# mlib_signaldtwkvectorpath_s16(3mlib) [opensolaris man page]

mlib_SignalDTWKVectorPath_S16(3MLIB) mediaLib Library Functions mlib_SignalDTWKVectorPath_S16(3MLIB)NAME

mlib_SignalDTWKVectorPath_S16, mlib_SignalDTWKVectorPath_F32 - return K-best path on vector dataSYNOPSIS

cc [ flag... ] file...[ library... ] #include <mlib.h> mlib_status mlib_SignalDTWKVectorPath_S16(mlib_s32 *path, mlib_s32 *lpath, mlib_s32 kpath, void *state); mlib_status mlib_SignalDTWKVectorPath_F32(mlib_s32 *path, mlib_s32 *lpath, mlib_s32 kpath, void *state);-lmlibDESCRIPTION

Each of these functions returns K-best path 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=1 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) = M N-delta <= py(Q) <= N 2. Monotonicity Conditions px(i) <= px(i+1) py(i) <= py(i+1) 3. Local Continuity Constraints See Table 4.5 on page 211 in Rabiner and Juang's book. Itakura Type: py | *----*----* |p4 |p1 |p0 | | | *----*----* | |p2 | | | | *----*----*-- px p3 Allowable paths are p1->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 Constraints Due to local continuity constraints, certain portions of the (px,py) plane are excluded from the region the optimal warping path can traverse. This forms global path constraints. 5. Slope Weighting See 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 ) | 7 ( 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) See Fundamentals of Speech Recognition by Lawrence Rabiner and Biing-Hwang Juang, Prentice Hall, 1993.----------------------------PARAMETERS

Each of the functions takes the following arguments: path The optimal path. lpath The length of the optimal path. kpath The path index, 0 <= kpath < kbest. state Pointer to the internal state structure.RETURN VALUES

Each of the functions returns MLIB_SUCCESS if successful. Otherwise it returns MLIB_FAILURE.ATTRIBUTES

See attributes(5) for descriptions of the following attributes: +-----------------------------+-----------------------------+ | ATTRIBUTE TYPE | ATTRIBUTE VALUE | +-----------------------------+-----------------------------+ |Interface Stability |Committed | +-----------------------------+-----------------------------+ |MT-Level |MT-Safe | +-----------------------------+-----------------------------+SEE ALSO

mlib_SignalDTWKScalarInit_S16(3MLIB), mlib_SignalDTWKVectorInit_F32(3MLIB), mlib_SignalDTWKScalar_S16(3MLIB), mlib_SignalDTWKVec- tor_F32(3MLIB), mlib_SignalDTWKScalarFree_S16(3MLIB), mlib_SignalDTWKScalarFree_F32(3MLIB), attributes(5)SunOS 5.1123 May 2007 mlib_SignalDTWKVectorPath_S16(3MLIB)