Speaker verification using speaker- and test-dependent fast score normalization

(1)

Repositorio Institucional de la Universidad Autónoma de Madrid https://repositorio.uam.es

Esta es la versión de autor del artículo publicado en:

This is an author produced version of a paper published in:

Pattern Recognition Letters 28.1 (2007): 90 – 98 DOI: http://dx.doi.org/10.1016/j.patrec.2006.06.008

Copyright: © 2007 Elsevier

El acceso a la versión del editor puede requerir la suscripción del recurso

Access to the published version may require subscription

(2)

!"#$%#&'"()*+ ,- .''/$01-'(+

,"2- 3"//$ "4'1-/(+ ,5' 6'&1$3'7(

89:;< = <>?? @A BCD <EFCBG HIJ@?KKECF LIJM>NO PK@M?GB HJGEQ?@CE@B <M >?IEJIO

9RDBS TIBC@EK@J :JUBK V ;BGE?CQ? WWO XBU>MK D? XBCQJYGBC@JO

ZCER?IKEDBD 9MQJCJUB D? [BDIED P\]^_ `a [BDIEDO <>BEC

bcdefghe

i jklmn opkqm jkqrsntusvtkj opwmrm xkq oymszmq lmqt{psvtkj to yqmomjvm|} ~wm yqk

wtpwpkrymjosvmo vmov|mymj|mjvlsqtstntvotjs{m|pkwkqv kxtrykovkqo}~wm

jm yqkpm|qmomnmpvos oymszmq|mymj|mjvoomvkxtrykovkq rk|mno xqkr vwm {m|

pkwkqv otj s |tovsjpmsom| pqtvmqtkj} mnmpvtkj kx vwm opkwkqv to rs|m otj

s |tovsjpm rmsoqm som| kj s xsov syyqktrsvtkj kx vwm nnspzmtnmq

|tlmqmjpmxkq sootsj tvqm k|mno }~wm yqkykom| vmpwjtm wso mmj

psnnm| ~jkqrsj| kvymqxkqro ~jkqr tj pkryvsvtkjsnmptmjp}ymqtrmj

vsn qmonvo otj ~ ymszmq mpkjtvtkj lsnsvtkj yqkvkpkn snok owk s

ovsnm ymqxkqrsjpm tryqklmrmjv kx kq rmvwk| kj ovsj|sq| oymszmq qmpkjtvtkj

oovmro}

?V JIDK oymszmq lmqt{psvtkjopkqm jkqrsntusvtkj~jkqrnnspzmtnmq

(3)

!" #$% &'&

( ) ( * ) (+ ,-./001234

&5 ( 6 +. ) &7 3 3 8

&6 ( (&

6 39 6 )6 ( +. :2 8&& (

( +.6 ) ( &; & 2 8&& ( (

+.6 ) ( 3 4 ( . ( (

( ( + (+ & + ( 6 )

, < && 3 /00=; >6 & 3 ?@@@23 A( (8

B && ( ( +.63

C) (B (+ . & &7 +3

3 ( ) , D & C&(?@@/;>6 &?@@E2 & ,A8

3 ?@@@2 + ,( 3 ?@@@; >6 & 3

?@@@23 F.6 ( + )&

* ,G. 3 ?@@H23A( (B &'& 8

) ( ) +' 6 &

& ( & + ( &

I J

kqqmoykj|tj svwkq}~mn}K LMNOP NOQMPR xsKLMNOP NOQM

PUBEG BDDI?KK?K STUVWXY

Z

T[\]^_T[YW] `sjtmn srko

J

sovqk

a

_XVTUY

b VW

ZZ

Wc^_T[ YW] dntsj etmqqmuitnsq

a

\Tf_VUY

g

\UcTXWc^_T[YW]

dkstj kjusnmuk|qtmu

a ThVW

Z Y\

Zi W

g

T^_T[YW] dsltmq jqvmssqpts}

(4)

* 3

6 * (B (+ . & ( 8

( ) 8 & 8&& +.6 ,G. 3

?@@H23 ) ( ( 8& # %#$"# ( &

& $" ,( 3 ?@@@23A( 8&& (B

&. ) ( .6 ) 8

) 8 ( ) &

$#3 A( 6 . ( & ( &

( *& ( &. 3A ( . &6 &

( 6 ( 6 & ' 8

+ 6 ) ) ,+ &

>6 ?@@E234 ( . 6 ( ,>6 & 3?@@@;C

& >6 &?@@H2( + ( 6 . (+& (

& . ( 8 & 8&& +.3 4 (

(B ( . ( +..6) )

) ( ) &) 8 * 3A( .

) ( ( ) ) ) ( .8 .

, 2 &+ & . & ) A ( 8

3 A( & (B 6 + ( 6 6

(+& A . ( ( 56 ) (

63 9 (+ & ( + (B 8A 3

A( *& ) 3 4 & & ( &)8

3 >& & + &.& C ?3 C E

&. ( & 8 * (B3 4 C ( )

.8 . &+ & .

(5)

( &.& C H3 4CA ?@@H C > 8

+ ,C> 2 & C 3 6

& C 13

#%

4 ) 6 ( &

& #$

# & 6 .

( & %"$# %$ 3A( & .& ) )

( ) 3 A( )

) & & ( 6 &

#$3A( 6 . '& #$

# & #$

# &&

(( ( & ( +6 & .6 (

&+& 3

A( 6 (( ( 6 & .6 ( 6 &'

&3 4 ( +' & ( 6 ( && ((

( &6 ) ( ( & 3 A(

& & .6 ) ( ( &

& ( & &63 A( ( &

(( & . ( ' & & &3 A(

( 6 )&

( (

&6 ( ( & ( (6 & "%#$%3

4 +' 6 ( 6 ) +' :)

, & & ( &2 & )

, ) ( &23A(

(6)

( 6 ( >- < A + , 3 /0012 ((

. ( 6 ) 8& (3

A( ) * ) 6 8 &

8&& +.6 3 6 ( (

. + &7 * (B 6 , 3

3 F 3 , ?@@H223 A( &. ) ( ( ( ((

.& & ( & ) && . & ( 3

+( . & & ( & . )6& &

& & () ( ( '6

6 63

( ( 6 (+ 8 & 8&& 8

* .& ( ) 8&& &

8&& (B3 6 ) ( ( . ) &

( )( & * .& ( ) , > 8

. 3 /00?23 - ( 8 & 8 * (B 6 8

& . ( ) ( .& ( ) ( &. ) (

( & ( .& ) ( &

) &3 ( >6 & ,/0012 & 3 ,/0012

( * ) +& ( ( ( & )

* &7 ) +6 3

>6 8&& ( ( ( . & ( 8

(7)

>6 & ?@@H23 4 ( ( ( & (

& & * ( ( 3 )

& . ( ( & ( & 3

& ( & ( (

& ) ( 3

A( & 8A (B ) A . &

.& )( .8 .&+ , - +

& A( /00/2 ) ,>6 & 3 ?@@@23 (

( ) + :

4 6 ) ) 8&& ) ( + G8

& & , G23

4 & B && . & &3

A( + ( ) ( &.&

. & 8&& ( ) 8

* 3 A( & & < , ?@@E2 & (

. )6 & &* & & ,G 3 ?@@

?@@H23 ( 5 & ( )

6 . ) &

* 3 , ?@@2; * & G( ,?@@H2; &. &

* , ?@@H2( )5 &' & +

& 6 . & + ) ( & ( & 63

(8)

A * ,A 2 & ,( 3?@@@2 &

) 3

( (+ B ) ) +

& ) & & & (

,

2 .6 ( .+ ( ( & 3 A

( ) &

. (

,

2

,

23A( *& &

) :

,

2

,

2

,/2

( &

+6 ( & && &+ )

( &. 3 ?

( (B3

! ""# $%& % ' ( )**

A( .8 . , 2 &+ . ..6 &6 )8

,- + & A( /00/2 + 6 &'& .6

( ) :

+ ,- .

.

./

-0 1 2 - -

/ -

, ?2

(9)

-

/ -

. & 6 ) ( &7 .

..6&. 3A( ) B ? 6 .&

.6 8+ ( ( 8- 3 +

( (B 6 && (( 6 (

((8& &. (&& . 8

3

4 ( . 6 ( ( , < ?@@E2 ( B ?

. 8. && .6 ( &&

+

&

,

2 + +&& () * ( (

3 6 -

-

&

/ -

/

/ -

. &) &

( ( & & & &

/

(

&

/

8+ . ,(2 &:

/ ;

/

-

,

2 ;

/ -

,

/

0

,E2

9 & . ) &) - &

/ -

. . ( &. ) ( G + 8

6

D &

3 9( ) 6 ( -

&

/ -

& ( 3 + ( &+ (

&' ) ( &+ . - &

/

- ( ) 6:

j mjkn|o mv sn} tv to owkj vwsv vwto s|syvsvtkj opwmrm kvymqxkqro

kvwmq i syyqkspwmo wmqm mtwvo kq pklsqtsjpmo sqm snok tjlknlm|}

(10)

+ ,- .

.

/ -

0

+

-

.

/

/ -

2

-

/

/ -

,2

9 & (

%" # , - + & A( /00/2:

, H2

(

&

) 8+ .3

G6 B H ( ( (& & B . )(

&+ & ) :

2

-

/

/ -

2

-

/

/ -

/

2 -

-

/ -

,2

A() ( &+ . ( &8. &&

.6 :

A( ' ( &+ . ( ( ) . ( &)3

A( & ( (& ) ( &+& &+ )

( & 3 A( &+& &+ .

& ( ) ) , < ?@@E2:

2 -

-

/ -

/

?

&,

2

& ,

/

0

& ,

2

,

/

0

,

/

2

/

,

/

2

, 12

(11)

D & , >6 & 3 ?@@@23 A() ( ( + &

+ ( . ( & & ( ' (

( (& ) B &3 A( &+

( && ( ) :

+ ,- .

.

./ -0

+

,- .

.

./ -0

2 -

-

/ -

?

,

/

2

,

/

2

,=2

A(

+ ,- .

.

./

-0 B = ( + + :

&

A( B&

+ ,

- .

.

./ -0

( & ( ((B ) &+

( 8- ( &3

+ ,- .

.

./

-0. 8&& ) ( G

6 33

+ ,- .

.

./ -0

+ ,

/

- -0 ,02

'

4 < , ?@@E2 ( (

+ ,- .

.

./

-0 .6

( ( 8- & &+3

G 3 ,?@@2 ( ( + ,- .

.

./

-0 ((6 & (

( 6 ) ( &+ & + 8-

6 +

,- .

.

./

-0 + ,- .

.

./ -0

+ ,

/ - -03

" ' ( *%

A(

8

( .& . & &) (+ (

+ 6 ,

2 &

/

,

/

2 &8

'& ) :

(12)

+

,

/

2

,

/

2

,

/

2

,/@2

C . & ( + ,- .

.

./

-0 (& ) ( . &8

. ( ) ( & (

3

A( ) & ) + ,- .

.

./

-0 ( & & 8

) ( 6 . 6 & . &

33 &* ,G 3?@@2& , G 3?@@H2

& ( & * 3

$& ""

A( ) &+ B = &

8&& ( ) A +' 639 (+

& ( +(B 8A 3 ( ,

2(

) 8A . &.& ) :

" (

( &

) &+ ( & ) + (

6 + + ,--2

+ ,--2

B =3

(

9 ( 8 &

,( 2 ) ( &+

& . ) &

.

3

" ( $&

9 (

(13)

8A '6 ) & :

,

2

,

2

,//2

(

&

+6 ( & &&

&+ )

&. 3

8A (B & E3 4

( 8A . & 6 8 6

3 () & 6 6 8A ( ( +'

(

+

&& ( (&

( 8A ( 3 A( 6 (& ( . &

. ,

2 &

&. B //3

#"

4 ( ( ( ( ( ) 8A

( ) +' 6 )

( A (B3A( *& ) 3A( .8

+' 6 & .6 (& C 3/3 A(

& &. &.&

C

3?3 >

& C 3 E & . ( &+ + & 8

+ & & ) 56 3

(14)

%%# " %$#

A( 6 .& ( & & ( & +

..6 &. && .6 & , >6 &

3 ?@@@23 A( 6 & .6 ) ( )

8( & ) :

,

2 - , 2 - ,

2 ,/?2

( - , 2 & - ,

2 ( ..6 &6 ) ) (

& & G , >6 & 3 ?@@@2(( && 8

) & ( B ) ) + ) (

3

A & &+& 8 6

D & ((

. &.& ) :'

& ( )

6 ( + G &

& , G

2 ((

( ) &. (& 3 A 8

& ( & .6 & ) ( G (

&3 A( & .6 8 6 D & 3 3 (

G +& ' ( & , >6 &

3 , ?@@@223 4 & ) ( & (

8

* ,

2 ( ( . & ,<& 3 ?@@/; >6 & 3

?@@@23

& . ( B ) (

(15)

& ) ( ( +& & 3 A(

& (+ ( ) ?@ 3 & (6 +& /@ 3 .&8

( . ) & ( & )3 ( (

6 7 ( ) ) 6+ (8

(B (+ . & ( .& ) +8

3 -

* ,-2 ( . & & 8

+ ( & 3 A( >CA ' , 6 &

8

/002 ( . ) &3 6 ( 8 * 6

) , D & C&( ?@@/2 ( . & &

(+ . ( & 73

%%# " %$#

A( CF 6 .& ( (8

) ( ( ( 6 &.& . +3 + (

( 6 .& &+ C F

( ,CF

2 ,-. 3?@@H23 ) &

( ( .+ B & (6 &

. ( ) & ( . & &3

AFC CF

6 6 ) & ,9

& -.?@@@2) & .6 *& < CB

, <C2 &.& -. ,?@@?23 9 ( 8

,C 7 3 ?@@2 & + & ( (

73

A( 6 ( ) ( 63A &8

(16)

& ) . & &3 8A * ) &

) ( &+ & ) &

&.& C H3

#!% % $" #$" $

(+ . ) & ( + & .6

4CA ?@@H C > + ,C> 2 , 4CA C> ?@@H2

(( ( & ?@@ ,+ 3 ?@@H23 A(

&. & ( + . ) ( 4 > &.

,-. 3 ?@@23 A( B & & &7 8

( ,&

C

-<

32 &7 (& &

( ,. . ( & 3 2 & &7

, ( . C(

& 3 23 A( +8

&' ( ) & : /@ & / E & =

+ &; & ( ) & : /@ & / +8

&E ) + & ( & ( (

&3 ( + & ( + & ) H ( ?3 H

) ( + ) +3 ( ( ( 8

) . ( & ( 8& &'&3 <

. ) & ( 4CA ?@@H C> + D , 4CA C> ?@@H23 9

6 ( AFC & CF 6 .&

4CA ?@@H C> (( &.& C 3/3

G) ( + &+ ) ( 4CA ?@@ C>

&. & (( . ) 4 >3 A ) &

(17)

3?@@H23&& . & & && ) &+ , G

* ( 3; 6 . & &2 & ) (

&+ 3 4CA ?@@H C> & 4CA ?@@ C>

&. . & &3 A() ( A ( ) (

4CA ?@@ C> & ) ( & 3 A( .

) & ( ( ( A. /3 A & ( &

& & & & ) & ( 3

A( ) & / + &) & . ( /

& = + &) ,/8/ & =8/ & +623

%#%

" # $" #%

* ( ) & ( &+ 3 9

+6 ( . ) & & ) 8A & ( > , 23

G6 .+ ( ) A , 2 &

+ ) 8A , ?H

/H@23 9 .+ (

8A + ( 6 ) ) B >

, >2 6 ) H@ & 1H39 .+ ( (

> + .& ) H@3 H ( ( <

- , <- 2 &'& .6 4CA + ,+ 3

?@@H2 ) ( 3 <- ( B6 )

( & ( +' 6 & '&

& & & & + ( 6

4CA + 39 .+ & ) <- +

(18)

# $" #%

4 & ) 8A 4CA ?@@H

C

> 1H ) . (

6 ,

& CF

2 & & ,/8/ & =8/23 (

( ) ) (

& CF

6 . ( /8/ & =8/

& ( * A & 8A &3

( A ( . & ( . ) &

( ( ,A. /23 9 + 6 ) )

8A ( A ( =8/ & ( (

& ) ( /8/ & 3

A( 56 ) 8A . & .6 ( 8

) A & 8A :

,/E2

(

( && ( )

(B & >6 & 3 ,?@@@2 &

( B&

) + B =

3 <'

.:

/

,/2

m wslm pkjot|mqm| vwm qmov kx yqkpmootj vtrmo okqvtj vwm |tovsjpmormrkq

sppmoomvp} jmnttnm pkrysqm| vk

sj|

(19)

& ) ( ( + + /@

& @E3 A() ( ) ( *

(B &&

@

3

%# # $" #%

4 & 8A A

) .& ( . ( )( (( .

) & ( ( 3 .) 1H & 8A )

3 4 6 6 A 1H &

& 6 & ) ( ( ( 3 4 & ) 6

' + ( 6 /@ &7 &

) A ( & + ( 3A. ? ) (

6 ( ' > + & ( 8A

&3 ( ((& ( + <- + &

3 A. E ( ( ) ( CF 63 4 (

( ) + ((3

4 ( (+ & + (B ) *

6 8A (( ) 8&& A .6

( & ( & ) + ( 3A( .8

)( ( (B &(( .&

) ) ( .8 . &+ )

&3 ) 4CA ?@@H C > +

(20)

) 3

+ (+ .+& . + + &

) . ) & ( ( & ) + 3 4

( & & ( 8A ) A

56 ( + & ) .6 ) @3 (

&& .( &'& .6 4CA3

8A ) && .8

( ) '& ) & &7 & 3 (

. & & ( && 6( & (B .

& 6 &3 ( (

. &6 & ( . 6 3 A( ( & 6 .

) ) & +.6 ( .

, **8> &* 3 ?@@H23 ) +

( . 6 . & ) (6 .& ( 8

8 & 8&&( ( , *8

3?@@H23 &( )&7 &

( , &. & * ?@@H2 & ( ) ( 8

& ( ( & 6 &7 * ( (

A , * & G( ?@@H2 & ( &

) 3

'

A( & .6 (

C

(

6 ) C &

A( 6 & A4-?@@E8@0@=8-@?8@/ & A4-?@@E8@=E=?8-@H8

@/3 A( ( <3 >38-3 & 3 383 ( - & &

(21)

& (3

(

* 3 G( <3 ?@@H3 5 &' & 8

+34: D 3 ) 4(3 3 ?EE ?E3

* 3 G( <3 3 ?@@3 C & &

(+ &34:D 3 )4-C D3

3 @0 /?3

( >3 -6 3 6&8A 3 ?@@@3 C * )

8&& +' 63 <

C

D /@

? H3

G

3 G

3 G. 3 + 3 ?@@3 C &* 8

. 8 .& 8&+& & .

&& 3 4: D 3 ) 4-C D3 3 ?E?0 ?EE?3

G

3+3 G. 3?@@H3 & ) ) 5

& 3 4: D 3 ) 4(3 3 E@/ E@3

G. 3G 3 3 & -3 + 3

8-(

43 C3 A3 8 3 D +8<* <3

>6 &<33?@@H3 A A84&& CF' 3

& C D E@ H/3

-. 3 D3 /0013 C +' : 3 D & ) (

4 =H /E1 /?3

-.3D3 3--3

<393

3 3

D*6.

3 3 ?@@3A(

C> . & ( )

( & + 34:D 3 )&6633?0 E?3

(22)

3 4: D 3 ) 4-CCD3 3 // /3

-. 93 -. 3 >6 & <3 C 3 A 8-B

D3 ?@@H3 C F ( ) & 3

- C( & , 23

- + A3

3 A( 3 3 /00/3 ) 4) A( 63 96

43

<

3 3 ?@@E3 ) .8 . & ) &8

& & && + &34 CD /@

//H //=3

< && 3 93 3 D*6. 3 >6 & <3 3

/00=3 C( . & +: 6 )

) ( 4CA /00= + 3 4: D 3 )

4-C D3

<& >3 3 D3 3 C <3 3 ?@@/3 D -' 3 963

*8 3 8 3 **8> &* 3 ?@@H3 A

&& * (B & (

+' 34 A3 C6

& -6. - EH , E2

/= ?H3

>3 C3<>3 /00134 ( )

+' 3 D > /= ==/

===3

&.3 * 3?@@H3 & . .&

( & ) & 3 4:

D 3 ) 4(3 3 /0=H /0==3

**8> &*3 *83> 8- <38

3?@@H3 G6 6 )') & +& (

(23)

/@3

6 3 3 /003 >CA )(34 A8

C( & & D ? ,2 H1= H=03

3 < && 3 A3 & 3 D*6. 3 /0013

A( < A + ) & ) 3 4: D 3 )

(3 3 /=0H /=0=3

+3>63?@@E3A( & 66 )A8 34:D 3

) (3 3 ?@@0 ?@/?3

4CA ?@@H3 C + :

(: 33 + ( ?@@H &3(3

D 3

C

&(

C

3 ?@@/3 ) . +'8

34: D 3 ) &663 3 ?/E ?/=3

>6 & <3 3 /0013 - ) . & * ( & )

8&& +' 34: D 3 ) (3 3 0E 0

>6 & <3 3 ?@@E3 -( . +' + ) 8

3 4: D 3 ) 4-

CC

D3 3 HE H3

>6 &<33A3 3<>3G3?@@@3

C

+'

&&

&3 < C D /@ /0 /3

> . 3 3 < 3 -3 3 G3 3 C 3 3 /00?3

A( ) ( *& ) +' 3 4: D 3 )

4-C D3 3 H008@?3

C 7 3 -3 -. 93 ?@@3 -( )

C F

34: D 3 ) &663 3 H1 ?3

C <3 >6 & <3 3 ?@@H3

C

&+ ( )

A 8&& +' 3 4: D 3 ) 4-CCD3 3

1/ 13

(24)

( . 34: D 3 ) 4-C D3 3 0H 0=3

+ <3 3 D*6. 3 G 3 ?@@H3 A( 4CA

?@@ & A 4 + 3- C( &

, 23

F >3G G3 C&(C3 ?@@H3

& +.6 8

&& +' 3 4: D 3 ) 4(3 3 E//1 E/?@3

9 93 -.93 ?@@@3 C F

( ) +'8

& &' 34:D 3 )4 4 9 (

) C D 3 3 11H 1=3

(25)

?@@/ ) +&& D &

&& C3 C ?@@ ( (

+&& & &&( ( 6 & (

D(3 <3 & ( ) 3 (

) & ( & . 8

( ) & G6 )3 ( &

( &+ ) ( AFC8D

6 ) (

4CA ?@@ & ?@@H + 3 ( . ) ( * 8

) &668@ A( 4C- C > 9 ( 3

4 4 >> 84 > +& ( 3C3 & 8

?@@/) +&& D &

&&3C ?@@ ( (

+&& &

&&( ( 6 & (

D(3 <3 & & . 3 ( &

& & . 3 ( 8

) ( G D & FGD ?@@E & & ( &+ ) (

D

+' 6 & ?&

C

F- ?@@3 (.

) ( * ) &668@A( 4

C -

C

>

9 ( 3

4 8><>4 +& ( D(3<3&

/000 ) +&& D & &&3 6

D ) +&& & &&3 (

) & ( & . ( )

& 3 +& . )

C 48

C 9 & ( . +8( ) &668@ A( 4C- C

> 9 ( 3

(26)

/00 ) +&& D &

&&3 6

D ) +&& & &&3 ( 8

) & ) . & 6

3 (& +' &(

& ( (& &668@ A( 4C- C > 9 ( 3

(27)

Feature Extraction Test speech

signal

SPEAKER VERIFICATION

SYSTEM

Enrolled Models Identity claim

Similarity Score

Normalization DECISION

THRESHOLD

Accepted or Rejected Pre-

Processing

POOL OF USERS TRAINING DATA

CLAIMED USER

et} P}mjmqsn opwmrm xkq s ymszmq mqt{psvtkj ovmr tvwpkqm kqrsntusvtkj}

Test speech features

TEST NORMALIZATION (Tnorm) Cohort

Models

Non-Target scores

Mean and Variance Norm.

Normalized Score Background Data

Unnormalized score

Distribution Estimation

et}}~movjkqrsntusvtkj ~mpwjtm ~jkqr}

Test speech features

SPEAKER-DEPENDENT TEST-NORMALIZATION

(KL-Tnorm) Cohort

Models

Distance Computation

Test-

Normalization Normalized Score Background Data

Unnormalized score Target model

K-Nearest Models

et}M}~jkqr}

(28)

25 50 75 100 125 150 Total=N 12.4

12.6 12.8 13 13.2 13.4

25 50 75 100 125 150 Total=N 17

17.5 18 18.5 19

25 50 75 100 125 150 Total=N 7.4

7.5 7.6 7.7 7.8 7.9

25 50 75 100 125 150 Total=N 14

14.5 15 15.5 16

GMM 1c−1c SVM 1c−1c

GMM 8c−1c SVM 8c−1c

EER in (%) EER in (%)

et} N} ymqxkqrsjpm tj vwm |mlmnkyrmjv omv} ~wm jrmq kx rk|mno tj vwm

pkwkqv to qmyqmomjvm| tj vwm wkqtukjvsnsto xkq vwm nmxv sj| qtwv

oovmro sj| xkq PpPp y sj| pPp |kj pkj|tvtkjo}

(29)

25 50 75 100 125 150 Total=N 0.046

0.047 0.048 0.049 0.05

25 50 75 100 125 150 Total=N 0.066

0.068 0.07 0.072 0.074 0.076 0.078

25 50 75 100 125 150 Total=N 0.0308

0.031 0.0312 0.0314 0.0316 0.0318 0.032

25 50 75 100 125 150 Total=N 0.058

0.059 0.06 0.061 0.062

SVM 8c−1c GMM 8c−1c

SVM 1c−1c GMM 1c−1c

DCF DCF

et}}` J

e ymqxkqrsjpm so |m{jm| ~tjvwm |mlmnkyrmjv omv}~wm jrmq

kx rk|mno tj vwm pkwkqv to qmyqmomjvm| tj vwm wkqtukjvsnsto xkq vwm nmxv

sj| qtwv oovmro sj| xkq PpPp y sj| pPp |kj pkj|tvtkjo}

(30)

2 5 10 20 2

5 10 20

False Alarm probability (in %)

Miss probability (in %)

1c−1c No−Tnorm 1c−1c Tnorm

1c−1c: KL−Tnorm K=75 8c−1c No−Tnorm 8c−1c Tnorm 8c−1c KL−Tnorm K=75

GMM NIST 2005 SRE 40

40 1

,2

2 5 10 20

False Alarm probability (in %)

Miss probability (in %)

1c−1c No−Tnorm 1c−1c Tnorm 1c−1c KL−Tnorm K=75 8c−1c No−Tnorm 8c−1c Tnorm 8c−1c KL−Tnorm K=75

SVM NIST 2005 SRE 40

1 40

,.2

et} }~jkqr tjntj| ~ }s oovmr sj| oovmr}

(31)

~snm P

~kvsn jrmq kx rk|mno tj mspw ~jkqr pkwkqv

PpPp pPp

rsnm xmrsnm rsnm xmrsnm

tj pkwkqv N MQ PQ

~snm

~jkqr sj| ~jkqr tj oovmr otj Q rk|mno xkq kvw vmpwjtmo

~jkqr lsnmo sqm slmqsm| xqkr P qsj|kr omnmpvtkj vqtsno

PpPp pPp

Q rsnm xmrsnm rsnm xmrsnm

~jkqr il} PPPN PN QQ O Q

~jkqr PQ PM Q OP

il}ryqklmrmjv MN NQ

` J

e ~jkqr il} NP N M MM

` J

e ~jkqr MO NQ O MP

(32)

~jkqr sj| ~jkqr tj oovmr otj Q rk|mno xkq kvw vmpwjtmo

~jkqr lsnmo sqm slmqsm| xqkr P qsj|kr omnmpvtkj vqtsno

PpPp pPp

Q rsnm xmrsnm rsnm xmrsnm

~jkqr il} PO PO Q P P QO

~jkqr PQPO PQ Q PNP PN O

il}ryqklmrmjv PP Q M PNQ PMP

` J

e ~jkqr il} QM Q

` J

e ~jkqr M QM Q O