dtwWindowingFunctions
Global constraints and windowing functions for DTW
Various global constraints (windows) which can be applied to
the window.type
argument of dtw
,
including the SakoeChiba band, the Itakura parallelogram,
and custom functions.
 Keywords
 ts
Usage
noWindow(iw, jw, ...);
sakoeChibaWindow(iw,jw, window.size,...);
slantedBandWindow(iw,jw,query.size,reference.size, window.size,...);
itakuraWindow(iw,jw,query.size,reference.size, ...);
dtwWindow.plot(fun,query.size=200,reference.size=220,...);
Arguments
 iw
 index in the query (row)  automatically set
 jw
 index in the reference (column)  automatically set
 query.size
 size of the query time series  automatically set
 reference.size
 size of the reference time series  automatically set
 window.size
 window size, used by some windowing functions  must be set
 fun
 a windowing function
 ...
 additional arguments passed to windowing functions
Details
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, FALSE
otherwise.
Userdefined functions can read variables reference.size
,
query.size
and window.size
; these are preset upon
invocation. Some functions require additional parameters which must
be set (e.g. window.size
). Userdefined 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.
The sakoeChibaWindow
function implements the SakoeChiba band,
i.e. window.size
elements around the main
diagonal. If
the window size is too small, i.e. if
reference.size
query.size
> window.size
, warping
becomes impossible.
An itakuraWindow
global constraint is still provided with this
package. See example below for a demonstration of
the difference between a local the two.
The slantedBandWindow
(packagespecific) is a band centered
around the (jagged) line segment which joins element [1,1]
to
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 reference.size
and query.size
arguments.
Value

Windowing functions return
TRUE
if the coordinates passed as
arguments fall within the chosen warping window, FALSE
otherwise. Userdefined functions should do the same.
Note
Although dtwWindow.plot
resembles objectoriented notation,
there is not a such a dtwWindow class currently.
A widely held misconception is that the "Itakura parallelogram" (as
described in reference [2]) 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.
References
[1] 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. 4349, Feb 1978 URL: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1163055 [2] 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. 6772, Feb 1975. URL: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1162641
Examples
## Display some windowing functions
dtwWindow.plot(itakuraWindow, main="Socalled Itakura parallelogram window")
dtwWindow.plot(slantedBandWindow, window.size=2,
reference=13, query=17, main="The slantedBandWindow at window.size=2")
## Asymmetric step with SakoeChiba 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, SC window")