I LITp*Pr*.----#t. :-.#- -@*'*-=a)
30
Trq;in+ NRs',\R^^s ( Lcoroi",g) = Bssdilen = Ge,,eco\ irhs.. r rF g*, gives u'gll <o tq \"rc-cegSg. Q. ll6en (;.n sJ proceJucer Hicrw,il e aa,ile-e-riterio^ p*,.fio, 5tor1 r.^r.s.tp : R"=.rlt vJ--.\f be- o- aa\ulUn *\Ut Us€- $codtenL desccnt o"r- flut) see.{oc \$. Le-t !g(\ = so\ulun *NI sec\cc oI i\e.tuh"o t, u\.e_re-.q.+ L\otelucr _.n d{rned. oa ukst {rr +\t $\t$=+*\9o !J(\rs) = +t- +btr-[r-+ r --: t orEnt* rrNrrc--ft ,^e ^r| "F ,-N"t'$lt"A . 5eg)->+--t'*tt-- ;- (ultg =o 1.. ^^N.1"*l+-d)- I_LITp*Pr*.----#t._:-.#- -@*'*-=a"")
Transcript of I LITp*Pr*.----#t. :-.#- -@*'*-=a)
Trq;in+ NRs',\R^^s ( Lcoroi",g)=
Bssdilen = Ge,,eco\ irhs.. r rF g*, gives u'gll <o
tq
\"rc-cegSg. Q.ll6en
(;.n sJ proceJucer Hicrw,il e aa,ile- e-riterio^ p*,.fio, 5tor1 r.^r.s.t p:
R"=.rlt vJ--.\f be- o- aa\ulUn *\Ut
Us€- $codtenL desccnt o"r- flut)
see.{oc \$.
Le-t !g(\ = so\ulun *NI sec\cc oI i\e.tuh"o t, u\.e_re-.q.+
L\otelucr _.n d{rned. oa ukst {rr +\t $\t$=+*\9o
!J(\rs) = +t- +btr-[r-+ r --: t orEnt*
rrNrrc--ft ,^ e ^r| "F ,-N"t'$lt"A .
5eg)->+--t'*tt-- ;- (ultg =o 1.. ^^N.1"*l+-d)-
I_LITp*Pr*.----#t._:-.#- -@*'*-=a"")
20
a
v]-Co =,2.(-$)_5e?
O
--Re9esf-=$c-st\ r^r+ Mz- [. +.\p"s .ta= -eqctilsmL.m,*-
Fac-hl.-iLif..+ur^ r 4(i) )o -r+-Ur{i}$<.o- Ihe"r ul(L+r)-=-rutt\*{tDg* - -
O$csurtse- - - !96*++-gIiL-
z. A!'snlr^tp CrtcceclxnRulc (gu..-""\."A Gnurr$+.rc")
2 l
g-fulb3.ds,c\€6€.- g,-fo. .nale-a\rqshoo *\ ; notr*oL b-U"\p.r$enc a
I s'ru*l- d(ttr) US t =a \ s'ar 5*[
I g4.I' lyd +0. $SJ'I$\ = x \ u't1 Ugl
--Jo-sllI-$S[ =-X, [ufiu g::If
qtrfr q0)Jfr .:J.l|r
--" 4 f,--\ +-oa.tlm-L1prg\ru
-- Ir\ tuir cose. \Lro) * g . ---
Notes:O ErrcA nxr'cr*"^t i\e*.te.t u^'trtl,*."-rtr$ugr-
F ne*4- S \**-61rg,rc-xu\u"^.
a
- F,. :gW.' F-.+:-s:.;r-i1:!H.F--:-::i.:i::-,--!W,.**"itqNmfXltII
q.0))o
22
I
g.^^d
qJ n*i' Lflgtl'
NoLl Nborre qrc- ""\+d
r$-orcI=-- g*Ilx-rorrs{ant
e.c $ ucu) \fo * +
ttqb, Con Tp\ o.,ttosik . so-c roi.r"^ultaneor-i[u ta o[
\p(L+r)= U.O+-!rct G
\t(t+Dr-= Sla}r!$I#.-
o
COMPUTER TECHNIOUES INIMAGE PATTERN RECOGNITIONAND ANALYSIS
PERCENROil ALGORITHH
A. tF THERE EI(ISTS A pROTOTypE <t FROM CT.ASS
sr sucH THAT
sTY ( l )
.a!
THEN INCREASE WEIGIT VECTOR. AT i-th STEP
g(i+l) = 3i) *"4$'
/( a. rF THERE Exrsrs A pRororypE
4f) rnorrr cr-Ass
sz suGH TIIAT
wTv(Z)J*II
TIIEN DECREASE WEIGHT VECTOR. AT i.th STEP
grtr*t) =:I( i )-o&f) )
WTIERE e Ei A CONSTAIYr :) Fizd Inci-e,*e,rt R.^Ie-
U SE RerLEcTFD ?ROrlT.I PES
D-14 @ copyrtght 1977, IalSc Asrociatcl
PERCEFT rcII ALGOR I THI'IEXAIIPLE . I
COMPUTER TECHNIQUES INITIAGE PATTERN RECOGNITIONAND ANALYSIS
U*! t
!2
23
Zaz .- t
Ztz -
5:
(h oc ̂ E rrraD sPcce)
PROTOTYPEB CI.ASS
I sz"
lSr
I 'sz
ts t
ls t
lsr
lSz
I
0
- l
I
- l
- l
- l
l - l 0 z
0 l z 0
- l t I 0
0 lz I
l 1 l0
-1 - t I 0
t I z I
- l - l I 0 -z- l
001201
I l - l - l 0 - l
4 0 LZ I I
- t I I I 0 I
-1 - t - l t 0 I
l - l - l - z - l - l
DESIRED CONDTTION
0
0
0
0
0
0
0
DESIRED CONDITION
0
0
0
0
0
0
0
cr.Ass
s2
sl
szst
s l
s l
s2
@ copyrtgbt l9?7, Iihegc Arsocilter
I
COMPUTER TECHNIOUES INITTAGE PATTERN RECOGilITIONANO ANALYSIS
O coprtgbt l9??, trm3c Acrociatcr
oq
PERCEPTROII ALGORITHIIIAGE PATTERN RECOGilITION I exnlPtj _ It{o ANALYSIS |
-'
,-\s) t
o((i)=Lw-. tierr.sctBo pnototvpes EgryjEcro& g'I
-' t A tb
. ..\\
: l I f - l - l l j 0 .#
ra , o o I z 0 I - ru t t \ 0 0 2 'L '3 0 . 0' - | - , _ . l
I l -t.- l o -l .!4cz) o o 3 l -3 I -5 irrGctcer.-r
4 0 L Z I I i ; . 1 | 2 O-3 0 \ , - - , 3 c . i s=c t- )dodt t.,ghfe
- l I I I O I i t ' t t 2 0 -3 0 / 2 ccscec t -i l
- l - l - l I o I , ' I I Z o-3 0 -4
l - l - l -Z - l - l - , , O O I t -3 t - l
t ll l
- l - t I o -Z- l l l l - l o - l -1 o 8t l
O O L 2 0 I 11 1- l 0 - l '1 0 -2
i : r - l I I -1 I -3
;r r z 0 0 o -4 o 4
I ' z o o o -{ o -2r ll l
I I I l -1 I - ll rl l' ,
O O O Z_4 Z -Zt ll l
l l
S(r\= S(o) + ! , - - - - l ;I
! ( z )=Ut r )+9 . - - - - -1
EXAIfLE - I I
o((d)= LrF
EI9EryJECTO& 3.I1ltr-
D-16
or
COMPUTER TECHNIOUES INIMAGE PATTERN RECOGNITIOIIAND ANALYSIS
PERCENROil ALGORITHI,I - III
REFLECTED PROTOTYPES WEICHT VECTOR Tt 9
- l - l I 0 -2 - l I - l -1 0 -5
I - t -1 '0 -5
l - l 0 2 -3
2 0 - l l -5
2 0 - l l -5
1 I O -? - -5
I I 0 Z -5
I
I
2
I
I
2
z
8
0
1
5
- l
z- l
- - r - - - "
- t - l _ l 0 -z - l zzz3
3
2
1
0- l 0 -6
0 - l 0 -6
0 0 z-6
I - t r -6
r -1 I -6
z 0 2-6
I - l 3 -6
I
I
zI
I
z3
8
0
-z
8
- t
0
-2
D-17 O copyrfgbt f9??, Inrgc Arsoclatcr
COMPUTER TECHNIQUES INIMAGE PATTERN RECOCNITIONAND ANALYSIS
- t - \ - l O -Z - l
WEIGHT VECTOR
2 0-Z l -7 2
z o-z l -7 z
z 0-z 1-? z
z o-z l -7 z
2 0-2 l -7 Z
I I - l 2 -7 3
I I - l z -? 3
1- l z -T
l -1 z -7
I - l z -7
2-2 l -?
z-2 l -?
2-2 l -7
z-2 l -?
ET.r,
3
3
3
zzzz
8
zI
3
- l
4
I
C
oR
Rr
cT
8
6
-z3
,l
,i
5
. - . . . . - . -
W (Fi,'',O =
2 Z-Z l -7 Z
z 2-z l -? z
z z-z l -7 2
PERCEPT.9.OI{ ALGORIT}III - IV
D-18 Tl9Zz, lmtgc Ascocistcc
23
C ue\e^ca ?..o+\"( -FixslXnce*e.\t Def,cr$son'
S* ,'issloss+"t + -g$-<o_-s----trU9+o
UIS+r) = U0r) +,v 3.n , r.''f,"nz rsrfu) Z* < .
Fired rnccermcnt . ot - ll \rr. L o$,-. Q,'lt\^.+ k*s .l te.ae.'.rf)
L ct tl U" a n^\rrL'cn
\\\{g*\= eb-l[' -< \\ u(B - "\\t- zac t F
t&t e- = bzc
t\ ruQ*D - * 01f< \\-ur-crl= e b1f-bz--
x$*r k @csedioos:
\ r,ret\ - L \\" <\ utc) --* Lft=kK-
a
At ^oru,rc-vol$p- k- ko (os s.o^er)---- RHS-
kof,= I\-urc.r-o-Nf
g-=_ tl upr - os fb'
TSle- ry,*- {r-cacres}nos rrf.\\ \rmnrsAc" "t_S"
L-Lt \$e=-9-*_:.F- L.*- "&\t$tf =---..u=I$tt' . -bz cl
LA\z.Fd{grs rL"tsn otrFGt coPlagr r'.e. rt^ r-..t Aiftic"l} t /sfq$a*
-o
rtLqo\
EE559a
Declslon Rule:
MULTICLASS PERCEPTRON
sr (x ) = t ( t ) t=
I f g r ( x ) > e r ( x ) f o r a l l j f i , a s s i g n x t o S . .
Alg.ol i thn I (given in class):
For each otoaoayp. y(t)
r f I ( i ) bS ' bu t mach ine ass lgns i t to s . :
n ( i ) ( t*r) = , ( i ) (k) + ry( i )
, ( j )1 r+ r ) = ' ( j ) (n l - o " ( i )
r ( l ) ( t * t ) - ! t ( g ) ( k ) a l l I i l , j
*trpd.lrs cll {'f. ctA3!3clf ..'
t rrd.{G , 31,31j1 --.
r f nachlne classl f t ." y( i ) correct ly, donft update
Next prototype
Algori thn 2 (correct version of Duda and l lart , p. L76)
For each ptoaoayp. a(t)
r f I (1 ) i s mlsc lass i f ied :
r ( i )1t+l) = w(1)(k) + uo"( i ) b= l t ' ' of d iscvi 'd 'er f c l rsscs
* ( j ) 1 t+r ) = w(J) (n ) - e " ( i ) a l l 3> r ( j ) ry ( i )> w( i ) ry ( i ) , i * i
r(,1) 1r+r) = r(-C) 16; a l - t t l , ( [ ) r " t l )< ! r ( i )T r (1 ) , [+ i
where b = no. of values of j for which r f f i )Tl( l )> w(1)TI(1)/ { \
I f L*^ ' l . s c lassL f ied cor rec t ly , donr t update .
Next PrototyPe
Both algorlthms are guaranteed to converge (for fixed increment). Algorithn 2
convergence ls proved in Duda and Hart pp. 174-177. Donrt use algori thn
on page 176 of Duda and tlart.
D-ltO
pa
..,- atal|l > S Flrtrt^r +
-.r f !l eenitt d+ llc erlrbqrr 1
25
t{u$,f\e C\sss R.cce?tscn ("c"r.+1pcs Ncit *P-ted)
I\ r.r.schrne- puts X? '**" si r,r\en i! aX""rd be- i*- \ r t*gn
ut.u= u$o,*JUnu6[*\= flo -( 5:u%ru=,uel; v[+$,r-
(tU.a*t nrprh-. r)
\)\\\ lccduce- q- a.ot o[ dxcCr*.ins^t \rurc]iots
-$*(fi[- "
h(u$ t ]i(S )e-Sk
ItuPL..ti+
c-s prc\i€- corsc-,sXunce--\"c- \rted-
n"esen*csH -ot>o* -
J ot*c rw.u.QJncless B\5nitv.n.s (=". U*irdo* -' Aflmittn^ Z\
Dt tt 5.lZ- ----I\ulllc\ess-(:oles\qbn_Pissesoa= Con-h{-.oauhl1uou"r (=\*tl
AU=+"I" Corestt'n- Gne e" "fl\ r
f\ .**clrrca*s s, i \" si .'*".f '
d=-lTuf,il - uH
cpmect ctas(o".*t lpsontee-
sc$\ Tt1b rf+ >u
26
a
! -u l l:l l'
--+-b- io- r.. .rno\in-+**"b\At
r(ur) )s--J:{S}:-.- -\'$_-S+>-r'- $g - e
z1
- 'Retslcqho
---
- \Aoug tt"diild-4-$$\orce- \*"" ui(k) tl\1et$eae uTelS;:b =e.-
---@onta-htr9tc*oAc--
-- ( <t =+ \D^drc-frls#sh$L-
--.{>f--+-crlc.G ce \ctaca'}l'dn
n^\t^Lx.. L^ s.-
--T{ b>o, ot ro , F"t-\}-\rilL-$u\bunt\t p\tef, SU>o- r€tio
s.-d ccirv.d^^*i.^,-!UsL calFa-- Ab'- INFrNrTult- -
Rcu)rt.s !{o\\^.Lq r
<t
o
_- R( z- ebss-R"{tcteA em\o\Fs- t{tn.rHruu,r }\enn Sqgore- Ecsrr GSe) :fcchniogo.
hohuc l**tItt esu\pes
l=
! u> b*-4
j -
t"'Vt uettr^r-
$SL s,\ulforu - *$=-!- [-- , r'r\^rrc- -]-=-e""&i*rrnc-{t
_ _ - - - - - _ - - T -
-yrs-- b- ,- .r r /.rT wf' .iT Iglur:$b- -+-- *-=ggJ b
v-r ) * r T v ^ i ^ . - l ^ r L
y-: g.s Ly'J . .flfi
,;";';:P-o-r1ff.ffi{il
z9
o
o
hlc* kAsllvAp ?nacpar^-np-
UU"n;re--$--r.us-u
30
Hirr''mninz--I rrr,c$.-b, t",'rh._\t-J_-b, n^\o1.ctt corstrarinL _b>e,_ _-
stqft ur\\" b> g_ y c'.\_sdd F.i|,.ue _dexrrests- rr$*^ rrgdsf\_L_
b$.D--bt++(Eg(k)l +g(C , or>s-
-__- _ Nn{cn on Ho - I(ASHV RP T
l. Crnurrtce il ;.. l\eS oce \rne"-\y .aq-^oHr
: e Ao\ step cath€r m^'rcp Ltrrrr\-hns \h.A. FfcoPlflo--- 3. \tfLla errtr'ce. b -s^ dr-S {rc
\"\Y. c\trss.B i,- e.,.\ LLe co}ie..r.
-- --- A\\er"o\rr" Fo<..^o\..\-an aI- \{o- KAsTIVAP
-Q(LL=Luttt i -bai ; 4)o
. - ---. r"itdf""{r,a>o ,.'r *=$'tt --rS(D>"c-
slror^,"hc^nve.gr u $^rtr #dshF il S - f^-hio dc$rr;I? {ntr,^pab}o il', -'. lq
3l
Exq-Fle l+ S=Q?) 'o1d.1z
s,^ A bo>= !-
=o\ulun $k\ \\r,b,6t \-incnr Lepst ry"
+lt \* o- $ven bt).
Exomro\eZ:
ll.tt cnrr-ha-on5 4- -tl{
Itu!
-TKts Xt.r-s hr-zal,^$ent-s.^$mcn\ohon \uI - coorrqrlu- xlo.rer -\ . ' \
,,sIS>\-
ei&\)o
\;a;6h\ blcl .^,rn"n-o&1}>o- -
sorrgdo|<-$t \\^,.(epa6M5 \gk) - So'f UUSg--r:fuhm-* $U + b-
-Doc\t@ - $dslsbsdGq-+cnty),
H t-kAsHsF- Conu\fince-_
l$--as^*gtes=- q*d
$-*u. a t
- ̂ -_e
_- +. Irs&t ) s nt\er :+ni\e 4 shF-- 8.1$ ..q.
U$.Trnour - Uoe e (uttt s.t.D
?sp^^A.rt-.t",ts, .
. is
33
vF.e€Abock n-chcru<_ f6 C"dr,.e- tsur4ph.on scCotrs_
\btsr rt updoLes- +* oS. gm\o\3cs-Ssclossl+\A { casecf\1 cbss,}reJ.)I
--_--r(- \s$ot\- ugdsles fts$ef e e.\a€-.
----lf- o((k\-=-AGD- {-r -cooVprqon ^u-.!-----k ,
NT^a4
5.1,-+-l3o:r-f t - - nlft)
o - Nontngqf,_Dlsstlru\rnqnL-tru -
nns^.c!
- __}r+^e-c. c\Lsrsln^ino\t $rs\W
-Qo.t r l\ec\slc F\gt\r-+Ylr-s-ilttr- to Por^t c\.rt )
,?Fl9'F"_4flPi'---', l,: .
Pcttcnt"l du,e' -b s.\\ b\k pt"\"\Fo oF "too, St!
Suel = -.!- H'*t-,$,)Mu -=
__a
'tY'[t,U) = horpirmusr l* t=.g1fG,U)*o f* 1i dsto{\t-F6" g-- -1f (trt\,,ahutA bc- .a-^"alb- r.--A -drspssz--ruro,ro+ortrcot\T
r^r'ilS-drsto^c4_dttr$L - __ * __fr 1f^(r,,9) = rf{t r$ th"cn- Fofitcrns- I+ "*d t.lr,d*n dqXcec- * n".^tlos\ -n pottfrr-$.
!
\r(rqu) =
A ?oln^tiol trncl"'or qlr.rr{s wis[s,b-aTor"ts z e\oss-es euott\-
-bcsisob\c- ptows\es oD fff I
l .
2,
3.
+.
2.
-3--.
_ .tf, it=o
t -
.t-; r'.'j
35
o-?=-Qless
/NloTESi- Gt*- Fsr"tr!
L ?erceptnon r-Rels{oJu^-t-e\e. _C.odt -:t^^\: Ftt*,J-+^--rnraltrc
3-_ Eac a.*o.tt-nuil.bgc
f,\or{- Nonlhcof Closs'Ptn.s-t-
Pr'scetDs.o-l-ineo-r--
(t-)---Htn. c\\\o.tco t-o Prrdloh#Dq olso enttr] Jg*'tc^sts_ ne,hhFr._
Sr- * ---CenhpoLq,rS z - Z I
se---t- -: ks{n f b Sp
*"StJr1a!1i.tej -Efl,-EKFqFr -,'r,oeffi'ffimlmn
t,.t
II
l r
_ ry.F-
36
I-st t = Extxzt -- - -r1(r{]I-TFi.
.\ f s,r{-. sodcn^a/\ ss$,o!$€-
Soint gsoUo\or\ dscr\ \,r.clu^
pt p(&) = d{,'x.r---r1(*\ ; p= scoL
-bteon oc ErcfechA \o[*c-
s = ETsl = So @dg-- --- +--,*+ -- Sf -=.-$ei p0,"4r=--rxnr)drrdryz ---drrat .-
{lr;et-)drL
A-tb'c"rce-lohio, tr- }\qtst--
v
3T;
*----fRL ----, r,$.cr-- f-.: t - - = - -
Dc&"iFrns:-
z-t\"adoG-\ler\rs -LoJ5 ece I
unrsccqlsLd.-+-E+{St=-e1 lr t el gJorsaf'L + e.{rr$}=sf^dTcnds\L + p((.t)-: p0r!+(g\---
o 0 , -lracotfo \otod 75 T".l.[^ d"qt -
l$otr"oL oc Gs*ssiq4-bcnstr\g --- 6i f* --. -*f
.,. tg)- eB^Y"f=lv"eyF.1-+.fu,*,g1
trthrc+ lEl - dotct"tnonbof _E _
-- " .; "r'(s*,=) - (g:l*jrg\(*-*>- tcl 5'(r-ee)e-sn"\-1
*3- t '
Ctl - Moholn nnhis t-I.\lonc z tcgrrn rE Ii ng
I
Gus\o.n dssst\io-c. \r.qe!,-rtn 4 : N n^ne..rr unl''ol q""d --
N[ U+t\ tl$\:$^^ce Ue\,LcS.2-
38
o atL-aq]s-- D,se-- ,*.*..e\"hd- t-,\* L+ i *-
-P00 -
rer.s -
Tten Ult - Amafr r e ^ T
= g-uDTe'eE'# A'gG-s*)
a
s.A X^-t":t"Art"**0.." 4 Egr -_
E*----I[e- co"rgcnen\s,4 U orr*-uNcosolqJp.t r
\o
€v:,S2asl
1*--( +=g$\E
C6i'= t
Cci =G. -) +i
. ). JKe- "{ U oce. \rncosrs\o\ed-e-^ J. \q.}. \nit rruis^ra-"
-crrsVsce* o r mb ?s"=.*ur'J .
---t[+)t+nttf
