View source: R/DISTANCES-lb-keogh.R
lb_keogh | R Documentation |
This function calculates a lower bound (LB) on the Dynamic Time Warp (DTW) distance between two time series. It uses a Sakoe-Chiba constraint.
lb_keogh( x, y, window.size = NULL, norm = "L1", lower.env = NULL, upper.env = NULL, force.symmetry = FALSE, error.check = TRUE )
x |
A time series (reference). |
y |
A time series with the same length as |
window.size |
Window size for envelope calculation. See details. |
norm |
Vector norm. Either |
lower.env |
Optionally, a pre-computed lower envelope for |
upper.env |
Optionally, a pre-computed upper envelope for |
force.symmetry |
If |
error.check |
Logical indicating whether the function should try to detect inconsistencies and give more informative errors messages. Also used internally to avoid repeating checks. |
The reference time series should go in x
, whereas the query time series should go in y
.
If the envelopes are provided, they should be provided together. If either one is missing, both will be computed.
The windowing constraint uses a centered window. The calculations expect a value in
window.size
that represents the distance between the point considered and one of the edges
of the window. Therefore, if, for example, window.size = 10
, the warping for an
observation x_i considers the points between x_{i-10} and x_{i+10}, resulting
in 10(2) + 1 = 21
observations falling within the window.
A list with:
d
: The lower bound of the DTW distance.
upper.env
: The time series of y
's upper envelope.
lower.env
: The time series of y
's lower envelope.
The version registered with dist
is custom (loop = FALSE
in
pr_DB
). The custom function handles multi-threaded parallelization
directly (with RcppParallel
). It uses all
available threads by default (see
RcppParallel::defaultNumThreads()
), but this can
be changed by the user with
RcppParallel::setThreadOptions()
.
An exception to the above is when it is called within a foreach
parallel loop made by dtwclust. If the parallel workers do not have the number of
threads explicitly specified, this function will default to 1 thread per worker. See the
parallelization vignette for more information (browseVignettes("dtwclust")
).
The lower bound is only defined for time series of equal length and is not symmetric.
If you wish to calculate the lower bound between several time series, it would be better to use
the version registered with the proxy
package, since it includes some small optimizations. The
convention mentioned above for references and queries still holds. See the examples.
The proxy version of force.symmetry
should only be used when only x
is provided or both x
and y
are identical. It compares the lower and upper triangular of the resulting distance
matrix and forces symmetry in such a way that the tightest lower bound is obtained.
Keogh E and Ratanamahatana CA (2005). “Exact indexing of dynamic time warping.” Knowledge and information systems, 7(3), pp. 358-386.
# Sample data data(uciCT) # Lower bound distance between two series d.lbk <- lb_keogh(CharTraj[[1]], CharTraj[[2]], window.size = 20)$d # Corresponding true DTW distance d.dtw <- dtw(CharTraj[[1]], CharTraj[[2]], window.type = "sakoechiba", window.size = 20)$distance d.lbk <= d.dtw # Calculating the LB between several time series using the 'proxy' package # (notice how both argments must be lists) D.lbk <- proxy::dist(CharTraj[1], CharTraj[2:5], method = "LB_Keogh", window.size = 20, norm = "L2") # Corresponding true DTW distance D.dtw <- proxy::dist(CharTraj[1], CharTraj[2:5], method = "dtw_basic", norm = "L2", window.size = 20) D.lbk <= D.dtw
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