Description Usage Arguments Details Value Note Author(s) References Examples
Various global constraints (windows) which can be applied to
the window.type
argument of dtw
,
including the Sakoe-Chiba band, the Itakura parallelogram,
and custom functions.
1 2 3 4 5 6 | 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,...);
|
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 |
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.
User-defined functions can read variables reference.size
,
query.size
and 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.
The sakoeChibaWindow
function implements the Sakoe-Chiba 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
(package-specific) 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.
Windowing functions return TRUE
if the coordinates passed as
arguments fall within the chosen warping window, FALSE
otherwise. User-defined functions should do the same.
Although 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 [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.
Toni Giorgino
[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. 43-49, 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.
67-72, Feb 1975. URL: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1162641
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ## 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")
|
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