mediaLib Library Functions mlib_SignalDTWKVector_F32(3MLIB)
NAME
mlib_SignalDTWKVector_F32 - perform dynamic time warping for
K-best paths on vector data
SYNOPSIS
cc [ flag... ] file... -lmlib [ library... ]
#include
mlib_status mlib_SignalDTWKVector_F32(mlib_d64 *dist,
const mlib_f32 **dobs, mlib_s32 lobs, void *state);
DESCRIPTION
The mlib_SignalDTWKVector_F32() function performs dynamic
time warping for K-best paths on vector data.
Assume the reference data are r(y), y=1,2,...,N and the observed data are o(x), x=1,2,...,M the dynamic time warping is to find a mapping function (a path) p(i) = {px(i),py(i)}, i=1,2,...,Q with the minimum distance.In K-best paths case, K paths with the K minimum distances
are searched. The distance of a path is defined as Q dist = SUM d(r(py(i)),o(px(i))) * m(px(i),py(i)) i=1SunOS 5.11 Last change: 23 May 2007 1
mediaLib Library Functions mlib_SignalDTWKVector_F32(3MLIB)
where d(r,o) is the dissimilarity between data point/vector r and data point/vector o; m(x,y) is the path weighting coefficient associated with path point (x,y); N is the length of the reference data; M is the length of the observed data; Q is the length of the path. Using L1 norm (sum of absolute differences)L-1
d(r,o) = SUM |r(i) - o(i)|
i=0 Using L2 norm (Euclidean distance)L-1
d(r,o) = SQRT { SUM (r(i) - o(i))**2 }
i=0 where L is the length of each data vector. To scalar data where L=1, the two norms are the same.d(r,o) = |r - o| = SQRT {(r - o)**2 }
The constraints of dynamic time warping are: 1. Endpoint constraints px(1) = 1 1 < py(1) < 1 + delta and px(Q) = MN-delta < py(Q) < N
2. Monotonicity Conditions px(i) < px(i+1) py(i) < py(i+1) 3. Local Continuity ConstraintsSunOS 5.11 Last change: 23 May 2007 2
mediaLib Library Functions mlib_SignalDTWKVector_F32(3MLIB)
See Table 4.5 on page 211 in Rabiner and Juang's book. Itakura Type: py |*----*----*
|p4 |p1 |p0 | | |*----*----*
| |p2 | | | |*----*----*-- px
p3 Allowable paths arep1->p0 (1,0)
p2->p0 (1,1)
p3->p0 (1,2)
Consecutive (1,0)(1,0) is disallowed. So path p4-
>p1->p0 is disallowed.
4. Global Path ConstraintsDue to local continuity constraints, certain por-
tions of the (px,py) plane are excluded from the region the optimal warping path can traverse. This forms global path constraints. 5. Slope WeightingSee Equation 4.150-3 on page 216 in Rabiner and
Juang's book. A path in (px,py) plane can be represented in chain code. The value of the chain code is defined as following. ============================ shift ( x , y ) | chain code----------------------------
( 1 , 0 ) | 0 ( 0 , 1 ) | 1 ( 1 , 1 ) | 2 ( 2 , 1 ) | 3 ( 1 , 2 ) | 4 ( 3 , 1 ) | 5 ( 3 , 2 ) | 6 ( 1 , 3 ) | 7SunOS 5.11 Last change: 23 May 2007 3
mediaLib Library Functions mlib_SignalDTWKVector_F32(3MLIB)
( 2 , 3 ) | 8 ============================ py | * 8 7 * | * 4 * 6 | 1 2 3 5 |x--0--*--*-- px
where x marks the start point of a path segment, the numbers are the values of the chain code for the segment that ends at the point. In following example, the observed data with 11 data points are mapped into the reference data with 9 data points py |9 | * * * * * * * * * *-*
| /| * * * * * * * *-* * *
| / | * * * * * * * * * * * | /| * * * * *-* * * * * *
| / | * * * * * * * * * * * | | | * * * * * * * * * * * | / | * * * * * * * * * * * | / | * * * * * * * * * * * | / 1 | * * * * * * * * * * * |+------------------------ px
1 11 The chain code that represents the path is (2 2 2 1 2 0 2 2 0 2 0)SunOS 5.11 Last change: 23 May 2007 4
mediaLib Library Functions mlib_SignalDTWKVector_F32(3MLIB)
See Fundamentals of Speech Recognition by Lawrence Rabinerand Biing-Hwang Juang, Prentice Hall, 1993.
PARAMETERS
The function takes the following arguments:dist The distances of the K-best paths.
dobs The observed data array. lobs The length of the observed data array. state Pointer to the internal state structure.RETURN VALUES
The function returns MLIB_SUCCESS if successful. Otherwise
it returns MLIB_FAILURE.
ATTRIBUTES
See attributes(5) for descriptions of the following attri-
butes:____________________________________________________________
| ATTRIBUTE TYPE | ATTRIBUTE VALUE |
|_____________________________|_____________________________|
| Interface Stability | Committed ||_____________________________|_____________________________|
| MT-Level | MT-Safe |
|_____________________________|_____________________________|
SEE ALSO
mlib_SignalDTWKVectorInit_F32(3MLIB),
mlib_SignalDTWKVector_F32(3MLIB),
mlib_SignalDTWKVectorPath_F32(3MLIB),
mlib_SignalDTWKVectorFree_F32(3MLIB), attributes(5)
SunOS 5.11 Last change: 23 May 2007 5