bab 1 pendahuluan baru jst
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JARINGAN SYARAF TIRUAN
BAB 1 PENDAHULUAN
Neuron McCulloch-Pi! "1#$%&
Neuron He'' "1#$#& BAB ( PERCEPTR)N
BAB % ADALINE
BAB $ BAC* PR)JECTI)N
JST DAN LOGIKA FUZZY ITF 306
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BAB 1 PENDAHULUAN Jaringan Syaraf Biologi
• )+, eriri +ri neuron-neuron "1.1( & +n /en0hu'un0 +n+rneuron "21.13& 4+n0 i!e'u !in+/!i! "synapse&
• Neuron eriri +ri !e5u6l+h enri7 !o6+ "cell body & +n +2on
• Denri 6eneri6+ !in4+l in/u 'eru/+ i6/ul! li!ri,
• Denri 6e6oi8,+!i !in4+l er!e'u +n ieru!,+n ,e !o6+
• So6+ 6en5u6l+h,+n !in4+l-!in4+l 4+n0 6+!u, +ri !e6u+
enri• Bil+ 5u6l+hn4+ 6ele'ihi !u+u '++! +6'+n0 "hre!hol&7 6+,+
!in4+l +,+n ieru!,+n ,e neuron l+in 6el+lui +2on
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Denri 9
In/u / i6oi8,+!ioleh /e6'o'o+n :6en5+i 9
p.wn =
• Neuron en0+n !+u in/u "!,+l+r&
Bi+! 'erh+r0+ 1en0+n/e6'o'o+n '
So6+ 9
Se6u+ in/u !eel+h /e6'o'o+n i5u6l+h,+n6en5+i 9 b pw pw pwn R R ,122,111,1 +++=
Sin+/!i! 9)u/u neuron 4+n0 +,+n ieru!,+n ,e
neuron l+in er0+nun0 /++ ;un0!i +,i
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0n,0
0n,1)n(f
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Neuron McCulloch-Pi!
• Neuron !eerh+n+ 4+n0 /er+6+ i/er,en+l,+n /++ 1#$%
• Di!e'u 5u0+ !e'+0+i Thre!hol Lo0ic Neuron "TLN&
/1 :1
∑ ; /(
/%
/$
:(
:%
:$
n +
• Se6u+ /e6'o'o+n /o!ii/ !+6+ ":1 = :(&
• Se6u+ /e6'o'o+n ne0+i/ !+6+ ":% = :$&
•Fun0!i +,i
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Conoh So+l 1>1Bu+ 6oel neuron McCulloch-Pi! unu, 6en4++,+n ;un0!i lo0i,+ AND
J+:+' 9 T+'el ,e'en+r+nn4+ AND ++l+h 9
p1 p2 a
. . .
. 1 .
1 . .
1 1 1
∑ ;
1
1
/1
/(
n +
p1 p2 n = p1 w1 +p2 w2 a = f(n)
. . .>1?.>1=. .
. 1 .>1?1>1=1 .
1 . 1>1?.>1=1 .
1 1 1>1?1>1=( 1
:1 = :( =1
Thre!hol = (
Neuron 4+n0 !e!u+i ++l+h "en0+nco'+-co'+&9
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Conoh So+l 1>(Fun0!i lo0i,+ )R en0+n u+ 6+!u,+n +,+n 6e6/un4+i ,elu+r+n . 5i,+ +nh+n4+ 5i,+ ,eu+ 6+!u,+nn4+ .> Bu+ 6oel neuron McCulloch-Pi! unu,6en4++,+n ;un0!i lo0i,+ )R J+:+' 9 T+'el ,e'en+r+nn4+ )R ++l+h 9
p1 p2 a
. . .
. 1 1
1 . 1
1 1 1
∑ ;
1
1
/1
/(
n +
p1 p2 n = p1 w1
+p2 w2
a = f(n)
. . .>1?.>1=. .
. 1 .>1?1>1=1 1
1 . 1>1?.>1=1 1
1 1 1>1?1>1=( 1
:1 = :( =1
Thre!hol = 1
Neuron 4+n0 !e!u+i ++l+h "en0+nco'+-co'+&9
$.
$*
1 p
w
b p
w
w p
1
2
1
2
12
+−=
−−=
$. /$* *
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Conoh So+l 1>%Bu+ 6oel neuron McCulloch-Pi! unu, 6en4++,+n ;un0!i lo0i,+ /1 ∧ ∼ /(
J+:+' 9 T+'el ,e'en+r+nn4+ /1 ∧ ∼ /( ++l+h 9
p1 p2 p2
p1 ∧ p2
. . 1 .
. 1 . .
1 . 1 1
1 1 . .
∑ ;
(
-1
/1
/(
n +
p1 p2 n = p1 w1 +p2 w2
a =f(n)
. . .>(?.>-1=. .
. 1 .>(?1>-1= - 1 .
1 . 1>(?.>-1=( 1
1 1 1>(?1>-1=1 .
:1 = (
:( = -1 Thre!hol = (
Neuron 4+n0 !e!u+i ++l+h "en0+nco'+-co'+&9
$ → ⇔ ∼ $ ∨
∼ 4$ → 5 / ∼ 4∼ $ ∨ 5 / $ ∧ ∼
$.
$*
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Conoh So+l 1>$Bu+ 6oel neuron McCulloch-Pi! unu, 6en4++,+n ;un0!i lo0i,+ @)R
J+:+' 9 T+'el ,e'en+r+nn4+ @)R ++l+h 9
p1 p2 XOR. . .
. 1 1
1 . 1
1 1 .
$.
$*
Tern4++ 5+rin0+n unu, 6en4++,+n ;un0!i lo0i,+ @)R i+, 'i!+ i'u+!e/eri conoh-conoh 4+n0 l+lu " i+, +/+ i/i!+h,+n oleh !e'u+h 0+ri!&>B+ru +/+ i/i!+h,+n en0+n u+ 'u+h 0+ri!7 !ehin00+ /erlu i0un+,+n!e'u+h l+4+r er!e6'un4i "hidden layer &
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∑
∑
;
∑
;
;
L+4+rer!e6'un4i
/1
/(
(
(
-1
-1
+
)R
1
1
1
(
/1 @)R /( ⇔ "/1 ∧ ∼ /(& ∨ " /( ∧ ∼ /1&
1 = "/1 ∧ ∼ /(& :1 =(7 :( = -17 hre!hol = (
( = "/( ∧ ∼ /1& :1 =-17 :( = (7 hre!hol
= (+ = /1 ∨ /( :1 =17 :( = 17 hre!hol= 1
p1 p2
p2
q1 = p1 ∧
p2
p1 q2 = p2 ∧
p1
q1 ∨ q2 = p1 XOR p2
. . 1 . 1 . .
. 1 . . 1 1 1
1 . 1 1 . . 1
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Soal La%ian **
Bua% 'o#!l 7,8ullo,-+i%%" un%u( '!nya%a(an fung"i logi(a NAND #!ngan #ua
'a"u(an &in!r
Soal La%ian *.
Bua% 'o#!l 7,8ullo,-+i%%" un%u( '!nya%a(an fung"i logi(a 9NO: #!ngan #ua
'a"u(an &in!r
p1 p2 NAND
. . 1
. 1 1
1 . 1
1 1 .
p1 p2 XNOR
. . 1
. 1 .
1 . .
1 1 1
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Soal La%ian **
Bua% 'o#!l 7,8ullo,-+i%%" un%u( '!nya%a(an fung"i logi(a NAND #!ngan #ua
'a"u(an &in!r
Ja;a& )
∑ ;
:1
:(
/1
/(
n +
'
*
p1 p2 NAND
. . 1
. 1 1
1 . 1
1 1 .
$.
$*
2 p3
4 p 12 +−= b4w3w
2w
b
3
4
w
w
2 p3
4
pw
b
pw
w
p
12
22
1
122
12
1
2
−==→=
=−−=−
+−=−−=
0n,1
0n,0)n(f a
%?.>$- =- 1
. 1 .>%?1>$- = - ( 1
1 . 1>%?.>$- =-% 1- =
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Soal La%ian *.
Bua% 'o#!l 7,8ullo,-+i%%" un%u( '!nya%a(an fung"i logi(a 9NO: #!ngan #ua
'a"u(an &in!r
Ja;a& )
p1 p2
p2
p1 ∨ p2
. . 1 1
. 1 . .
1 . 1 1
1 1 . 1
9NO: / ∼ 9O: / ∼
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p1 p2 n = p1 w1 +p2
w2
+ b
a = f(n)
. . .>-1?.>1- .7=-.7
1
. 1 .>-1?1>1- .7 =.7
.
1 . 1>-1?.>1- .7 =-17
1
1 1 1>-1?1>1- .7 =-.7
1
;. / *1 ;* / -*1 &/ - 0120n,1
0n,0)n(f a
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Neuron He''
• P++ 6oel neuron McCulloch-Pi! /e6'o'o+n +n'i+! h+ru! ienu,+n !ec+r+ co'+-co'+ ++u !ec+r+
+n+lii!• Di/erlu,+n !u+u c+r+6eo+ erenu unu,
6enenu,+n /e6'o'o+n +n 'i+!
• P++ 1#$# He'' 6e6/er,en+l,+n 6oel neuron
4+n0 +/+ 6enenu,+n /e6'o'or+n +n 'i+!!ec+r+ ier+i;
• Al0ori6+ /el+ih+n He'' en0+n Ini!i+li!+!i !e6u+ 'o'o = . +n ' = .
> Se 6+!u,+n /i = !i "i=17(7 R&
> Se ,elu+r+n + =
> Per'+i,i 'o'o 9 :i "'+ru& = :i "l+6+& ? ∆: en0+n ∆: = /i
> Per'+i,i 'i+! 9 '"'+ru& ='"l+6+& ? ∆ ' en0+n ∆' =
8 % S l * 2
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8on%o Soal *2
Bua% ?aringan @!&& un%u( '!nya%a(an fung"i logi(a AND ?i(a r!$r!"!n%a"i yang #i$a(ai
a#ala )
a5 7a"u(an #an (!luaran &in!r
&5 7a"u(an &in!r #an (!luaran &i$olar
,5 7a"u(an #an (!luaran &i$olar
Ja;a& )
a5
Masukan Target
/1 /( 1 . . 1 .
. 1 1 .
1 . 1 .
1 1 1 1
∑ ;
:1
:(
/1
/(
n +
*
&
+ola u&ungan 'a"u(an-%arg!% )
@ il l %i
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Masukan Target
Perubahanbbt
w = p! t
b = t
"bt baruwbaru = w#a$a
+ w
bbaru = b#a$a +
b
/1 /( 1 ∆:1 ∆:( ∆' :1 :( '
Ini!i+!i . . .
. . 1 . . . . . . .
. 1 1 . . . . . . .1 . 1 . . . . . . .
1 1 1 1 1 1 1 1 1 1
;* / *1 ;. / *1 & / *
p1 p2 n = p1 w1 +p2
w2+ b
a =f(n)
. . .>1?.>1?1 = 1 1
. 1 .>1?1>1?1= ( 1
1 . 1>1?.>1?1= ( 1
1 1 1>1?1>1?1= % 1
0n,0
0n,1)n(f
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&5
Masukan Target
/1 /( 1
. . 1 -1
. 1 1 -1
1 . 1 -1
1 1 1 1
+ola u&ungan 'a"u(an-%arg!% )
Masukan Target
Perubahanbbt
w = p! t
b = t
"bt baruwbaru = w#a$a
+ w
bbaru = b#a$a +
b
/1 /( 1 ∆:1 ∆:( ∆' :1 :( '
Ini!i+!i . . .
. . 1 -1 . . -1 . . -1
. 1 1 -1 . -1 -1 . -1 -(
1 . 1 -1 -1 . -1 -1 -1 -%-
@a"il $!la%ian )
;* / 01 ;. / 01 & / - .
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p1 p2 n = p1 w1 +p2
w2+ b
a =f(n)
. . .>.?.>. - ( = -( -1
. 1 .>.?1>. -( = - ( -1
1 . 1>.?.>.-( = - ( -1
1 1 1>.?1>. - (= -( -1
@a"il a(ir )
0n,10n,1)n(f
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Masukan Target
Perubahanbbt
w = p! t
b = t
"bt baruwbaru = w#a$a
+ w
bbaru = b#a$a +
b
/1 /( 1 ∆:1 ∆:( ∆' :1 :( '
Ini!i+!i . . .
-1 -1 1 -1 1 1 -1 1 1 -1
-1 1 1 -1 1 -1 -1 ( . -(1 -1 1 -1 -1 1 -1 1 1 -%
1 1 1 1 1 1 1 ( ( -(
;* / .1 ;. / .1 & / -.
p1 p2 n = p1 w1 +p2
w2+ b
a =f(n)
-1 -1 -1>(?-1>(-( = - - 1
-1 1 -1>(?1>(-(= - ( - 1
1 -1 1>(?-1>(-(= - ( - 1
1 1 1>(?1>(-(= ( 1
0n,1
0n,1)n(f
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La%ian Soal *3
Bua% ?aringan @!&& un%u( '!ng!nali $ola $a#a %a&!l #i &a;a ini
Ja;a& )
p1 p2 p% 1 t
-1 1 1 1 -1
1 -1 1 1 -11 1 -1 1 -1
1 1 1 1 1
Masukan Target Perubahan bbt
w = p! t b = t
"bt baru
wbaru = w#a$a + w
bbaru = b#a$a + b
/1
/(
/%
1 ∆:1
∆:(
∆:%
∆'
:1
:(
:%
'
Ini!i+li!+!i . . . .
-1 1 1 1 -1
1 -1 1 1 -1
1 1 -1 1 -1
1 1 1 1 1
@a"il $!la%ian )
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