mlib_SignalDTWKScalar_F32(3mlib)

1mlib_SignalDTWKScalar_F32(3mMeLdIiBa)Lib Library Funcmtliiobn_sSignalDTWKScalar_F32(3MLIB)
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NAME

6       mlib_SignalDTWKScalar_F32  -  perform  dynamic  time warping for K-best
7       paths on scalar data
8

SYNOPSIS

10       cc [ flag... ] file... -lmlib [ library... ]
11       #include <mlib.h>
12
13       mlib_status mlib_SignalDTWKScalar_F32(mlib_d64 *dist,
14            const mlib_f32 *dobs, mlib_s32 lobs, void *state);
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16

DESCRIPTION

18       The mlib_SignalDTWKScalar_F32() function performs dynamic time  warping
19       for K-best paths on scalar data.
20
21
22       Assume the reference data are
23
24             r(y), y=1,2,...,N
25
26
27
28       and the observed data are
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30             o(x), x=1,2,...,M
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32
33
34       the dynamic time warping is to find a mapping function (a path)
35
36             p(i) = {px(i),py(i)}, i=1,2,...,Q
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40       with the minimum distance.
41
42
43       In  K-best  paths  case,  K  paths  with  the  K  minimum distances are
44       searched.
45
46
47       The distance of a path is defined as
48
49                     Q
50             dist = SUM d(r(py(i)),o(px(i))) * m(px(i),py(i))
51                    i=1
52
53
54
55       where d(r,o) is the dissimilarity between data point/vector r and  data
56       point/vector  o;  m(x,y)  is  the path weighting coefficient associated
57       with path point (x,y); N is the length of the reference data; M is  the
58       length of the observed data; Q is the length of the path.
59
60
61       Using L1 norm (sum of absolute differences)
62
63                      L-1
64             d(r,o) = SUM |r(i) - o(i)|
65                      i=0
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67
68
69       Using L2 norm (Euclidean distance)
70
71                             L-1
72             d(r,o) = SQRT { SUM (r(i) - o(i))**2 }
73                             i=0
74
75
76
77       where L is the length of each data vector.
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79
80       To scalar data where L=1, the two norms are the same.
81
82             d(r,o) = |r - o| = SQRT {(r - o)**2 }
83
84
85
86       The constraints of dynamic time warping are:
87
88           1.     Endpoint constraints
89
90                        px(1) = 1
91                        1 ≤ py(1) ≤ 1 + delta
92
93                  and
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95                        px(Q) = M
96                        N-delta ≤ py(Q) ≤ N
97
98
99           2.     Monotonicity Conditions
100
101                        px(i) ≤ px(i+1)
102                        py(i) ≤ py(i+1)
103
104
105           3.     Local Continuity Constraints
106
107                  See Table 4.5 on page 211 in Rabiner and Juang's book.
108
109                  Itakura Type:
110
111                        py
112                        |
113                        *----*----*
114                        |p4  |p1  |p0
115                        |    |    |
116                        *----*----*
117                        |    |p2  |
118                        |    |    |
119                        *----*----*-- px
120                              p3
121
122                  Allowable paths are
123
124                        p1->p0    (1,0)
125                        p2->p0    (1,1)
126                        p3->p0    (1,2)
127
128                  Consecutive  (1,0)(1,0) is disallowed. So path p4->p1->p0 is
129                  disallowed.
130
131           4.     Global Path Constraints
132
133                  Due to local continuity constraints, certain portions of the
134                  (px,py) plane are excluded from the region the optimal warp‐
135                  ing path can traverse. This forms global path constraints.
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137           5.     Slope Weighting
138
139                  See Equation 4.150-3 on page  216  in  Rabiner  and  Juang's
140                  book.
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142
143       A  path in (px,py) plane can be represented in chain code. The value of
144       the chain code is defined as following.
145
146             ============================
147             shift ( x , y ) | chain code
148             ----------------------------
149                 ( 1 , 0 )   |     0
150                 ( 0 , 1 )   |     1
151                 ( 1 , 1 )   |     2
152                 ( 2 , 1 )   |     3
153                 ( 1 , 2 )   |     4
154                 ( 3 , 1 )   |     5
155                 ( 3 , 2 )   |     6
156                 ( 1 , 3 )   |     7
157                 ( 2 , 3 )   |     8
158             ============================
159
160                 py
161                 |
162                 *  8  7  *
163                 |
164                 *  4  *  6
165                 |
166                 1  2  3  5
167                 |
168                 x--0--*--*-- px
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170
171
172       where x marks the start point of a path segment, the  numbers  are  the
173       values of the chain code for the segment that ends at the point.
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175
176       In  following example, the observed data with 11 data points are mapped
177       into the reference data with 9 data points
178
179                 py
180                 |
181              9  | * * * * * * * * * *-*
182                 |                  /
183                 | * * * * * * * *-* * *
184                 |              /
185                 | * * * * * * * * * * *
186                 |            /
187                 | * * * * *-* * * * * *
188                 |        /
189                 | * * * * * * * * * * *
190                 |       |
191                 | * * * * * * * * * * *
192                 |      /
193                 | * * * * * * * * * * *
194                 |    /
195                 | * * * * * * * * * * *
196                 |  /
197              1  | * * * * * * * * * * *
198                 |
199                 +------------------------ px
200                   1                   11
201
202
203
204       The chain code that represents the path is
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206             (2 2 2 1 2 0 2 2 0 2 0)
207
208
209
210       See Fundamentals of Speech Recognition by Lawrence Rabiner  and  Biing-
211       Hwang Juang, Prentice Hall, 1993.
212

PARAMETERS

214       The function takes the following arguments:
215
216       dist     The distances of the K-best paths.
217
218
219       dobs     The observed data array.
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222       lobs     The length of the observed data array.
223
224
225       state    Pointer to the internal state structure.
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227

RETURN VALUES

229       The  function  returns MLIB_SUCCESS if successful. Otherwise it returns
230       MLIB_FAILURE.
231

ATTRIBUTES

233       See attributes(5) for descriptions of the following attributes:
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237
238       ┌─────────────────────────────┬─────────────────────────────┐
239       │      ATTRIBUTE TYPE         │      ATTRIBUTE VALUE        │
240       ├─────────────────────────────┼─────────────────────────────┤
241       │Interface Stability          │Committed                    │
242       ├─────────────────────────────┼─────────────────────────────┤
243       │MT-Level                     │MT-Safe                      │
244       └─────────────────────────────┴─────────────────────────────┘
245

NAME

SYNOPSIS

DESCRIPTION

PARAMETERS

RETURN VALUES

ATTRIBUTES

SEE ALSO