続分かりやすいパターン認識 4章後半(4.7以降)
26
続・わかりやすい パターン認 2015/2/10 続パタ 脇 宗也
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Transcript of 続分かりやすいパターン認識 4章後半(4.7以降)
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2015/2/10
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ltwitterIDwwacky n
l n1 n
l nKroneckerKhatri-RaoHadamard
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l
l n n[0,1] n()
p(|x(n))=Be(r+1, n-r+1)
n:r:
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00 Be(1,1)
11 Be(2,1)
22 Be(3,1)
=0.82 0.8
33 Be(4,1)
44 Be(5,1)
54 Be(5,2)
65 Be(6,2)
76 Be(7,2)
86 Be(7,3)
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(=0.8)
100 88
1000 805
10 7
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Be(3, 9)102
100 88
1000 805
107
Be(3, 9)
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l n u
n
l n() u u u
n
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l
p | x n( )( ) =P x n( ) |( )P x n( )( )
p ( )
= argmax
p | x n( )( ){ }
= argmax
P x n( ) |( )P x n( )( )
p ( )"#$
%$
&'$
($
= argmax
P x n( ) |( ) p ( ){ }= argmax
P x n( ) |( ){ }
P(x(n)|)x
p()=
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p | x n( )( ) =P x n( ) |( )P x n( )( )
p ( )
P(x(n)|)x
l
= argmax
p | x n( )( ){ }
= argmax
P x n( ) |( )P x n( )( )
p ( )"#$
%$
&'$
($
= argmax
P x n( ) |( ) p ( ){ }= argmax
P x n( ) |( ){ }
p()=
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4
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K
K
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P n;( ) = n!n1!!nm!
1n1!m
nm
p | x n( )( ) =P x n( ) |( )P x n( )( )
p ( ) =p ( )P x n( )( )
1n1!1
nm
x(n) P x n( ) |( ) =1n1!mnm x(n)
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P n;( ) = n!n1!!nm!
1n1!m
nm
p | x n( )( ) =P x n( ) |( )P x n( )( )
p ( ) =p ( )P x n( )( )
1n1!1
nm
x(n) P x n( ) |( ) =1n1!mnm x(n) (=)
-
P n;( ) = n!n1!!nm!
1n1!m
nm
p | x n( )( ) =P x n( ) |( )P x n( )( )
p ( ) =p ( )P x n( )( )
1n1!1
nm
x(n) P x n( ) |( ) =1n1!mnm x(n) (=)
1
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P n;( ) = n!n1!!nm!
1n1!m
nm
p | x n( )( ) =P x n( ) |( )P x n( )( )
p ( ) =p ( )P x n( )( )
1n1!1
nm
x(n) P x n( ) |( ) =1n1!mnm x(n)
1/Z2
0k1 P(|x(n))1
kk=1
m
=1
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P n;( ) = n!n1!!nm!
1n1!m
nm
x(n) P x n( ) |( ) =1n1!mnm x(n)
p | x n( )( ) =P x n( ) |( )P x n( )( )
p ( ) =p ( )P x n( )( )
1n1!1
nm =1Z2
1n1!1
nm
0k1 P(|x(n))1
kk=1
m
=1
1
Z2 = 1n1!1nmdDm
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p | x n( )( ) = 1Z21
n1!1nm
111!1
m1dDm =
1( )! m( ) 1,!,m( )
k = nk+1
p | x n( )( ) = n+m( ) n1 +1( )! nm +1( )1
n1!1nm
ak = n+mk=1
m
http://www.cis.nagasaki-u.ac.jp/~masada/DirDistNorm.pdf
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p | x n( )( ) = 1Z21
n1!1nm
111!1
m1dDm =
1( )! m( ) 1,!,m( )
k = nk+1
p | x n( )( ) = n+m( ) n1 +1( )! nm +1( )1
n1!1nm
ak = n+mk=1
m
k = nk+1
http://www.cis.nagasaki-u.ac.jp/~masada/DirDistNorm.pdf
Dir 1,!,m( ) = ( )
1( )! m( )1
11!1m1
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p | x n( )( ) = 1Z21
n1!1nm
111!1
m1dDm =
1( )! m( ) 1,!,m( )
k = nk+1
p | x n( )( ) = n+m( ) n1 +1( )! nm +1( )1
n1!1nm
ak = n+mk=1
m
Dir 1,!,m( ) = ( )
1( )! m( )1
11!1m1
k = nk+1
http://www.cis.nagasaki-u.ac.jp/~masada/DirDistNorm.pdf
m=2
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3 v1, v2, v3
1,4,5 3?
Dir 1,!,m( ) = ( )
1( )! m( )1
11!1m1 k = nk+1
nkvk
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9 n1=1, n2=3, n3=7
9 n1=7, n2=1, n3=1
0 9 n1=3, n2=3, n3=3
x(n)
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l
l
p | x n( )( ) =P x n( ) |( )P x n( )( )
p ( )
-
p | x n( )( ) =P x n( ) |( )P x n( )( )
p ( )
=1n1!1
nm
P x n( )( )
( ) 1( )! m( )
111!1
m1
=1
P x n( )( )
( ) 1( )! m( )
11+n11!1
m+nm1
=1Z3
11+n11!1
m+nm1
=Dir 1 + n1,!,m + nm( )
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==
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l
E [ ] = 1,!,k
,!,m
!
"#
$
%&
V [ ] = 1 1( ) 2 +1( )
,!,k k( ) 2 +1( )
,!,m m( ) 2 +1( )
!
"##
$
%&&
M [ ] = 1 1 m ,!,
k 1 m ,!,
m 1 m
!
"#
$
%&
http://d.hatena.ne.jp/a_bicky/20100402/1270139105
