!"#$%&'(!)*+
,-(.!)*+!)*+,/0&1%23%4, 567%
"4&8%9,:;!")<;=%9%(2>%2>?@*
;,+)A%$+%23.,+)=%B.?@*!)*/*C
DE&8 &2F;,+)%4% G;HI?;!+*J;
*+&K %L%23.9%1#$%*,$%#A*+#$%*7&J& /
D+)%#$%&'!)%*+!)$%1!"%$%)M
2>.%L2>-?B=4%2>&$9%2HB.!K&BN/DO?P2
2>-?B,H!Q%4N4!(="%>.?@*;?;!+R
)B.7& .23?8A C&8N#$%&'! H,-.
$&H%4 )!Q!S,-/TN&Q%,$%,+)U2
&&-*L?-*LS.)2&%B*L!)*LHV.=(S&%W
BXB%(&Q&2F=("%Y). &$&%E/W
&*3?+%4#$%&'AN)S&$1%-%7%=SA
-%/*39(%A#.!K&S)%23.%4#$%&'A
N!(#&$*E)+)%&7%23.?B%/*O?P2*+,Z9A%E
+[(\A.%E&9[-(//!)2I*%&]*E)+?B
%%/L& %%7^)%#$%&' %")#%N2%$." )%
+]%F#$%&'!,-%8%$%5K/
,-,]=&_9.%-5%4*J`aTbcd9?P
+]%F#$%&'/
e&B.%-5&2F6!>)H&$\`fgfM\Q.2>&K%E
%B)%J&S%;,$%1J%H=*J)-NUT+]%F#$%&'V.
&8%- HI,$%1&8 %8*$%&2F=%S/
c,$%1WSh.=%S %8 ; %7%&'.
)%"*9=S i&8=%S%+H/
HVTH: Nhan Thanh Nhã
_jRT+T]Fke$%'\`ffl\Tm
?=99_)9"ORTno`pRqDrs.
Thuật toán ID3
!"##
„…6!O*3%E?;!+&"*†
Thông tin
_jRT+T]Fke$%'\`ffl\Tm
- Minh họathuật toán với tập dữ liệu sau:
Bảng 1:
9
%2>
F
~%=8?
&
J=N%
=8]!(
23Q% 0$%#
p =4 k7% !3
t J 0- k7% 0- !3
d J !3
y =4 =4 0- !3
| J =4 !3
‡ J k7% !3
ˆ J 0- =4 0- !3
‰ =4 0- k7% 0- !3
Š =4 0- =4 0- !3
L=2>&=8 %8?@=9 !3,-&8‚%J
S%$
Bảng 2:
9
%2>
f‚*‚ ty ‚? pd [?
< |t ‚? d| ‚ [?
< dd f!‚ p| [?
f‚*‚ t‡ f!‚ pŒ `?
f‚*‚ ty ‚? ‰ [?
‚! tŠ f!‚ pt ‚ [?
‚! t‰ f!‚ pŠ [?
L=%%7?@&9&2F,9%,-&Q
,ŽS/
Bảng 4:%L=%%7+]%F#$%&']%F%!ƒ
*@%$
23%8 `)B !2 f% f:%E
* ,- ,- ,-
* 0- 0- ,- 0-
D 0- 0-
9 •% 0-
9 ,-
D 0- ,-
D O%
9
D
Bảng 5: +]%F#$%&'&2F?•%*+N!@#S9=.
!K&S/
e5‚)5Z%.B%O=?;!+)•.=% )%X%%(‘9=&2
*#S.#%4%2+#S.%%7 J$%2I&$
-%9#S9=/(."Q%NB%O;$%O
R
%]„c%†R t&%]&2F5‚)5Z%,’%‚%(‘#S
9=!RR%(yŒ%]*?23yŒ%]/ %8,2R?23yŒ%]
„yŒg†.%LyŒ%]%I!(„yŒ“†/
%] c e$%'
yŒg ?# Œ%% w‚
yŒ“ ?# Œ%% w‚
yŒg ?# Œ%% 0-
yŒ“ ?# Œ%% 0-
yŒg ?% Œ%%
yŒ“ ?% Œ%% w‚
C C C C C
yŒ“ ?% 0- ,- w‚
HVTH: Nhan Thanh Nhã Page:
_jRT+T]Fke$%'\`ffl\Tm
HVTH: Nhan Thanh Nhã Page:
_jRT+T]Fke$%'\`ffl\Tm
Tno`tRofuvTwx
3.1. $%&%' ( )*
T+M%F#$%&'!2H9!7%%1&Q&8#$%&'
F!i*&Q!Q* )1OF!i/
!@,$%F;%%1**+%S!E#$%&'/„0‹!‚?‚˜
c‚),†/
09+)+M%F#$%&'&2F&J57%=I‚!f/f%%%*
;Y)pŠˆŒ/T+M%F#$%&'=_)R
• \")J))9%O/
• 1YM%F#$%&'/
• )*+*3=%9 7%Q$/
• TS%&%‚9%2H%9*32>?•/
• 2F%='J)-4B%O*)-4?;!+/
+, /*$%&%' ( )
HVTH: Nhan Thanh Nhã Page:
_jRT+T]Fke$%'\`ffl\Tm
3.2. 0123!!4)%' ( )*
f%‚)
\B%O*7%(&'!i
\fR\%•!‚)‚%
f%‚)
2*7*#%'&"%2
kfR?%!k‚!%
•)%
\B%O7%!2F*=%OB!@
%57%
\kš›œšk TS&',$S%O
•\fR%‚%*‚•!\!
f%‚)
\B%O%O.9%.‘)
[k{c{c
\B%O%'%2>.B9.#
9
3.4. !<=!4)&>%' ( )*
%94?*J9%"A)%+M%F#$%&'„ccf
˜?‚%%‚)†*#+;Q!6?P9,9+)&%S
„?!†.?;!+„?%†*)-4„)?‚!†/*3;2>%$%,$+%
ccf2;2>6?P+%.&J#%N!8&2F9%
"&2F%$%,$2%$/2>6?P"=$% %8("94
Iccf/2>%$%,$=$%&2Fccf %8794/
HVTH: Nhan Thanh Nhã Page: 10
_jRT+T]Fke$%'\`ffl\Tm
+, ?*,%' ( )
9,’%E%)3 J2I&$9%"&%S.?;!+.*
)-4–*O?P2?+&_NHI?;!+#+/%O%+B
%S79,Y=8?•*6?P)-4%;4%1
)3/
W )%U-;V,92/
%*ccf6?P•)&8E™57%?;!+/2>?•&J?;!+&"
*„%†?••)*E?;!+&"„%%†%(•)/
`?+&_N7)%2H9%$E,9/9=8%2F
„†.&2F?•&8&S?+9&%2F2%!+.%E%C.2>?•
6?P%&8%9&!(9&%2F& „2?8.N)‚C†
`N !)%!S-;&.*("-+E
?SN „‚‚‚%†/D3@9%%8A-+.Q%
%8%-&FJccf6?PN !)-;&H/
)!S.=O),-!@!@N?7%. %8,8&$9!@
N,92%.9%$%='%:?•%@%$%()4!)/
$!%
HVTH: Nhan Thanh Nhã Page: 12
_jRT+T]Fke$%'\`ffl\Tm
%23.)9!)%_57%?;!+/0Y&_NA)4
7J9%8+)3/4 %8%8+94.&_%'/
B)%&2F5‚)5Z%2)%,Y)3/
&'%!()"*+
]F9,8%@+9%"2HI%%1.-;
&*-;%4=.%&2FJ,8%"%S,9/
%ccf%(*J=O)*=2>?•39%]FO)&8%@
%9!+/%ccf%@#H%4Z2>?•?•%&8%9
&!(9&S?+A9&%2F"%%9/
=/ <=:A2%*
ccf,-?•9?S?;!+%-%&2F%9#9%4?'
A9%]1/c;!+%2>&2F% )%X%.-&N%23,&2F6?P
=Iccf/i%2I7%!-*+&2F%@&=)9%O/2
&-!Q&2F%@+=%,,-%#9J-1-*+
&W:*+56!i%%$A2>/-%2>"?•)%+#%'
HI?;!+„c[f†/
• 0 ,Y%*+EE% )-4/
• f@%$%E&*3)-4A2>?•/
• •% @F7%.%OF;9)-4/
• f@%2H%9$„Ÿ†;)-4*2>?•/
• 2>?•, )%S)-4A(N/
• 9)-4%2>O%&2%O*J?;!+57%„%%†/
3!()"*+
• 9,9+)%"?;!+.%"&%S*%")-4
7)%2H9;+&889%"A)%ccf*9%2H%9
;Q*3/
• "?;!+7?;!+&85B?@.,8)%*U=?2žV)-4/
0$%57%A)-4!S&2F!2%HI?;!+( %8!)?;!+E
9)-4,9.?& %8%OFJ)-4!S*3/
HVTH: Nhan Thanh Nhã Page: 14
_jRT+T]Fke$%'\`ffl\Tm
• "&%S,-€Q2>?•6?P%%)-4.6?P
)%ccf +#&8#$%&')WQ2>?•5B?@)-4A
(N.;"A(N/
3.5. *
B#$%&'=_)=%"R9.Q%#$%&'.Q%=$
*,$%#/9!)%=$$!2FQ%)%Q%*,$%#/
Q%#$%&'!)%&8)%(B&2F=8?•=4*-*%L& }9%
57%J9/M9%LQ%#$%&'!)%$!2F,?ƒ}&2F2>
#$%&'5‚)5Z%/Q%=$!)%&8)%(B#$%&'&2F=8?•
=4%W*%L& }9%57%J9.)M9!)%=$
%85/0$%#!)%M$!2F*=$%S%)%&2>?
7%%(B#$%&'%L&8)&"&$&8)/
HVTH: Nhan Thanh Nhã Page: 15
œyR=$y
‰
p
t
y
y
|
‡
ˆ
\p
\t
\d
\y
\|
\‡
\ˆ
\‰
t
y
y
Š
pŒ
\Š
\pŒ
\pt
\pd
\py
pŒ
\p|
\p‡
pŒ
_jRT+T]Fke$%'\`ffl\Tm
?+%„%O%LQ%&$Q%+%S†/1!.Q%)?@&99%'A
HVTH: Nhan Thanh Nhã Page: 17
_jRT+T]Fke$%'\`ffl\Tm
%%O=9?@*!2F;*7:7%%(%];
*7%=4„)1&%E*O59%4}&2FN†
DO?PRQ%K5Z%=%9B!S5‚)% &H%‚¡1*3
%>%$%& ,-/`%E%cd}NB#$%&'%L%EF9*O?PR
E?;!+=_)py*O?P/M*O?P=8?•%4%S%>%$%
_)9%%O#.+%&.&‘)* –*&J )%%%OB
!S H‚¡„ .,-†/ 0-¡ƒ!,-&H%‚1*3%>%$%
& . ¡ƒ!2F!S/`9%'B!SI&B€ !S„ .,-†.W
% B!SA%E*O?PA,9+)%!3„!‚†/%O
H%‚¡W&2FN!%%O&O„%‚%%%=%‚†/
M%%O&J )%%E99%';S/%O#
=9%'„B).)2.X†.+%& =9%'„ .)9%.7)9†.&‘) 9
%'„.[†* 9%'„)S.h†/99%'O!,i+
„)=!†?•&8=8?•=%9/
L%E?;!+Ÿ!+.%E%cd}N)%B#$%&' ,
YB!S&Q&X9*O?P%%E.&_%>*N%%2H!.
}B!S&Q9*O?P,-)%%E/%B#$%&'*O?P
)%E%cd %8#S&2F!R
HVTH: Nhan Thanh Nhã Page: 18
_jRT+T]Fke$%'\`ffl\Tm
9Q%%B#$%&'=8?•)%@,8)%%()%%
%O& .)M9%' %8 A%%O& %2H1*3)%9AB/
9Q%!9%8+@B!SA9*O?P%9& .O!9%'A
%%OB!S/
f,%E%&K#S&2FB#$%&'.%4B}&2F6
?P&8B!S%7%9*O?P%8+„%‚†%%2H!/DB#$%
&'},-%&]&$,%%@+!S%E%cd%()%%E?;
e&H.cdP%7%J*%(‘N!@%X+)&8!)
AB/8&H."€)-%%E%?•&85B?@Be.*3
*+&')%)N%X+)%OF/\",$%$}%4=‚%
N!@Acd/
HVTH: Nhan Thanh Nhã Page: 20
_jRT+T]Fke$%'\`ffl\Tm
DO?P.K5‚)5Z%95B?@BeAcd%L*O?P%23&
[X%&"*3=&"&A_)py*O?PŸ!+.cdN%%O#
&8!)%%O6?P)N!@%%O)-%%",$%$/
X+)B%E*O?P2%7%=%(.*3"%6A
)MB*•&2F!+%,(=I%1%@AQ%=/
3.3. JGHI*
cd¤!%)„¤f‚%.!¤=‚!.{%%=%‚†
SQ%k%AB#$%&'
•%7%9*O?PA¤f‚%%•!3
k‚%B#$%&' Q%k%&2FX*3„ K†!3
•E%%O{%%=%‚!M
k‚% B #$% &' Q% k% &2F X *3 K !3 ¥
¦%¤!¤=‚!„f‚%†
{§%O%%E{%%=%‚ ,YB!SU%%7%V&*3
¤f‚%
%O,8)%Q%k%§{
•‚`9%' %8*A%%O{
[])%9B)3?23Q%k%.%2H1*3%2>FRU`9%'
A{!*V
…9&'¤f‚%*”•*O?P5¨5 ¤f‚%.5{”*—⊆
•„¤f‚%*!M†‚
HVTH: Nhan Thanh Nhã Page: 21
_jRT+T]Fke$%'\`ffl\Tm
S)%Q%!9*3K!3¥¦%¤!¤=‚!„¤f‚%†
€19*O?P%•)%!3%%/%B*•€ *O?P%
•)%!3.% B*•& %O%"7%/DE.&8N%%O,8)%
%8)%8JBABe.%")%Z&&8&%O%"7%A
9B*•.*N%%O,8)%%SJB*•%"7%
%%/cd6?P!i%$%%-%&8%@+&J/
3.4. >!T2>!T:Q1P<2@5U
e!„pЉd†!2>&"%(&J57%*+6?P!i%$%%-%&8
%S9B#$%&'*-%4A-!HI"%4=I&B/i
%$%%-%Af„pŠy‰†7,9+)‚%&8&%O%"7%
„2F!S!&%†A)%%EF/%%EF!%"7%$2%7%
9"%6A%EF&J%•)%!S.*,& % %EF &
HVTH: Nhan Thanh Nhã Page: 23
_jRT+T]Fke$%'\`ffl\Tm
%!%77%/%2>FA%E*O?P.%4%E*O?P!%"7%$
2%7%9*O?P&J •9%'B!S/
0%E*O?P!%"7%%4 %8 R%=$%XX*J9%'B!S
A)%*O?P%%E.% !2F%-%*J%E& !7%/0%E*O
?P &%7%.ƒ!!2F9*O?P •9%'B!S
)M!S!%2H&2H.%4,& %,-%8&9O59&2F)%*O?P
%8 9%'B!S4. ,9H.!2F%-%% &2F*J%E
!O%7%/DE.&J%))I&B!!)N%%O&8:
%8%E*O?P=&"%9%E*O?P%"7%%%/DE
%23$%.%" )%Z&&8&&%"7%A)%%EF.%L& )3 %8
9%E*O?P%4%%H/\",$%$}%4=-%1%O‚%A
)%%EF/
3.4.1. V <T=!4)G<T:;
09+)‚%A)%%Ef&2F&'ƒ%i%$%%-%!
!2F)&F9=O%"%$%&8)K %-%*J!3A)%%*(Q%
)%9•(%L%Ef/%2>F%2.)K &?X7%/
‚!i%$%%-%.)K &?%2!)K9˜!t=%%-&+
<
X
%9%]#9%H.$9*O?PA%Ef%JH!S.6
! 9%'B!S%4-%1‚%%]#9%!R
V <RCSW
3.4.2. 7F(11F(!&9!>1&" <&1(
œ%!)%&&&%A)%%E*O?P.=B>Q%}
&'ƒ)%Z&+7%B!S9*O?PA)%%%O/\Z&
N!!2F%-%%&2F. &H!!2F)‚%)&FB
=I*+B9*O?P%‚%%O/
%9O59H.`„f.{†A%%O{.%(%Ef.&2F&'
ƒ2R
HVTH: Nhan Thanh Nhã Page: 25