The connected word recognition problem
Problem definition:

Given a fluently spoken sequence of words, how
can we determine the optimum match in terms
of a concatenation of word reference patterns?
To solve the connected word recognition problem, we
must resolve the following problems
connected word recognition
Test pattern sequence of vectors :
T  {t (1), t (2), , t ( M )}  {t (m)}mM1
The set of word reference patterns (templates or models) :
Ri  {ri (1), ri (2), , ri ( N i )} 1  i  V
N i is the duration of the i - th reference pattern
The problem is to find R* , the optimum sequence of word
reference patterns :
R *  {Rq*(1)  Rq*(2 )  Rq*(3)    Rq*( L ) }
connected word recognition
consider constructi ng an arbitrary " super reference" pattern
R s of the form :
R  Rq (1)  Rq ( 2)  Rq (3)    Rq ( L )   {r (n)}
s
s
Ns
n 1
in which N s is the total duration of the concatenat ed refernce
pattern R s
connected word recognition
The time aligned distance between R s and T is :
D( R s , T )  min
M
w( m )
s
d
(
t
(
m
),
r
( w(m)))

m 1
where d(.,.) is a local spectral distance measure and
w(.) is a warping function.
Optimize D :
D *  mins D( R s , T )
R

M
min
min
Lmin  L  L max q (1), q ( 2 ),, q ( L )
1 q ( i ) V
and
min
w( m )
R *  arg mins D( R s , T )
R
s
d
(
t
(
m
),
r
( w(m)))

m 1
connected word recognition
The required computatio n is :
 M .L N q (  ) 
M .L.N L
L
 1
V 
CL  
V (grid points)
3
3




e.g., M  300, L  7, N  40, and V  10,
then, C L  2.8  10 (grid points)
11
connected word recognition
The alternative algorithms:



Two-level dynamic programming approach
Level building approach
One-stage approach and subsequent
generalizations
Two-level dynamic programming algorithm
Two-level dynamic programming algorithm

D(v, b, e)  min
w( m )
e
 d (t (m), r (w(m)))
m b
v

~
D(b, e)  min [ D(v, b, e)]  best score
1 v V

~
N (b, e)  arg min [ D(v, b, e)]  best reference index
1 v V
Two-level dynamic programming algorithm
~
D (e)  min [ D(b, e)  D 1 (b  1)]
1b  e
Step 1, Initializa tion
D 0 (0)  0,
D  (0)  ,
1    Lmax
Step 2, Loop on e for   1
~
D 1 (e)  D(1, e), 2  e  M
Step 3, Resursion, Loop on e for   2,3, , Lmax
~
D 2 (e)  min [ D(b, e)  D1 (b  1)], 3  e  M
1b  e
~
D 3 (e)  min [ D(b, e)  D2 (b  1)], 4  e  M
1b  e
~
D  (e)  min [ D(b, e)  D 1 (b  1)],   1  e  M
1b  e
Step 4, Final Solution
D *  min [ D  ( M )]
1   Lmax
Two-level dynamic programming algorithm
Computation cost of the two-level DP algorithm is:
C 2 L  V . M . N (2 R  1) (grid points)
The required storage of the range reduced algorithm is:
S 2L  2M (2 R  1)
e.g., for M=300, N=40, V=10, R=5
C=1,320,000 grid points
And S=6600 locations for D(b,e)
1
1
D (m), m11 (1)  m  m12 (1)
2
1
D (m), m21 (1)  m  m22 (1)

D (m), mV 1 (1)  m  mV 2 (1).
V
1
m1 (1)  min [mv1 (1)]
1 v V
m2 (1)  min [mv 2 (1)]
1 v V
D (m)  min [ D (m)]
B

v

1 v V
N (m)  arg min [ D (m)]
B

1 v V
F (m)  F
B
N B ( m )
v

( m)
m1 (2)  min [mv1 (2)]
1 v V
m2 (2)  min [mv 2 (2)]
1 v V
D  min [ D (m)].
*
1   Lmax
B

R  RB  RA  RA  RB
*
L(m)  (m  1) / 2
U (m)  2(m  1)  1
 m 1

L(m)  max 
,2(m  M )   ()
 2

1


U (m)  min 2(m  1), (m  M   ( Lmax )
2


CLB  V . Lmax . N . M / 3
S LB  3M . Lmax
grid po int s
 D (m) 
 1  min 
.

m1 ( 1)mm2 ( 1)
m


B
 1
 D ( m)
1
S  arg
max
 M T . 1  m  S  

m1 (  1)  m  m2 (  1)
 m

B

D 1 (m)
2
2
S   arg
max
 M T . 1  m  S  .

m1 (  1)  m  m2 (  1)
 m

B
 1
1

c(m)  arg
D*  min
min
c ( m 1)   n  c ( m 1) 
min
1   Lmax M  END  m  M
[ D (m  1, n)]
v

[ DB (m)].