Subspace Modeling and Selection Subspace Modeling and Selection for - - PowerPoint PPT Presentation

Subspace Modeling and Selection Subspace Modeling and Selection for Noisy Speech Recognition for Noisy Speech Recognition

Chuan-Wei Ting

Advisor: Jen-Tzung Chien

De pa rtme nt o f Co mpute r Sc ie nc e a nd I nfo rma tio n E ng ine e ring Na tio na l Che ng K ung Unive rsity

2

Outline Outline

► I

ntro duc tio n

► No isy Spe e c h Re c o g nitio n ► Sub spa c e Mo de ling a nd Se le c tio n ► E

xpe rime nts

► Co nc lusio ns a nd F

uture Wo rks

3

Outline Outline

► Intr

• duc tion

► No isy Spe e c h Re c o g nitio n ► Sub spa c e Mo de ling a nd Se le c tio n ► E

xpe rime nts

► Co nc lusio ns a nd F

uture Wo rks

4

Motivation Motivation

► Why ASR pe rfo rma nc e de g ra de s

Ac o ustic mo de l

Dong Dong Dong Dong

Turn on the light OK!

I

nsuffic ie nt tra ining da ta

Unsuita b le mo de l

Misma tc h o f e nviro nme nts

5

Solutions for Noisy Speech Recognition Solutions for Noisy Speech Recognition

► Mo de l-b a se d c o mpe nsa tio n

MAP a da pta tio n ML

L R a da pta tio n

Spe c tra l sub tra c tio n SPL

I CE

Sig na l sub spa c e

► Spe e c h e nha nc e me nt

6

Outline Outline

► I

ntro duc tio n

► Noisy Speec h R

ec ognition

► Sub spa c e Mo de ling a nd Se le c tio n ► E

xpe rime nts

► Co nc lusio ns a nd F

uture Wo rks

7

Spectral Subtraction Spectral Subtraction

► T

his a ppro a c h is wide ly use d b e c a use o f its simplic ity a nd e a se o f imple me nta tio n.

► Ho w to e stima te c le a n spe e c h

E

stima te sho rt-te rm no ise spe c trum

Sub tra c t no ise spe c trum fro m no isy spe c trum

8

Flowchart of Spectral Subtraction Flowchart of Spectral Subtraction

9

Problems of Spectral Subtraction Problems of Spectral Subtraction

► Unde re stima tio n o r o ve re stima tio n o f no ise

le ve l

► Whe n no isy spe e c h spe c trum is ne a r the

e stima te d no ise spe c trum, spe c tra l sub tra c tio n ma y o b ta in ne g a tive va lue s a nd the se re sult in lo w-le ve l to ne s (“music

noise”) in e stima te d c le a n sig na l.

10

SPLICE SPLICE

► SPL

I CE (Ste re o -b a se d Pie c e wise L ine a r Co mpe nsa tio n fo r E nviro nme nts) is a te c hniq ue o f e stima ting the c e pstrum o f the c le a n spe e c h fro m the o b se rve d no isy spe e c h.

11

Assumptions for SPLICE Assumptions for SPLICE

► No isy spe e c h c e pstra l ve c to r ha s a

distrib utio n o f mixture o f Ga ussia ns

whe re

► T

he distrib utio n fo r c le a n ve c to r g ive n no isy spe e c h is Ga ussia n who se me a n ve c to r is a line a r tra nsfo rma tio n o f the no isy spe e c h ve c to r.

∑

=

s

s p s p p ) ( ) | ( ) ( z z

) , ; ( ) | (

s s

N s p Σ μ z z =

) , ; ( ) , | (

s s

N s p Γ r z y z y + =

correction vector expected variance

12

MMSE Speech Enhancement MMSE Speech Enhancement

► Assumptio ns o f SPL

I CE a re due to the inhe re nt simplic itie s in de riving a nd imple me nting MMSEe stima tio n.

► Be c a use , we ha ve

[ ] [ ]

∑

= =

s

s E s p E , | ) | ( | ˆ MMSE z y z z y y

y y

[ ]

s

s E r z z y

y

+ = , |

∑ ∑ ∑

+ = + =

s s s s s

s p s p s p r z z r z z z y ) | ( ) | ( ) | ( ˆ MMSE

13

Parameter Estimation Parameter Estimation

► I

f ste re o da ta is a va ila b le , the pa ra me te rs

• f c o nditio na l PDF

c a n b e tra ine d using ML c rite rio n

whe re

) , | ( s p z y

s

r

∑ ∑

− =

i i i i i i s

s p s p ) | ( ) )( | ( ˆ z z y z r

∑

=

s i i i

s p s p s p s p s p ) ( ) | ( ) ( ) | ( ) | ( z z z

14

Signal Subspace Approach Signal Subspace Approach

► Pro je c t no isy sig na l o nto two sub spa c e s

Sig na l Sub spa c e (c le a n spe e c h a nd no ise ) No ise Sub spa c e (o nly no ise )

► L

ine a r mo de l o f c le a n sig na l

whe re

y

SS SS

W x y ⋅ =

M K W M

SS SS

× × is 1 is x

15

Noisy Signal in Signal Subspace Noisy Signal in Signal Subspace

► L

ine a r mo de l o f no isy sig na l

Co rre spo nding c o va ria nc e ma trix is

SS SS SS SS

W n y n x z + = + ⋅ =

z

n ss x ss ss ss ss ss ss ss

] ) )( [( R W R W W W E R

T T z

+ = + ⋅ + ⋅ = n x n x

16

Clean Speech Estimation Clean Speech Estimation

► R

emoving the c o mpo ne nts in no ise

sub spa c e

► R

etaining the c o mpo ne nts in sig na l

sub spa c e

Rz W WT

=

K K M M K

Remove Noise Subspace Retain Speech in Signal Subspace

17

Perceptual Property on Human Auditory System Perceptual Property on Human Auditory System

► Huma n is mo re se nsitive to sig na l disto rtio n

c o mpa re d to re sidua l no ise

► Ma sking pro pe rty

Ce rta in a udib le so und b e c o me s ina udib le in the

pre se nc e o f a no the r so und

18

Noise Speech Noisy Speech Noisy Speech (Remove Silence) Distorted Noise Speech Distorted Noisy Speech (Remove Silence)

Demonstration Demonstration

19

Masking Property Masking Property

Clean Signal Noise Signal

20

Analysis of Estimated Signal Analysis of Estimated Signal

► E

stima tio n e rro r

► E

ne rg y o f e rro rs ˆ ( I)

SS

H H ε ε ε = − = − ⋅ + ⋅ = +

y n

y y y n

Signal distortion Residual noise

( )

2

[ ] tr [ ]

T T

E E ε ε ε ε ε = =

y y y y y

( )

2

[ ] tr [ ]

T T

E E ε ε ε ε ε = =

n n n n n

) ( ˆ

SS

H n y y + =

21

Filter Estimation Filter Estimation

► I

nc o rpo ra te d with pe rc e ptua l c rite rio n

Sub je c t to

► Sig na l sub spa c e filte r is o b ta ine d b y

2

min

H ε y 2 2

ε γσ ≤

n

1

( )

• pt

H R R R μ

−

= +

y y n

22

Implementation Implementation

► Re write the filte r using the de c o mpo sitio n

• f the c o va ria nc e ma trix

We c a n re pre se nt a s a

g a in func tio n

T

W W R

y y

Λ =

T T

• pt

W W R W W H

1 n

) (

−

+ Λ Λ = μ

y y

1 n

) (

−

+ Λ Λ W R W T μ

y y

μ

G

T

• pt

W G W H ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ =

μ

⎪ ⎩ ⎪ ⎨ ⎧ + = = + = K M k M k g

k y k y kk

,..., 1 , ,..., 2 , 1 ,

) ( ) (

μ λ λ

23

Outline Outline

► I

ntro duc tio n

► No isy Spe e c h Re c o g nitio n ► Subspac e Modeling and Selec tion ► E

xpe rime nts

► Co nc lusio ns a nd F

uture Wo rks

24

Factor Analysis Factor Analysis

► F

ind la te nt va ria b le s in o b se rve d da ta

Math Language Music Chemical Geography Memory Intellect Artistry

25

Factor Analysis Model Factor Analysis Model

► L

ine a r mo de l fo r no isy sig na l

► Assumptio ns o n F

A mo de l

r f z + Φ =

Factor loadings Common factors Specific factors

(diagonal) ] [ Ψ =

T

E rr

M T

E I ff = ] [

] [ =

T

E fr ] [ , ] [ , ] [ = = = z f r E E E

26

FA Solution Using PCA FA Solution Using PCA

► I

n this wo rk, we find F A so lutio n b y e ig e nde c o mpo sitio n o f c o va ria nc e ma trix.

whe re

] [

m p

W W W =

T T T T

W W W W W W R

m m m p 2 1 p 2 1 p p

Λ + Λ Λ = Λ = Ψ + ΦΦ =

z

] [ diag

m p

Λ Λ = Λ

27

FA Solution FA Solution

► F

• rmula te no isy sig na l in PCA fo rm, .

► T

he white ne d sa mple with c a n b e o b ta ine d b y a nd pa rtitio ne d b y .

► T

he c o mmo n fa c to r a nd spe c ific fa c to r c a n b e o b ta ine d fro m

c z

2 1

Λ = W c

K T

E I cc = ] [

z c

T

W

2 1 −

Λ =

T T T

] [

m p

c c c =

f

r

r f c c z + Φ = Λ + Λ =

m 2 1 m m p 2 1 p p

W W

28

Covariance Matrix of Noisy Signal Covariance Matrix of Noisy Signal

► Co mmo n fa c to rs

in F A c o me fro m the so urc e s o f c le a n sig na l a nd no ise sig na l , .

y

f

f

n

f

n y

f f f + =

r

y

r

n

r

n y

r r r + =

n y rn fn ry fy n n y y n n y y z

r f r f r f r f R R R R R R E R

T T T

+ = + Φ Φ + + Φ Φ = + Φ + + Φ + Φ + + Φ = ] ) )( [(

► Spe c ific fa c to rs

c a n b e e xpre sse d a s the sum o f re sidua l c le a n sig na l a nd re sidua l no ise , .

29

Analysis of Estimated Signal Analysis of Estimated Signal

► Using F

A, c le a n sig na l is e stima te d fro m princ ipa l sub spa c e a nd mino r sub spa c e

pn py p p p p p p p

) ( ˆ e e n y I y y e + = + − = − = H H

K

z z y y y

m p m p

ˆ ˆ ˆ H H + = + =

Signal Distortion Residual Noise

► F

• r the c a se o f princ ipa l sub spa c e , the

e stima tio n e rro r is g ive n b y

30

Filter Estimation Filter Estimation

► Sig na l e stima to r is de rive d b y

with a nd

{ } [ ] { }

2 pn p fn p p p fy p 2 pn 2 pn p 2 py p

tr ) ( ) ( tr ) ( ) , ( γσ μ γσ ε μ ε γ − Φ Φ + − Φ Φ − = − + =

T T T K T K

H R H H R H H L I I

p

ˆ H

2 pn 2 pn 2 py

: subject to min

p

γσ ε ε <

H

] ) ( ) [( tr ] [ tr

p fy p py py 2 py T K T K T

H R H E E I I e e − Φ Φ − = = ε ] [ tr ] [ tr

p fn p pn pn 2 pn T T T

H R H E Φ Φ = = e e ε

► T

he c o rre spo nding o b je c tive func tio n is

31

Optimal FA Filter Optimal FA Filter

► Diffe re ntia te the c rite rio n with re spe c t to

filte r a nd se t it to b e ze ro

p

H

1 fn p fy fy p

) )( ( ˆ

−

Φ Φ + Φ Φ Φ Φ =

T T T

R R R H μ

) , (

p p

p

= ∇ μ H L

H

1 rn m ry ry m

) ( ˆ

−

+ = R R R H μ

Optima l F

A filte r fo r pr

inc ipal sub spa c e

Simila rly, o ptima l filte r fo r minorsub spa c e c a n

b e o b ta ine d b y

32

Dimension Decision Approaches Dimension Decision Approaches

► Cumula te d e ig e nva lue s fo r c o va ria nc e

ma trix o r c o rre la tio n ma trix.

τ λ λ ≥

∑ ∑

= = K l l M k k 1 1

1 ≥

k

λ

► K

a ise r’ s rule :

33

Scree Scree Graph of Eigenvalues Graph of Eigenvalues

34

Motivation Motivation

► F

ixe d thre sho ld is no t suita b le fo r e a c h c o va ria nc e ma trix.

► No e xa c t c rite ria a re a va ila b le to de fine

the thre sho ld. T

• dyna mic a lly de c ide the thre sho ld, we

use hypothesis test theor

y to o b ta in the

• ptima l dime nsio n.

35

Optimal Subspace Dimension Optimal Subspace Dimension

: T he la st K-M e ig e nva lue s a re e q ua l

: At le a st two o f la st e ig e nva lue s a re diffe re nt

H

1

H

λ λ λ λ ˆ ...

2 1

= = = =

+ + K M M

( )

⎭ ⎬ ⎫ ⎩ ⎨ ⎧ Λ Λ − ⋅ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ Δ Λ Δ − ⋅ Λ =

− − + = − − = − − − −

∑ ∑

1 2 2 2 1 2 ) ( 1 1 2 2 2 2 ) (

tr 2 exp 1 ) 2 ( 2 1 exp ) 2 ( ) ( N M K H L

N K M k k M K N N i T i i N M K N

λ π π x x

( )

⎭ ⎬ ⎫ ⎩ ⎨ ⎧ Λ Λ − ⋅ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

− − + = − −

∏

1 2 2 2 1 2 ) ( 1

tr 2 exp ) 2 ( ) ( N H L

N K M k k M K N

λ π

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Λ Λ = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = Λ = =

+ 2 1 1 1 m m p

], [

K M M T

W W W W λ λ λ λ O O z x

36

( ) ( )

2 1 1 1 2 2 2 1 2 ) ( 1 2 2 2 1 2 ) ( 1 FA

1 tr 2 exp ) 2 ( tr 2 exp 1 ) 2 ( ) ( ) (

I

N M K K M k k K M k k N K M k k M K N N M K K M k k M K N

M K N N M K H L H L q ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ Λ Λ − ⋅ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ Λ Λ − ⋅ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = =

− + = + = − − + = − − − − − + = − −

∑ ∏ ∏ ∑

λ λ λ π λ π

2 ) ( 1 FA

~ log log ) ( log 2

I

ν

χ λ λ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − ⋅ = −

∑

+ = K M k k

M K N q

37

Motivation Motivation

► T

he o b je c tive o f F A mo de l is to use c o mmo n fa c to rs to de sc rib e a ll o ff-dia g o na l c o rre la tio ns in c o va ria nc e ma trix .

z

R

► I

f the numb e r o f se le c te d c o mmo n fa c to rs a re suffic ie nt, the re c o nstruc te d c o va ria nc e ma trix fro m mino r sub spa c e will b e dia g o na l.

L

e t b e the re c o nstruc te d c o va ria nc e ma trix fro m mino r sub spa c e , a nd de no te s the re c o nstruc te d re sidua l spe e c h ve c to r fro m mino r sub spa c e .

ry

R

y

r

38

Test of Covariance Matrix of Noise Test of Covariance Matrix of Noise

: Co va ria nc e ma trix o f no ise is dia g o na l : Co va ria nc e ma trix o f no ise is no t dia g o na l

H

1

H

j i j i H ≠ = for ) , ( :

2 ry 0 σ

⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − ⋅ − ⋅ = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ − − − ⋅ =

∑ ∑

= − − − = − − − N n T n n N NK N n n T n N NK

R R R R H L

1 y , y y , y 1 ry 2 ry 2 1 y , y 1 ry y , y 2 ry 2 1

) )( ( tr 2 1 exp ) 2 ( ) ( ) ( 2 1 exp ) 2 ( ) ( r r r r r r r r π π ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − ⋅ =

∑ ∏

= − = ⋅ − N n i n i n N K i K N

r r i i i i H L

i

1 2 , , y , , y 2 ry 2 1 2 ry 2

) ( tr ) , ( 2 1 exp ) , ( ) 2 ( ) ( σ σ π

39

2 ) ( FA

~ log

II

ν

χ ζ q −

( )

2 1 2 ry ry 2 ry 2 1 2 2 ry 2 1 FA

) , ( 2 1 exp ) 2 ( 2 1 exp ) , ( ) 2 ( ) ( ) (

II

N K i N NK K i N NK

i i R NK R NK i i H L H L q ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧− ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡− = =

∏ ∏

= − − = − −

σ π σ π

Signal Subspace Factor Analysis

Clear Signal Noisy Signal Basic Idea Project data onto two subspaces and reconstruct data from signal subspace Find common factors and specific factors to describe the observed data Decomposition Definition First M dimensions : signal & noise Last K-M dimensions : only noise First M dimensions : common factors Last K-M dimensions : specific factors Dimension Decision Rule

Eigenvalue > threshold Hypothesis Testing

Objective Function

, subject to: ,subject to:

Optimal Filter

y

r f y + Φ =

n y

r r f z + + Φ =

SS SS SS SS

W n y n x z + = + ⋅ =

2

min

H ε y 2 2

ε γσ ≤

n 2 2

ε γσ ≤

n

2

min

H ε y

1 fn p fy fy p

) )( ( ˆ

−

Φ Φ + Φ Φ Φ Φ =

T T T

R R R H μ

1 n)

(

−

+ = R R R H SS μ

y y

SS SS

W x y ⋅ =

1 rn m ry ry m

) ( ˆ

−

+ = R R R H μ

41

FA Modeling & Selection Flowchart FA Modeling & Selection Flowchart

Z

Y ˆ

42

Outline Outline

► I

ntro duc tio n

► No isy Spe e c h Re c o g nitio n ► Sub spa c e Mo de ling a nd Se le c tio n ► E

xper iments

► Co nc lusio ns a nd F

uture Wo rks

43

Experimental Setup Experimental Setup

► E

nha nc e me nt

40 sa mple po ints pe r fra me L

a g ra ng e multiplie r:

t-4 t-3 t-2 t-1 t t+1 t+2 t+3 t+4

7 , 3

m p

≤ ≤ ≤ ≤ μ μ

► Re c o g nitio n

Re c o g nize r: HT

K to o lkit

39-D MF

CC-b a se d fe a ture ve c to r

16 sta te s pe r wo rd 3 Ga ussia ns pe r sta te

44

Aurora2 Database Aurora2 Database

► T

his c o rpus c o nta ins the re c o rding s o f ma le a nd fe ma le US-Ame ric a n a dults spe a king se q ue nc e s

• f dig its.

A B C Subway Restaurant Babble Street Subway M Car Airport Street M Exhibition Station

► E

nviro nme nt de sc riptio ns

► T

ra ining mo de s

Cle a n tra ining Multi-c o nditio n tra ining

45

Subway_SNR0 7ZZZ9Z6A Subway_SNR0 7ZZZ9Z6A

Orig ina l no isy sig na l SS pro c e ssing F A pro c e ssing

46

Orig ina l no isy sig na l SS pro c e ssing F A pro c e ssing

47

OV OV-

• 10A cockpit recording

10A cockpit recording

(* http:// (* http://cslu.ece.ogi.edu/nsel/main.html cslu.ece.ogi.edu/nsel/main.html) )

Orig ina l no isy sig na l SS pro c e ssing F A pro c e ssing

48

Orig ina l no isy sig na l SS pro c e ssing F A pro c e ssing

49

Comparison with Fixed Dimensions Comparison with Fixed Dimensions

► Ca r_SNR-5 8169ZZ8 Signal Subspace Factor Analysis Original M=15 M=30 M=40 Spectrum Subtraction

50

SNR Evaluation SNR Evaluation

► Me a sure fo rmula :

2 1 1 10 2 1 1

( ) SNR=10log 100% ( ( ) ( ))

T K t t k T K t t t k

y k z k y k

= = = =

× −

∑ ∑ ∑ ∑

Enhanced signal E Enhanced signal nhanced signal Clean signal C Clean signal lean signal

51

Original SNR SNR of Perceptual FA Enhanced Signal

Subway Babble Car Exhibition Average Restaurant Street Airport Station Average 20 dB 18.30 18.30 18.40 18.30 18.33 18.39 18.39 18.43 18.39 18.40 15 dB 13.30 13.50 13.30 13.50 13.40 13.40 13.51 13.56 13.50 13.49 10 dB 8.84 8.87 8.95 8.91 8.89 8.91 8.92 8.95 8.91 8.92 5 dB 4.93 4.92 4.97 4.96 4.95 4.96 4.95 4.92 4.93 4.94 0 dB 0.06

• 0.04

0.00 0.07 0.02 0.06 0.07

• 0.05

0.23 0.08

• 5 dB
• 4.81
• 4.92
• 5.09
• 5.00
• 4.96
• 5.01
• 5.12
• 5.09
• 5.01
• 5.06

Average 6.77 6.77 6.76 6.79 6.77 6.79 6.79 6.79 6.83 6.80 A B

Aurora 2 original SNR

Subway Babble Car Exhibition Average Restaurant Street Airport Station Average 20 dB 19.80 19.00 20.10 19.80 19.68 18.73 19.44 19.11 18.81 19.02 15 dB 15.80 15.20 16.20 15.78 15.75 13.86 14.36 13.91 14.30 14.11 10 dB 11.10 10.20 12.60 11.06 11.24 9.84 10.70 10.01 10.97 10.38 5 dB 7.82 6.03 8.31 6.75 7.23 5.67 6.57 6.32 6.61 6.29 0 dB 4.45 3.05 4.95 4.17 4.16 2.55 3.05 2.91 3.17 2.92

• 5 dB

1.31 0.78 1.81 1.28 1.30 0.86 1.00 0.99 1.12 0.99 Average 10.05 9.04 10.66 9.81 9.89 8.59 9.19 8.88 9.16 8.95 A B

Aurora 2 SNR after enhanced

52

Aurora2 Evaluation Aurora2 Evaluation

(Clean Training) (Clean Training)

60 62 64 66 68 70 72 74 76 78 80 Subway Babble Car Exhibition Restaurant Street Airport Station SubwayM StreetM Baseline SS FAI FAII

Baseline SS FA I FA II Clean

99.1 99.3 99.3 99.3

20 dB

97.4 97.7 97.7 97.9

15 dB

93.8 94.5 94.7 94.9

10 dB

81.7 85.0 86.0 87.2

5 dB

56.8 64.0 66.3 70.1

0 dB

30.3 38.3 41.8 44.7

• 5 dB

15.2 19.8 21.3 22.7

Average

67.8 71.2 72.4 73.8

53

Aurora2 Evaluation Aurora2 Evaluation

(Multi (Multi-

• condition Training)

condition Training)

70 72 74 76 78 80 82 84 86 88 90 Subway Babble Car Exhibition Restaurant Street Airport Station SubwayM StreetM Baseline SS FAI FAII

Baseline SS FA I FA II Clean

98.9 98.9 99.0 99.0

20 dB

98.3 98.6 98.6 98.6

15 dB

97.6 98.0 98.0 98.1

10 dB

95.6 96.4 96.4 96.5

5 dB

88.3 90.9 91.3 91.5

0 dB

63.0 75.3 75.8 76.6

• 5 dB

27.5 45.1 45.7 46.5

Average

81.3 86.2 86.4 86.7

54

Outline Outline

► I

ntro duc tio n

► No isy Spe e c h Re c o g nitio n ► Sub spa c e Mo de ling a nd Se le c tio n ► E

xpe rime nts

► Conc lusions and F

utur e Wor ks

55

Conclusions Conclusions

► We intro duc e fa c to r a na lysis mo de l fo r

no isy spe e c h re c o g nitio n a nd it mo de ls the no isy sig na l mo re g e ne ra lly.

► Pe rc e ptua l c o nstra ints a re use d in princ ipa l

sub spa c e a nd mino r sub spa c e .

► Sub spa c e dime nsio n is de te rmine d b y two

diffe re nt hypo the sis te sting a ppro a c he s.

56

Future Works Future Works

► Spe e c h E

nha nc e me nt

F

ind a n o ptima l c rite rio n to dyna mic a lly c ho o se the L a g ra ng e multiplie r in e a c h fra me .

I

nc o rpo ra te mo re sig na l kno wle dg e , e .g . pha se info rma tio n to a c hie ve b e tte r pe rfo rma nc e .

E

stima te fa c to r lo a ding ma trix a nd c o mmo n fa c to rs using pro b a b ilistic F A mo de l.

► Spe e c h Re c o g nitio n

E

xplo it fa c to r a na lysis in a c o ustic mo de l.

57

References References

► T

. W. Ande rso n, “Asympto tic the o ry fo r princ ipa l c o mpo ne nt a na lysis”, Anna ls o f Ma the ma tic a l Sta tistic s, vo l. 34, pp.122- 148, 1963.

► A. Ba sile vsky, Sta tistic a l F

a c to r Ana lysis a nd Re la te d Me tho ds

• T

he o ry a nd Ap p lic a tio ns, Jo hn Wile y & So ns, 1994.

► S. F

. Bo ll, “Suppre ssio n o f a c o ustic no ise in spe e c h using spe c tra l sub tra c tio n”, I E E E T ra ns. Ac o ustic , Sp e e c h a nd Sig na l Pro c e ssing , vo l. 27, pp. 113–120, 1979.

► G. E

. P. Bo x, “A g e ne ra l distrib utio n the o ry fo r a c la ss o f like liho o d c rite ria ”, Bio me trika, vo l. 36, pp.317-346, 1949.

► J.-T

. Chie n a nd C.-W. T ing , “Spe a ke r ide ntific a tio n using pro b a b ilistic PCA mo de l se le c tio n”, I CSL P, vo l. 3, pp. 1785- 1788, 2004.

58

► Y. E

phra im a nd H. L . Va n T re e s, “A sig na l sub spa c e a ppro a c h fo r spe e c h e nha nc e me nt”, I E E E T ra ns. Sp e e c h a nd Audio Pro c e ssing , vo l. 3, no . 4, pp. 251-266, 1995.

► F

. Ja b lo un a nd B. Cha mpa g ne , “I nc o rpo ra ting the Huma n He a ring Pro pe rtie s in the Sig na l Sub spa c e Appro a c h fo r Spe e c h E nha nc e me nt,” I E E E T ra ns. o n Sp e e c h a nd Audio Pro c e ssing , Vo l. 11, NO. 6, NOVE MBE R 2003

► L

. K . Sa ul a nd M. G. Ra him, “Ma ximum like liho o d a nd minimum c la ssific a tio n e rro r fa c to r a na lysis fo r a uto ma tic spe e c h re c o g nitio n”, I E E E T ra ns. Sp e e c h a nd Audio Pro c e ssing , vo l. 8, no . 2, pp. 115-125, 2000.

► M. E

. T ipping a nd C. M. Bisho p, “Mixture s o f pro b a b ilistic princ ipa l c o mpo ne nt a na lyze rs”, Ne ura l Co mp uta tio n, vo l. 11,

• pp. 443-482, 1999.

59

Thank you for your attention! Thank you for your attention!