 36 Exemple simple! Nouvelle pondéraion des exemples d apprenissage! Exemples bien classés! Exemples mal classés

10 Exemple simple Exemple simple! Nouvelle pondéraion des exemples d apprenissage! Taux d erreur :! Exemples bien classés! Exemples mal classés! Sous-pondéraion des bien classés :! Sur-pondéraion des mal classés : Boosing 37 Boosing 38 Exemple simple Exemple simple! Sous-pondéraion des bien classés :! Sur-pondéraion des mal classés :! Taux d erreur :! Sous-pondéraion des bien classés :! Sur-pondéraion des mal classés : Boosing 39 Boosing 40

11 Exemple simple Exemple joue! Sous-pondéraion des bien classés :! Sur-pondéraion des mal classés : Boosing 41 Boosing 42 Éape 1 Éape 2 Boosing 43 Boosing 44

12 Éape 3 Hypohèse finale Boosing 45 Boosing 46 Boosing : Des demos en ligne D]BMzz666Z)&.&3)7DZ3]Z7$4z{L$3Xz3A3[$$.#z%"A&WZD#4-' Exercice D]BMzz666Z43#D6$)8.Z7$4z43#-3[7&"#)3-zcW i-&.z:q:<tzpz [$$.@"V A&4$ZB"V' Boosing 47 Boosing 48

13 Boosingdemo de Richard Sapenhurs Boosingdemo de Richard Sapenhurs Boosing 49 Boosing 50 Dérivaion de l algorihme du boosing Analyse héorique du boosing Boosing 51 Boosing 52

14 T"54I30%+)&').*3.1%54#$,')&>)-%%(0+1)! >?"'7D$%.%..3"#'*"&'6%+:0%+)&')='5#')(>55%1"''A&' V%%(0+1)'#)#*.*(+#'56$0-! Boosing 53 Boosing 54 AW!)'#),"#$%&'()X)+%B3>P) Bornes en apprenissage e en généralisaion Boosing 55 Boosing 56

15 Bornes sur l erreur en apprenissage Evoluion des courbes d erreur (apprenissage & es) Boosing 57 Boosing 58 Comporemen de l erreur en généralisaion? Argumens pour expliquer les propriéés du boosing (he unreasonable power of boosing)! HC&))&*)'&"'#&.#'"9@&2,%"+%#)@$9'4}4&'3B)J.'P;;;'+#3B&.' S:ZP; R '"~*A.'#&.#'U' > Ä$$.@"V'A&'(<ZT'.*)'-3'[3.&'A&'A$""+&.'/'-&]&)'0' Boosing 59 Boosing 60

16 Une explicaion par la «marge» Éude de la disribuion des marges des x i! `A+&'M' > HC&))&*)'&"'3BB)&"@..3V&'"&'4&.*)&'m*&'-&'#3*W'AC&))&*)'&"' B)+A%7@$"' > `-'c3*#'3*..%'#&"%)'7$4b#&'a&''@#?/"h@"?%'a&'-3'b)+a%7@$"' > Å"'B&*#'&.@4&)'7&]&'7$"i3"7&'B3)'-3',@*2%# ''''''I'B$%A.'A&.'7-3..%i&*).'3L3"#'X$#+'7$))&7#&4&"#'' '''Y'B$%A.'A&.'7-3..%i&*).'&"'&))&*)' Boosing 61 Boosing 62 Argumen de la maximisaion de la marge Analyse héorique : maximisaion de la marge! Ç'7D3m*&'+#3B&9'!A3Ä$$.#'B-37&)3%#'-&')'&$#.%#)/3.$#$&*#'%$# %(%,)'%$#7 3 #.%#)'&$#A@3-'%#,@*2%'#$*#'&"'7$"@"*3"#'h' 34+-%$)&)'-3'43)V&'.*)'-&.'3*#)&.'! HCDLB$#DJ.&'i"3-&'.&)3%#'?/,)'%(%#43%.')*/?8%#.9&"%# 8I)/+8J$%#$3,)'%'AC&))&*)'AC3BB)&"@..3V&'B)$7D&'S&#'A$"7' AC&))&*)'&"'V+"+)3-%.3@$"'c3%[-&'3*..%U' Boosing 63 Boosing 64

17 Analyse héorique : maximisaion de la marge Plus echniquemen Boosing 65 Boosing 66 Bornes en généralisaion Aures perspecives pour expliquer les propriéés du boosing Boosing 67 Boosing 68

18 Aures perspecives! H3'#D+$)%&'A&.',&*W' > > É*&'B-*.'D3*#'S&#'B-*.'-$%"U' Bilan! Boosing 69 Boosing 70 Avanages praiques de AdaBoos Performances du boosing! c3%[-&'s"&*)$'"&#9'(<zt9'vu'! _&*#'}#)&'3A3B#+'3*'73.'$x'$ # 'M'X'#'R'k'-3'7-3..&'&.#'A+i"%&'B3)'-&'.%V"&'A&'$ # SPU'k'-3'7$"i3"7&'&.#'A$""+&'B3)'Ñ'$ # SPU'Ñ'! _&*#'}#)&'3A3B#+'3*W'B)$[-J4&.'4*-@Y7-3..&.'' $x'b 4) "'P9ZZ9:u'&#'3*W'B)$[-J4&.'4*-@Y+@m*&]&.'! _&)4&#'A&'#)$*X&)'-&.'&W&4B-&.'3[&))3"#.'S$*#-%&).U' Boosing 71 Boosing 72

19 Quand es-ce que ça ne marche pas Aspecs praiques! w3bb&-'m':/0a*%%0'&"?80+8%/*%,#! > > 7/,3+1#SAC3BB)&"3"#.'c3%[-&.U'+*/)#*%$+*%3"+# > G > \$""+&.'-*&3+1%$# Avanages Un mea-algorihme d apprenissage : uiliser n impore quel algorihme d apprenissage faible En principe, un seul paramère à régler (le nombre T d iéraions) Facile e aisé à programmer Performances héoriques garanies Difficulés Difficile d incorporer des connaissances a priori Difficile de savoir commen régulariser Le meilleur choix d un appreni faible n es pas éviden Les fronières de décision en uilisan des méhodes parallèles aux axes es souven rès irrégulière (non inerpréable) Boosing 73 Boosing 74 Boosing : résumé! H3'B)+A%7@$"'i"3-&'&.#'%..*&'AC*"&'7$4[%"3%.$"'SX$#&' B$"A+)+U'A&'B-*.%&*).'B)+A%7@$".''! K+#D$A&'M' > `#+)3@X&' > (D3m*&'7-3..%i&*)'A+B&"A'A&.'B)+7+A&"#.' '''S-&.'7-3..%i&*).'"&'.$"#'A$"7'B3.'%"A+B&"A3"#.'7$44&'A3".'AC3*#)&.' 4+#D$A&.'A&'X$#&U' > H&.'&W&4B-&.'.$"#'B$"A+)+.'A%o+)&44&"#' > H&'B$%A.'A&.'&W&4B-&.')&ÖJ#&'-3'A%q7*-#+'A&.'7-3..%i&*).' B)+7+A&"#.'h'-&.'3BB)&"A)&' Aures algorihmes de boosing Boosing 75 Boosing 76

20 Foncions «surrogées» LogiBoos! > _3.'A&'B$%A.'&W$)[%#3"#'.*)'-&.'B$%"#.'3[&))3"#.' > Boosing 77 Boosing 78 Applicaions Applicaions du boosing Boosing 79 Boosing 80

21 Face deecion idea! PU'%"'!A3[$$.#'*.&'B3)3--&-Y3W%.'S#)&&'A&7%.%$"U'7-3..%i&)'' a discussion of his sysem and is relaionship o re- :U'%"'É%$-3''2$"&.9'#D&'6&38'7-3..%i&)'%.'#D&'.B&7%3--L'A&.%V"&A' laed sysems %i&)'A&.7)%[&A'%"'#D&'B3B&)Z'' Les descripeurs ogeher yield an exremely reliable and efficien face deecor. Secion 5 will describe a number of experimenal resuls, including a deailed descripion of our experimenal mehodology. Finally Secion 6 conains 2. Feaures Robus Real-Time Face Deecion 139 Our face deecion procedure classifies images based on he value of simple feaures. There are many moivaions for using feaures raher han he pixels direcly. ii(x, y) = i(x, y ), The mos common reason is ha feaures can ac o encode x x,y y ad-hoc domain knowledge ha is difficul o learn using a finie quaniy of raining daa. For his sysem where ii(x, y) is he inegral image and i(x, y) is he here is also a second criical moivaion for feaures: original image (see Fig. 2). Using he following pair of he feaure-based sysem operaes much faser han a recurrences: pixel-based sysem. The simple feaures used are reminiscen of Haar s(x, y) = s(x, y 1) + i(x, y) (1) basis funcions which have been used by Papageorgiou e al. (1998). More specifically, we use hree kinds of ii(x, y) = ii(x 1, y) + s(x, y) (2) feaures. The value of a wo-recangle feaure is he difference beween he sum of he pixels wihin wo (where s(x, y) is he cumulaive row sum, s(x, 1) = recangular Adaboos regions. v.2c The regions have he same size Boosing 81 and shape and are horizonally or verically 81 adjacen (see Fig. 1). A hree-recangle feaure compues he sum wihin wo ouside recangles subraced from he sum in a cener recangle. Finally a four-recangle feaure compues he difference beween diagonal pairs of recangles. Given ha he base resoluion of he deecor is 24 24, he exhausive se of recangle feaures is quie large, 160,000. Noe ha unlike he Haar basis, he se of recangle feaures is overcomplee Inegral Image Recangle feaures can be compued very rapidly using an inermediae represenaion for he image which we call he inegral image. 4 The inegral image a locaion x, y conains he sum of he pixels above and o he lef of x, y, inclusive: Robus real-ime face deecion [Viola & Jones, 2004]! `43V&.''ÜF<'W':FF'S"%X&3*W'A&'V)%.U'! \+#&7#&)'A&.'X%.3V&.'h'#$*#&'+7D&--&'!?"'#&4B.')+&-'SPT'%43V&.'z'.U'.*)'*"'.43)#BD$"&''! _)$[-J4&.'' 0, and ii( 1, y) = 0) he inegral image can be compued in one pass over he original image. Using he inegral image any recangular sum can be compued in four array references (see Fig. 3). Clearly he difference beween wo recangular sums can be compued in eigh references. Since he wo-recangle feaures defined above involve adjacen recangular sums hey can be compued in six array references, eigh in he case of he hree-recangle feaures, and nine for four-recangle feaures. One alernaive moivaion for he inegral image comes from he boxles work of Simard e al. > `A&"@i&)'A&.'.%$?*3)+%&*$#B&)@"&"#.' > H&.'73-7*-&)'*@)3.%,%"+## > H&.'$)V3"%.&)'B$*)'c3%)&'*"'$I$+J,%#B&)c$)43"#' G N3%[-&'Nd' G N3%[-&'N_' Useful Feaures Learned by Boosing Boosing 82! _-*.'A&'Ü';;;';;;';;;''' > ^$*#&.'+7D&--&.' > 5&*%-'h'A+i"%)' Figure 1. Example recangle feaures shown relaive o he enclosing deecion window. The sum of he pixels which lie wihin he whie recangles are subraced from he sum of pixels in he grey recangles. Two-recangle feaures are shown in (A) and (B). Figure (C) shows a hree-recangle feaure, and (D) a four-recangle feaure. Boosing 83 Figure 2. The value of he inegral image a poin (x, y) is he sum of all he pixels above and o he lef. Adaboos v.2c Boosing 84

22 Sélecion des descripeurs x, in he range [0, d 1], he x-h dimension uiles is se o!?"'*@-%.3"#'!a3ä$$.#' > H&.'A&.7)%B#&*).'.$"#'3..$7%+.'h'A&.'/'A&7%.%$"'.#*4B.'0' G :;;'A3".'7&]&'+#*A&' K3%.'#)$B'7$á#&*W' &"'#&4B.'73-7*-'M'{;ZE() on feaure variance. They demonsraed good resuls selecing 37 feaures ou of a oal 1734 feaures. While his is a significan reducion, he number of feaures evaluaed for every image sub-window is sill reasonably large. Roh e al. (2000) propose a feaure selecion process based on he Winnow exponenial percepron learning rule. These auhors use a very large and unusual feaure se, where each pixel is mapped ino a binary vecor of d dimensions (when a paricular pixel akes on he value 1 and he oher dimensions o 0). The binary vecors for each pixel are concaenaed o form a single binary vecor wih nd dimensions (n is he number of pixels). The classificaion rule is a percepron, which assigns one weigh o each dimension of he inpu vecor. The Winnow learning process converges o a soluion where many of hese weighs are zero. Neverheless a very large number of feaures are reained (perhaps a few hundred or housand) Learning Resuls While deails on he raining and performance of he > H&'[$$.@"V'.+-&7@$""&'*"&'.+m*&"7&'A&'A&.7)%B#&*).' final sysem are presened in Secion 5, several simple resuls meri discussion. Iniial experimens demon- sraed ha a classifier consruced from 200 feaures would yield reasonable resuls (see Fig. 4). Given a deecion rae of 95% he classifier yielded a false posiive rae of 1 in on a esing daase. This is promising, bu for a face deecor o be pracical for real applicaions, he false posiive rae mus be closer o 1 in 1,000,000. For he ask of face deecion, he iniial recangle feaures seleced by AdaBoos are meaningful and easily inerpreed. The firs feaure seleced seems o focus on he propery ha he region of he eyes is ofen darker han he region of he nose and cheeks (see Fig. 5). This feaure is relaively large in comparison wih he deecion sub-window, and should be somewha insensiive o size and locaion of he face. The second feaure seleced relies on he propery ha he eyes are darker han he bridge of he nose. In summary he 200-feaure classifier provides iniial evidence ha a boosed classifier consruced from recangle feaures is an effecive echnique for face deecion. In erms of deecion, hese resuls are compelling bu no sufficien for many real-world asks. In erms of compuaion, his classifier is very fas, requiring 0.7 seconds o scan an 384 by 288 pixel image. Unforunaely, he mos sraighforward echnique for improving deecion performance, adding 4. The Aenional Cascade This secion describes an algorihm for consrucing a cascade of classifiers which achieves increased deecion performance while radically reducing compuaion ime. The key insigh is ha smaller, and herefore more efficien, boosed classifiers can be consruced which rejec many of he negaive sub-windows while deecing almos all posiive insances. Simpler classifiers are used o rejec he! majoriy s-%4%"&)'-&'b-*.'#à#' of sub-windows before more complex classifiers are called upon o achieve low false posiive raes. B$..%[-&'-&.'"+V3@c.' Sages in he cascade are consruced by raining classifiers using AdaBoos. Saring wih a wo-feaure srong classifier, an effecive face filer can be obained by adjusing he srong classifier hreshold o minimize false negaives. The iniial AdaBoos hreshold, 1 T 2 =1 α,is designed o yield a low error rae on he raining daa. A lower hreshold yields higher deecion raes and higher false posiive raes. Based on performance measured using a validaion raining se, he wo-feaure classifier can be adjused o deec 100% of he faces wih a false posiive rae of 50%. See Fig. 5 for a descripion of he wo feaures used in his classifier. The deecion performance of he wo-feaure classifier is far from accepable as a face deecion sysem. Neverheless he classifier can significanly reduce he high deecion raes. A posiive resul from he second classifier riggers a hird classifier, and so on. A negaive oucome a any poin leads o he immediae rejecion of he sub-window. The srucure of he cascade reflecs he fac ha wihin any single image an overwhelming majoriy of sub-windows are negaive. As such, he cascade aemps o rejec as many negaives as possible a he earlies sage possible. While a posiive insance will Organisaion des déeceurs en cascade Figure 6. Schemaic depicion of a he deecion cascade. A series of classifiers are applied o every sub-window. The iniial classifier eliminaes a large number of negaive examples wih very lile processing. Subsequen layers eliminae addiional negaives bu require addiional compuaion. Afer several sages of processing he number of sub-windows have been reduced radically. Furher processing can ake any form such as addiional sages of he cascade (as in our deecion sysem) or an alernaive deecion sysem. Figure 4. Receiver operaing characerisic (ROC) curve for he 200 feaure classifier. Boosing 85 Boosing 86 Face deecion using boosing Applicaions! w&7$""3%..3"7&'a*'7$"#$*)'a*')&%"' Boosing 87 Boosing 88

23 Bagging [Breiman,96] Le bagging! ''! X$#&'S.%4B-&U'A&.'7-3..%i&*).' Boosing 89 Boosing 90 Bagging (suie)! `-'&.#'.$*X&"#'A%#'m*&'M '' > [%3%.'%"7D3"V+'! K3%.9'&"7$)&'%"7$4B-J#&4&"#'7$4B)%.' > É$%)''[Yves Grandvale : «Bagging equalizes influence», Machine Learning, 55(3), pages , 2004.] Les forês aléaoires (Random foress) Boosing 91 Boosing 92

24 Les forês aléaoires Toy Fores Classificaion Demo! _)%"7%B&'M'' > K))*%".*%#A&.'3)[)&.' > 5*)'A&.'Q%&(#.%#./""1%$#A%o+)&"#.'S7$44&'-&'[3VV%"VU' > Boosing 93 S'7-3..&.'%"'3'T'A%4&".%$"3-'c&3#*)&'.B37&Z' U)'3+#A&"?E/"$'3)&'-%"&.'%"'#D%.'.B37&Z' Boosing 94 Toy Fores Classificaion Demo Toy Fores Classificaion Demo g%#d'3'.%)+8#t'#)&&9'l$*'73"'"$#'.&b3)3#&'3--'.%w'7-3..&.z' Boosing 95 g%#d'3'.%)+8#v'#)&&9'l$*'3)&'a$%"v'[&]&)9'' Boosing 96

25 Toy Fores Classificaion Demo Toy Fores Classificaion Demo g%#d'3'.%)+8#w'#)&&9'l$*'"$6'd3x&'3#'-&3.#'3.'43"l'-&3c'"$a&.' 3.'7-3..&.93"A'.$'3)&'3[-&'#$'7-3..%cL'4$.#'&W34B-&.'7$))&7#-LZ' Boosing 97 \%o&)&"#'#)&&.'6%#d%"'3'c$)&.#'73"'v%x&')%.&'#$'x&)l'a%o&)&"#'a&7%.%$"' Boosing 98 Toy Fores Classificaion Demo Bilan sur les forês aléaoires! > _&)#&'AC%"#&)B)+#3[%-%#+' >?#'B-*.'7$á#&*W'&"'#&4B.'73-7*-' #D3#'-$$8'X&)L'.&".%[-&9'3"A'3)&'&X&"'m*%#&'7-$.&'#$'#D&'43W'43)V%"'7-3..%i&)Z' S5D3A%"V')&B)&.&"#.'&"#)$BL'>'A3)8&)'%.'D%VD&)'&"#)$BLUZ' Boosing 99 Boosing 100

26 ($A3V&'' Error Correcing Oupu Codes > 5*)'T'[%#.'a' > 5*)'P;'[%#.'' (ECOC) h 1 h 2 h 3 h 4 h 5 h 6 h 7 h 8 h 9 h 10 A B C <' R' <' Boosing 101 Boosing 102 ECOC h 1 h 2 h 3 h 4 h 5 h 6 h 7 h 8 h 9 h 10 A B C Références bibliographiques! Ä$['5D3B%)&'3"A'â$3X'N)&*"A' V%%(0+1/)_%>+&30%+()3+&)`.1%54#$,(' K`^'_)&..9':;P:'! Å"'3BB)&"A'P;'7-3..%i&*).'[%"3%)&.'! w$"'k&%)'3"a'o*""3)'wä#.7d'!"'%"#)$a*7@$"'#$'ä$$.@"v'3"a'h&x&)3v%"v' `"'`&I3+:'&)a':#>5'()%+)!3:$4+')a'35+4+1'SHd!`Y:R;;U9':;;Ü' D]BMzz666Z[$$.@"VZ$)VzB3B&).zK&%w3&;ÜZBAc'! Å"'73-7*-&''$ E S7U9'$ K S7U9'$ Y S7U9'$ Z S7U9'$ [ S7U9'$ M S7U9'$ \ S7U9'$ ] S7U9'$ F S7U9'$ EL S7U'! Å"'A+7$A&'^S7U'B3)'B-*.'B)$7D&'X$%.%"'z'3*'7$A3V&'A&'!9'Ä9'(9'v' Boosing 103! ãd%yy*3'ãd$*' Q+(',-.')!'#$%&(b)_%>+&30%+()3+&)`.1%54#$,(' (w('_)&..9':;p:'!!"#$%"&'($)"*+,$-.'&#'h3*)&"#'k%7-&#' `==5'+0((31')350@:4'.b)?%+:'=#()'#)3.1%54#$,'('?L)$--&.9':;P;' Boosing 104

27 Quels ingrédiens? PZ ($44&"#'$1'%?E/""%*#A&.'/'&WB&)#.'0'a' > å*c&.#y7&'m*c*"'%()%*+#a' Des méhodes d ensemble en apprenissage non supervisé? > å*c&.#y7&'m*c*"'-/"#)@"%''ac&wb&)#.'a' :Z ($44&"#'-&*)'3])%[*&)'*"')/3.$#S+X&"#*&--&4&"#U'a' ÜZ ($44&"#'?/,-3"%*#-&*)'3X%.'a' Boosing 105 Boosing 106 Références bibliographiques! Ä$['5D3B%)&'3"A'â$3X'N)&*"A' V%%(0+1/)_%>+&30%+()3+&)`.1%54#$,(' K`^'_)&..9':;P:' Références! w$"'k&%)'3"a'o*""3)'wä#.7d'!"'%"#)$a*7@$"'#$'ä$$.@"v'3"a'h&x&)3v%"v' `"'`&I3+:'&)a':#>5'()%+)!3:$4+')a'35+4+1'SHd!`Y:R;;U9':;;Ü' D]BMzz666Z[$$.@"VZ$)VzB3B&).zK&%w3&;ÜZBAc'! ãd%yy*3'ãd$*' Q+(',-.')!'#$%&(b)_%>+&30%+()3+&)`.1%54#$,(' (w('_)&..9':;p:'!!"#$%"&'($)"*+,$-.'&#'h3*)&"#'k%7-&#' `==5'+0((31')350@:4'.b)?%+:'=#()'#)3.1%54#$,'('?L)$--&.9':;P;' Boosing 107 Boosing 108

28 Ea de l ar (hisorique)! 1É3-%3"#CF<=' '%"#)$A*7&A'#D&$)&@73-'_!('4$A&-'c$)'.#*AL%"V'437D%"&'-&3)"%"V'! 1ç&3)".'é'É3-%3"#CFF=' '$B&"'B)$[-&4'$c'i"A%"V'3'[$$.@"V'3-V$)%#D4'! 157D3B%)&CFQ=9'1N)&*"ACQ;=' 'i).#'b$-l"$4%3-y@4&'[$$.@"v'3-v$)%#d4.'! 1\)*78&)9'57D3B%)&'é'5%43)A'CQ:=' 'i).#'&wb&)%4&"#.'*.%"v'[$$.@"v' Ea de l ar (suie)! 1N)&*"A'é'57D3B%)&'CQT=' > %"#)$A*7&A'!A3Ä$$.#'3-V$)%#D4' >.#)$"V'B)37@73-'3AX3"#3V&.'$X&)'B)&X%$*.'[$$.@"V'3-V$)%#D4.'! &WB&)%4&"#.'*.%"V'!A3Ä$$.#M' 1\)*78&)'é'($)#&.'CQT= ' '157D3B%)&'é'5%"V&)'CQF=' $"'é'()3X$"'CQR= ' '1K37-%"'é'ÅB%#è'CQE=' 1N)&*"A'é'57D3B%)&'CQR= ' '1Ä3*&)'é'ç$D3X%'CQE=' 1å*%"-3"'CQR= ' ' '157D6&"8'é'Ä&"V%$'CQF=' 1Ä)&%43"'CQR= ' '1 '\%&]&)%7DCQF='! 7$"@"*%"V'A&X&-$B4&"#'$c'#D&$)L'é'3-V$)%#D4.M' 157D3B%)&9N)&*"A9Ä3)#-&]'é'H&&'CQE='157D3B%)&'é'5%"V&)'CQF=' 1Ä)&%43"'CQE= ' ' '1K3.$"9'Ä3)#-&]'é'Ä3W#&)'CQF=' 1O)%X&'3"A'57D**)43".CQF='1N)%&A43"9'y3.@&'é'^%[.D%)3"%'CQF=' Boosing 109 Boosing 110