Various global constraints (windows) which can be applied to
window.type argument of
including the Sakoe-Chiba band, the Itakura parallelogram,
and custom functions.
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index in the query (row) – automatically set
index in the reference (column) – automatically set
size of the query time series – automatically set
size of the reference time series – automatically set
window size, used by some windowing functions – must be set
a windowing function
additional arguments passed to windowing functions
Windowing functions can be passed to the
window.type argument in
dtw to put a global
constraint to the warping paths allowed. They take two integer
arguments (plus optional parameters) and must return a boolean value
TRUE if the coordinates fall within the allowed region
for warping paths,
User-defined functions can read variables
window.size; these are pre-set upon
invocation. Some functions require additional parameters which must
be set (e.g.
window.size). User-defined functions are free to
implement any window shape, as long as at least one path is allowed
between the initial and final alignment points, i.e., they are
compatible with the DTW constraints.
sakoeChibaWindow function implements the Sakoe-Chiba band,
window.size elements around the
main diagonal. If
the window size is too small, i.e. if
itakuraWindow global constraint is still provided with this
package. See example below for a demonstration of
the difference between a local the two.
slantedBandWindow (package-specific) is a band centered
around the (jagged) line segment which joins element
[query.size,reference.size], and will be
window.size columns wide. In other words, the "diagonal" goes
from one corner to the other of the possibly rectangular cost matrix,
therefore having a slope of
M/N, not 1.
dtwWindow.plot visualizes a windowing function. By default
it plots a 200 x 220 rectangular region, which can
be changed via
Windowing functions return
TRUE if the coordinates passed as
arguments fall within the chosen warping window,
otherwise. User-defined functions should do the same.
dtwWindow.plot resembles object-oriented notation,
there is not a such a dtwWindow class currently.
A widely held misconception is that the "Itakura parallelogram" (as
described in reference ) is a global constraint, i.e. a
window. To the author's knowledge, it instead arises from the local
slope restrictions imposed to the warping path, such as the one
implemented by the
typeIIIc step pattern.
 Sakoe, H.; Chiba, S., Dynamic programming algorithm optimization for spoken word recognition,
Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing], IEEE Transactions on ,
vol.26, no.1, pp. 43-49, Feb 1978 URL: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1163055
 Itakura, F., Minimum prediction residual principle applied to speech recognition, Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing], IEEE Transactions on , vol.23, no.1, pp. 67-72, Feb 1975. URL: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1162641
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## Display some windowing functions dtwWindow.plot(itakuraWindow, main="So-called Itakura parallelogram window") dtwWindow.plot(slantedBandWindow, window.size=2, reference=13, query=17, main="The slantedBandWindow at window.size=2") ## Asymmetric step with Sakoe-Chiba band idx<-seq(0,6.28,len=100); query<-sin(idx)+runif(100)/10; reference<-cos(idx); asyband<-dtw(query,reference,keep=TRUE, step=asymmetric, window.type=sakoeChibaWindow, window.size=30 ); dtwPlot(asyband,type="density",main="Sine/cosine: asymmetric step, S-C window")