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Phương pháp học máy với Support vector machine trong nhận dạng chữ viết tay trực tuyến

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6Z=A()!=+E+0!> A+e!* 0=
Λ
∞→

$

U
T
N ?  N+, E (& L (C! E(S 
B

α

 C  =&. J(

α

4+,=+/&0!*/>=()?EB!N'>1+&E+)'-


0=
Λ
∞→

$
&

U
T
N ?  T*?9bW
N+,E (&L (C!E&QE(S1G.C =&.!+,'N+,!+!4(2&/>=()??(C!E(1+&-
 0=
Λ
∞→



U
T
N ?  T*?9)cW
=F1G.C =&./&Q+!*&'()!=+^/;+8&&+8&)%(.)1&8)&%
:)*&-&*/&Q+/+>/?+I&4+)'N+,?C=?(C!E(M&+!=A.!*4(2&=+1GQH&.!*$
Λ

+'$
Λ
&
=F/&>!*K&.=&C/J+,K+)!R2]+>/1&+2=?+I&J+,HE>E(S=!=+>!



3a

EG@.//&>!*N+,R+2=L+Q= 4,!
Λ
=FL)!*K&.=&C/K+)!R2]+>/1&+2=D/w
K&.=&C/J+,=+CK
Λ
!()!/>=(S=!EG@./
Λ
H(IH+,!*@!4
+O?3dVb+K! LJ+,(AJ!(!L 1E+0/G>!*? !EG@./=!/+2=1+&/
E+. NG@.!*N
Λ
E
!
E

3E

-+\/N+,R+e!*

+\/N+,RB* @> +.!R@Q -





EEN








Λ
UD444DT
1
  
=A!*E>J(2K+Q /wK&.=&C/J+,?C==+?12TN+,=+?12E+\/=AG!*/
=+CK
Λ
DEG@./*. N+,5RB)J+,1(0EG@./E(/+CK=A!*K+!1+&U4G,=!/+2=
=A()!/>=(S1&'A+=!/+2=/&Q+
Λ

• +\/
Λ
?N!
• +\/
UTN!N!UT 1+=







Λ














8'$?9\2N4$d61O,)
8E>/w/+!]+>/EB!RB/+\!=F 0=
Λ
∞→



U
T
N ? JF
Λ
=+O!*=(?G>/
N!N+,?G>/=+O!*A+2=/+C?T/+C?@!/+Q  U4



Λ




N!

SP!T



3%

?*\$,-7'75.</7<5'Q72'61O,4,.+$,B<'$,.'/,0'(
6ZK+!#4aE+0!> E(2!L+> ! (C?N
Λ
E
!
E

3E

!*l+N+,12L+Q!+O!*E+>!
12"3+'3//+>/K+!=GQ
!


3

4:+> ! (C?5RB)/&0!*HG.+J+,
J (C/E+>!12/+>/K+!=GQJ+,EG@./K+>=R (S&!G1+&-
5RB)9&B)1&1&8B
α


α∈Λ
&8))*;-&*&)))-
A).0+;.&=+9
!


3

B&8-()-A0+;.0&-)*G!&!)
&*&9

+;(&-
>=(S/>!G0!*H+0'
!


3

?+,J (C/E+>!12EG@./=+2=/+Q

KG@!*+>!
L)!*=G./ (C!EG@./4&'! ()!/w/+!=!=+. ?C=H+0'
!


3

?+,J (C/E+>!
12=G./ (C!EG@./=FE+0/>=(SL(2=N&+C!5RB)N+,

G.L+>/!+&* G0+N
Λ
E
!
E

3E

J+,5RB)N+,N
Λ
E
!
E

3E

K&.=&C/
J+,
Λ
N+I!H+0'E
!
E

3E

4,!5RB)=F/wK&.=&C/J+,
Λ
?+,=) D!()!
E+. NG@.!*5RB)EG@./H&,!*N+,?E+\/=AG!*/=+CK
Λ

+&E+)'N+,JH&.J(
5RB)-
34 5RB)/&Q+=+CK/+>/1 ()&K+g!*R+C/=A!*L)!** +!

-

( )





<−
=+=

=
01
01
0
1


(;-(




UTUTD
ααα


N+,P!4TF!#cVN+,JH&.J@> ?U
 
8'$?9]7<5Q72'61O,4,.+F%&B'(4$,;'(432'(
#

$&



3[

#4 5RB) /&Q+=+CK+,?-
α
?(
α

α



!
N+,L)!*]+>/
EB!Dx∞h3`i4
8E>/>=(SL(2=N&+C!5RB)/&Q+?C==+CK+,?N+,L)!*=A&,!*J@> 12
/ (&/&Q+=+CK+,?E>4+)'/!N+,G&E (S?/&Q+5RB)JF=A!*L * +Q 
M&'(2=J+2!E(!+C!H+.!*D/>!G0!*=AG@,!*@.K12/ (&/&Q++,?!+C!H+.!*N+,
A+2=N@>!=A!*L E>5RB)=FN+. A+2=!Q4
A@Q N+.  J@>  L+>  ! (C? 
Λ
TNUD @Q =A()! =+ E+0 !>  !(2&  ]+>/ EB! =F

0=
Λ
∞→



U
T
N ? 4GJ+C'5RB)]+>/EB!N+,E (&L (C!/&Q+1G.C =&./&Q+
!*&'()!=+^/;N+,JG,+!+!JG,+L)!*K&.=&C/J+,K+)!R2]+>/1&+2=/&Q+
=+CK?+I&4
?*]d'$U%&0'(Q%0$2.741061O,'(1E5:'4,S6
A!*?&./#4#E+0E(/+CKE(2!1G.C =&.E(&=(]+>/1&+2=-

00 >∀=






>−
Λ∈
∞→
εεαα
α
UUTUTT1&KN ?
B

K


+,@Q?&./#4%D#4[E+0E(/+CKE(2!E (&L (C!E(S1G.C =&.!+,'N+,JG,+!+!
JG,+L)!*K&.=&C/J+,K+)!R2]+>/1&+2=/&Q+=+CK?+I&4,!N+. J+2!E(N+,/>
=(S!> *FJ(E+. NG@.!*
ε
=A!*R (S&=G>/* @> +.!=A()!u
+K! LE+0E(]&+2=A+e!*-





4
1
2
η
ε
N!UTN! −+
=  T*?9))W
+'!> /+>/L+>/=FJ@> ]+>/1&+2=3cηR+2=E+g!*=G>/1+&N+,E&>!*






B
4
1
2

η
αα
N!UTN!
UTUT
−+
≤− 


3V

+'





B
4
1
2
η
αα
N!UTN!
UTUT
−+
+≤  T*?9)?W
P+2=E+g!*=G>/T*?9)?W/G>!*=QA+e!*=+'JF=F?
α
E(S1+ 12=G./
α

!Q
TL>=G./ (C!UD=+/>=(S=F?
α
E(S=S!*R()!J(2K+Q N+,!QDN&>/E>/+^//+^!N+,

α
/&0!*1(0!Q42+.!*=G>+ /&Q+=S!*R()!K+Q EG@./*. N+,5R)
=!EG@./M&+5RB)/&Q+=+CK
Λ
2+.!*=G>!+2=N+,1+ 12=G./!* (C?
HB &4+*. J(2K+Q /&Q+R+2=E+g!*=G>/=A()!N+,&)*(;-&./&Q+
α

P+2=E+g!*=G>/!+,'=(S (C!?C=12=!/+2=1+&-
3U (2&=+=F??C=+,?!+C!H+.!*=A!*?C==+CK+,?/>jL+Q!+O!*kM&+>
N@>!T
Λ
/-N@>!U=F?+\/H&,=+/>EG@./
B

α
!Q!G!*K+Q =A+Q* +>
N+,5R)N+. N@>!4
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