Распознавание речи. Курс лекций

. /Introduction.pdf1

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. /Introduction.ppt

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. /Lecture 1.pdf

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. /Lecture 2.ppt f =11.025 - 8 ( ) 5 - 4 5.51 , 4.14 , 2.76 , 1.38 0 16 - 8 ; 1024 - 512 - (11.025 )/N

100 f =1 1000 500 1 330 165 ~3

950900.04960930.11970960.14980990.859901020.1910011050.1510101080.0910201110.0210301140.001

910.04910.0011930.11930.013960.14960.021990.85990.931020.191020.141050.151050.0111080.091080.0031110.021110.00151140.0011140.0001

16384 f =11.025 < 1 ; t > 1

1024 f =11.025 ~ 11 ; t < 0.1

;

-

M+1. 0 i > M. M / 2.

. /Lecture 3.ppt

100 - 10

, ITU. , . , , ITU, , ITL ( ). . IZCT, . 25 . 3 , , . .

; k=0, . . k; .

0, ,2,

900 ; 10 . 30 (300 ) 10 . 20 . 100 . , 50 . ~70% , 100 . , 30% . - , - , .

. /Lecture 4.ppt

1.

2.

3.

4.

5.

6.

7.

8.

. /Lecture_5_(CodeBook).pdf1

2

:

3

-

- - ( )

125 34 396 7 89 715 173 19

)(tS

1X 2X NX

1n 2n Nn

4

-

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-

:

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5

(. Data clustering) , () , , , , ( http://ru.wikipedia.org/wiki/)

cluster - , ,

6

1. :

-

-

2.

4. ( )

3.

-

-

7

dij 0 - dij = dji - dij + djk dik - dij 0, i j - dij = 0, i = j -

pn

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1

1

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=n

k

jk

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1

22 - - 2=p

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1

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- Manhattan ( - city-block ) - 1=p

( ) ( )jiTjiij XXSXXd = 12 -

8

X

Y ( ) ( )2 2d X Y= +

X

Yd X Y= +

Manhattan

9

Manhattan

P=3

10

( )lkXXij

XXdjl

ik

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= - (nearest neighbor)

( )lkXX

ij XXdjl

ik

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( )jiij CCd ,= - ()

ij

ij 1 2

11

( agglomero , )

1. .

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( dendron- )

1

2

3

4

5

6

7

C1 C2 C3 C4 C5 C6

12

- (K-mean)

1. . () - iC

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ji

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1

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1( ) ( 1)

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( )

13

ART - Adaptive Resonance Theory( )

- MAX ,

1. , , : .

1X1 1C X=

2. :

( )min ,m i kkd d X C=2.1. ( )

2.2. md , mC

( )1m m iC C X = +

1k iC X+ =

, K+1 iX

14

1

2

3

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3C

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.

0.1250.6330.471

0.282

iD

15

1. jX :

( )1

argmin ,j ii K

i d X C

=

2. jX :

jX i

125 34 396 7 89 715 173 19

1X 2X NX

1n 2n Nn

16

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1,2 11 == V 6.1,4 22 == V 6.0,6 33 == V0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1,2 11 == V 6.1,4 22 == V 6.0,6 33 == V

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1321 === CCC 2,1 231 === CCC 1,4,10 321 === CCC

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1321 === CCC 2,1 231 === CCC 1,4,10 321 === CCC1321 === CCC 2,1 231 === CCC 1,4,10 321 === CCC

( )=

=

M

m jm

jmjmj

VXCXb1

2

2

exp)(

- jmV2jm -

. /Lecture_5_(CodeBook).ppt

- -

( )

(. Data clustering) , () , , , , ( http://ru.wikipedia.org/wiki/)cluster - , ,

1. :- - 2. 4. ( )3. - -

- -

Manhattan

( agglomero , ) 1. . 2. ( dendron- )

- (K-mean)3. 4. ( )

ART - Adaptive Resonance Theory ( )2. : 2.1. ( )

....0.1250.6330.4710.282

:

. /Lecture_6_(dynamical methods).pdf1

2

NP-

N , , .

.

:

1 2

34

3

32

4

54

(.. , )

:

3

NP-

1 2

34

3

32

4

54

1-2-3-4-1 3+4+4+5=16

1-3-2-4-1 2+4+3+5=141-2-4-3-1 3+3+4+2=12

1-3-4-2-1 2+4+3+3=121-4-2-3-1 5+3+4+2=141-4-3-2-1 5+4+4+3=16

N=4 - 6

4

1 2

34

3

32

4

54

NP-

5

423

5

1-2-3-4-5-1 3+4+4+2+5=18

N=5 ?

5

NP-

n n! 1 1 0.0000012 2 0.0000023 6 0.0000064 24 0.0000245 120 0.0001206 720 0.0007207 5040 0.0050408 40320 0.0403209 362880 0.362880

10 3628800 3.62880011 39916800 39.916800 0.712 479001600 479.001600 8.0 0.1313 6227020800 6227.020800 103.8 1.7314 87178291200 87178.291200 1453.0 24.22 115 1.30767E+12 1307674.368000 21794.6 363.24 1516 2.09228E+13 20922789.888000 348713.2 5811.89 242 0.717 3.55687E+14 355687428.096000 5928123.8 98802.06 4117 11.318 6.40237E+15 6402373705.728000 106706228.4 1778437.14 74102 203.0

N (N-1)! ! 1 2 3n n=

1/

6

:

, : , .

( ) ( )( )max 1i j jijA k A k d= +

( )iA k - k- i- jid - j- i-

k - ,i j -

7

1.

( ) ( )( )max 1i j jijA k A k d= +

( )0 0iA =( )0 0i =

2.

( ) ( )( ), argmax 1j jii k A k d = +

3.

( )argmaxN ii A N=

( ) ( )( )1 , 1i k i k k= + +

1, ,k N=

1, ,i M=

1, ,0k N=

1, ,i M= 1, ,j M=

8

0

1

2

1

2

1

2

1

2

0

1 2 3 4 50

3

3

4

3

5 6

3

4

2 5

3

2

2 3

1

1

0 1 2 3 4 51 0 3 3+6=9 8+5=13 13+3=16 16+1=172 0 3 3+5=8 8+4=12 13+2=15 15+1=16

k= 0 1 2 3 4 51 - 0 2 2 1 12 - 0 1 2 1 1

( )1A k( )2A k

k=

( )1,k( )2,k

9

0

1

2

1

2

1

2

1

2

0

1 2 3 4 50

3

3

4

3

5 6

3

4

2 5

3

2

2 3

1

1

2. 1 : max(3+4,3+6)=9 ( 2 )2. 2 : max(3+5,3+3)=8 ( 1 )

3. 1 : max(9+3,8+5)=13 ( 2 )3. 2 : max(9+2,8+4)=12 ( 2 )

4. 1 : max(13+3,12+3)=16 ( 1 )4. 2 : max(13+2,12+2)=15 ( 1 )

10

0 1 2 3 4 51 - - - - - 172 - - - - - 16

k= 0 1 2 3 4 51 - 0 2 2 1 12 - 0 1 2 1 1

( )1A k( )2A k

k=

( )1,k( )2,k , !

0

1

2

1

2

1

2

1

2

0

1 2 3 4 50

3

3

4

3

5 6

3

4

2 5

3

2

2 3

1

1

Max

11

1 3 5 2 1 1 7 4 3

3 5 2 1 1 7 4 3

7 2 5 2 1 1 7 4 3

1 3 5 2 1 1 7

1 3 2 1 7 4 3

?

: 1. 2. (.. )

12

1 3 5 2 1 1 7 4 3

1

3

2

1

7

4

3

0

2

3

6

0

1

2

2

0

1

4

2

1

0

4

2

1

2

4

3

2

1

1

2

5

1

0

2

0

2

3

6

0

1

2

0

2

3

6

0

1

2

6

4

3

0

6

5

4

3

1

0

3

3

2

1

2

0

1

4

2

1

0

2

M

N ,

13

1.

( ) ( )( )min 1i j jijA k A k d= +

( )0 0iA =( )0 0i =

2.

( ) ( )( ), argmin 1j jii k A k d = +

3.

( )argminN ii A N=

( ) ( )( )1 , 1i k i k k= + +

2, ,k N=

1, ,i M=

1, ,1k N=

, ,j k k= +

1, ,i M=

( )min iiP A N= -

14

1 3 5 2 1 1 7 4 3

3 5 2 1 1 7 4 3

7 2 5 2 1 1 7 4 3

1 3 5 2 1 1 7

1 3 2 1 7 4 3

1P

2P

3P

4P

argmin in P= -

15

1. .

2. .

. /Lecture_6_(dynamical methods).ppt

NP- (.. , ):

NP- N=4 - 6

332454 NP- 42351-2-3-4-5-13+4+4+2+5=18N=5 ?

NP- N (N-1)! 1/

1

nn!

110.000001

220.000002

360.000006

4240.000024

51200.000120

67200.000720

750400.005040

8403200.040320

93628800.362880

1036288003.628800

113991680039.9168000.7

12479001600479.0016008.00.13

1362270208006227.020800103.81.73

148717829120087178.2912001453.024.221

1513076743680001307674.36800021794.6363.2415

162092278988800020922789.888000348713.25811.892420.7

17355687428096000355687428.0960005928123.898802.06411711.3

186.402373705728E156402373705.728000106706228.41778437.1474102203.0

1

2

3

: , : , .

1. 2. 3.

k=

0123451033+6=98+5=1313+3=1616+1=172033+5=88+4=1213+2=1515+1=16

k=0123451 -022112- 01211

2. 1 : max(3+4,3+6)=9 ( 2 )2. 2 : max(3+5,3+3)=8 ( 1 )3. 1 : max(9+3,8+5)=13 ( 2 )3. 2 : max(9+2,8+4)=12 ( 2 )4. 1 : max(13+3,12+3)=16 ( 1 )4. 2 : max(13+2,12+2)=15 ( 1 )

k= , !Max

0123451-----172-----16

k=0123451 -022112- 01211

?: 1. 2. (.. )

1352117431321743 2M N ,

1. 2. 3. -

-

.2. .

. /Lecture_7 ( ).pdf1

(HMM Hidden Markov Models)

2

{ }MvvV ,,1 = - { }NSSS ,,1 = - { }TooO ,,1 = -

tq - , t

{ }i = - , .. )( 1 ii SqP ==

( )itjtij SqSqPa === 1 - iS jS( )jtktj SqvoPkb ===)( - kv jS

( ) ,, BA= -

3

ToooO ,,, 21 = - , T

{ }, ,V R G Y= - { }1, 2,3S = -

4

HMM

. ?

{ }TooO ,,1 = ( ) ,, BA=( )OP

. , ?

{ }TooO ,,1 = ( ) ,, BA=TqqqQ 21=

( )QOP ,{ }TooO ,,1 =

. , ?

{ }TooO ,,1 = ( ) ,, BA= ( )OP

1

2

3

5

1. .

- , t , t tooo 21 iS

)(it

( ) ittt SqoooPi == ,)( 21

1.

)()( 11 obi ii = Ni 1

)()()( 11

1 +=

+

= tjN

iijtt obaij

2. : 1,,2,1 = Tt

Nj 1

3. :

( ) =

=N

iT iOP

1

)(

6

1. .

( ) ,)( 21 itTttt SqoooPi == ++ -

1)( =iT

1.

Ni 1

2. : 1,,2,1 = TTt

Ni 1=

++=N

jttjijt jobai

111 )()()(

3.

( ) =

=N

iii iobOP

111 )()(

: 2TN : TTN2

7

2. (Viterbi Algorithm)( ) ,,max)( 21121

121

ttitqqq

t oooqqqSqPit

==

1.

)()( 11 obi ii =

0)(1 =i

Ni 1

2.

[ ]ijtNi

t aij )(maxarg)( 11

=

[ ] )()(max)( 11 tjijtNit obaij = Nj 1 Tt 2

3.

[ ])(max1

iP TNi = [ ])(maxarg

1iq T

NiT

=

4.

)( 11++

= ttt qq .1,,2,1 = TTt

-

8

3. - (Baum-Welsh)

( ) ,,),( 1 OSqSqPji jtitt === + -

( ) = =

++

++++ == N

i

N

jttjijt

ttjijtttjijtt

jobai

jobaiOP

jobaiji

1 111

1111

)()()(

)()()()()()(),(

=

=N

jtt jii

1

),()( - , t

OiS

=

1

1

)(T

tt i iS

=

1

1

),(T

tt ji iS jS

:

9

3. - (Baum-Welsh)

:

)( iti =

=

== 1

1

1

1

)(

),( T

tt

T

tt

ij

i

jia

=

==

= T

tt

T

kot

t

j

j

j

kb t

1

1

)(

)(

)(

:

- =1.

( ) ( ) OPOP >2. - , .


. /Lecture_7 ( ).ppt


HMM 1 2 3

1. .1. 3. :

1. .1. 3.

2. (Viterbi Algorithm)1. 2. 3. 4. -

3. - (Baum-Welsh) :

3. - (Baum-Welsh) :

. /Lecture_8 ( HMMs ).pdf1

2

1 2 3 4

44

3433

242322

14131211

00000

0

aaaaaaaaaa

A =

>=

=1011

jj

j

(Left-to-Right).

( )BA,=

,

3

Left-to-Right

1

2

3

4

5 6

>=

=1011

jj

j ( )BA,=

,

4

,

- , .

11a 22a 33a 44a 55a

12a 23a 34a 45a

)(1 xb )(2 xb )(3 xb )(4 xb )(5 xb

2

21

( )( ) expM

mj jm

m m

X Vb X C=

=

>=

=1011

jifjif

j

mV - ( )

m - jmC -

5

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1,2 11 == V 6.1,4 22 == V 6.0,6 33 == V0 1 2 3 4 5 6 7 8 9 10

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1,2 11 == V 6.1,4 22 == V 6.0,6 33 == V

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1321 === CCC 2,1 231 === CCC 1,4,10 321 === CCC

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1321 === CCC 2,1 231 === CCC 1,4,10 321 === CCC1321 === CCC 2,1 231 === CCC 1,4,10 321 === CCC

( )22

1

( ) expM

mj jm

m m

X Vb X C

=

=

- mV

m -

6

11a 22a

12a 23a11 , NN

a

iia ,1

1,1 iia

1 21N

11a 22a

12a 23a22 ,NN

a

iia ,1

1,1 iia

1 22N

11a 22a

12a 23aKK NN

a ,

iia ,1

1,1 iia

1 2KN

Word 1

Word 2

Word K

( )111 , BA=

( )222 , BA=

( )KKK BA ,=

11a 22a

12a 23a11 , NN

a

iia ,1

1,1 iia

1 21N

11a 22a

12a 23a11a 22a

12a 23a11 , NN

a

iia ,1

1,1 iia

1 21N

11a 22a

12a 23a22 ,NN

a

iia ,1

1,1 iia

1 22N

11a 22a

12a 23a11a 22a

12a 23a22 ,NN

a

iia ,1

1,1 iia

1 22N

11a 22a

12a 23aKK NN

a ,

iia ,1

1,1 iia

1 2KN

11a 22a

12a 23a11a 22a

12a 23aKK NN

a ,

iia ,1

1,1 iia

1 2KN

Word 1

Word 2

Word K

( )111 , BA=

( )222 , BA=

( )KKK BA ,=

( ), ,i i i iA B N =

7

112

11 1T

OOO

222

21 2T

OOO

KT

KKK

OOO 21

112

11 1T

VVV

222

21 2T

VVV

KT

KKK

VVV 21

Speaker 1

Speaker 2

Speaker K

.

112

11 1T

OOO

222

21 2T

OOO

KT

KKK

OOO 21

112

11 1T

VVV

222

21 2T

VVV

KT

KKK

VVV 21

Speaker 1

Speaker 2

Speaker K

.

112

11 1T

OOO

222

21 2T

OOO

KT

KKK

OOO 21

112

11 1T

OOO

222

21 2T

OOO

KT

KKK

OOO 21

112

11 1T

VVV

222

21 2T

VVV

KT

KKK

VVV 21

112

11 1T

VVV

222

21 2T

VVV

KT

KKK

VVV 21

Speaker 1

Speaker 2

Speaker K

.

( )

8

-> _ _ _ _ _ _

11a 22a 33a 44a

12a 23a 34a12,12a

12,11a11,11a

N = 2 x ( ).

11a 22a

12a 23a

11a 22a

12a 23a

11a 22a

12a 23a

_ _

_

_ _

11a 22a

12a 23a

11a 22a

12a 23a

11a 22a

12a 23a

_ _

_

_ _

9

ijiji

Na

N= -

ijN - tO iS 1+tO jS .

iN - tO iS .

iia jjaija

- , , 1i j i= +

10

( )22

1

( ) expM

mj jm

m m

X Vb X C

=

=

j - 1V - j 1r , 2V - j 2r , .., : k nr r M .

1

mjm M

ii

rCr

=

=

,

2m - , jS , mV .

11

( -)

:

=

== 1

1

1

1

)(

),( T

tt

T

tt

ij

i

jia

=

==

= T

tt

T

kot

t

j

j

j

kb t

1

1

)(

)(

)(

:

- =2.

( ) ( ) OPOP >1. - , .

12

1. : )(log)( tjtj obob , Nj 1 ,

ijij aa log , Ni 1 , Nj 1 . 2. .

)()( 11 obi i= , Ni 1 .

3. . [ ] )()(max)( 11 tjijtNit obaij ++= , Nj 1 , Tt 2 ,

4. .

[ ])(max1

iP TNi = -

Tooo 21 , ( )*1 ,, TqqQ = .

( )

ToooO ,,, 21 =

13

11a 22a

12a 23a11 ,NN

a

iia ,1

1,1 iia

1 21N

11a 22a

12a 23a22 ,NN

a

iia ,1

1,1 iia

1 22N

11a 22a

12a 23aKK NN

a ,

iia ,1

1,1 iia

1 2KN

Word 1

Word 2

Word K

( )111 , BA=

( )222 , BA=

( )KKK BA ,=

11a 22a

12a 23a11 ,NN

a

iia ,1

1,1 iia

1 21N

11a 22a

12a 23a11a 22a

12a 23a11 ,NN

a

iia ,1

1,1 iia

1 21N

11a 22a

12a 23a22 ,NN

a

iia ,1

1,1 iia

1 22N

11a 22a

12a 23a11a 22a

12a 23a22 ,NN

a

iia ,1

1,1 iia

1 22N

11a 22a

12a 23aKK NN

a ,

iia ,1

1,1 iia

1 2KN

11a 22a

12a 23a11a 22a

12a 23aKK NN

a ,

iia ,1

1,1 iia

1 2KN

Word 1

Word 2

Word K

( )111 , BA=

( )222 , BA=

( )KKK BA ,=

ToooO ,,, 21 =

( ) ( )*1 1P O W P O =

( ) ( )*2 2P O W P O =

( ) ( )*K KP O W P O =

.

.

.

14

( )iP O W - i-

( )iP W - () i-

( ) ( )arg max i ii

i P O W P W= -

. /Lecture_8 ( HMMs ).ppt

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PAGE 10

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. /.doc

1. , , .

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Documents

Распознавание речи. Курс лекций