Manual Pages for UNIX Operating System command usage for man mlib_SignalDTWVector_S16

mediaLib Library Functions        mlib_SignalDTWVector_S16(3MLIB)



NAME
     mlib_SignalDTWVector_S16 - perform dynamic time  warping  on
     vector data

SYNOPSIS
     cc [ flag... ] file... -lmlib [ library... ]
     #include 

     mlib_status mlib_SignalDTWVector_S16(mlib_d64 *dist,
          const mlib_s16 **dobs, mlib_s32 lobs, mlib_s32 sobs,
          void *state);


DESCRIPTION
     The  mlib_SignalDTWVector_S16()  function  performs  dynamic
     time warping 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






SunOS 5.11          Last change: 23 May 2007                    1






mediaLib Library Functions        mlib_SignalDTWVector_S16(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) = M
                    N-delta < py(Q) < N


         2.   Monotonicity Conditions

                    px(i) < px(i+1)
                    py(i) < py(i+1)


         3.   Local Continuity Constraints



SunOS 5.11          Last change: 23 May 2007                    2






mediaLib Library Functions        mlib_SignalDTWVector_S16(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 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  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 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



SunOS 5.11          Last change: 23 May 2007                    3






mediaLib Library Functions        mlib_SignalDTWVector_S16(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_SignalDTWVector_S16(3MLIB)



     See Fundamentals of Speech Recognition by  Lawrence  Rabiner
     and Biing-Hwang Juang, Prentice Hall, 1993.

PARAMETERS
     The function takes the following arguments:

     dist     The distance of the optimal path.


     dobs     The observed data array.


     lobs     The length of the observed data array.


     sobs     The scaling factor  of  the  observed  data  array,
              where    actual_data    =    input_data   *   2**(-
              scaling_factor).


     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_SignalDTWVectorInit_S16(3MLIB),
     mlib_SignalDTWVector_S16(3MLIB),
     mlib_SignalDTWVectorPath_S16(3MLIB),
     mlib_SignalDTWVectorFree_S16(3MLIB), attributes(5)








SunOS 5.11          Last change: 23 May 2007                    5