View source: R/DISTANCES-dtw-basic.R
dtw_basic | R Documentation |
This is a custom implementation of the DTW algorithm without all the functionality included in
dtw::dtw()
. Because of that, it should be faster, while still supporting the most common
options.
dtw_basic( x, y, window.size = NULL, norm = "L1", step.pattern = dtw::symmetric2, backtrack = FALSE, normalize = FALSE, sqrt.dist = TRUE, ..., error.check = TRUE )
x, y |
Time series. Multivariate series must have time spanning the rows and variables spanning the columns. |
window.size |
Size for slanted band window. |
norm |
Norm for the LCM calculation, "L1" for Manhattan or "L2" for (squared) Euclidean. See notes. |
step.pattern |
Step pattern for DTW. Only |
backtrack |
Also compute the warping path between series? See details. |
normalize |
Should the distance be normalized? Only supported for |
sqrt.dist |
Only relevant for |
... |
Currently ignored. |
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. |
If backtrack
is TRUE
, the mapping of indices between series is returned in a list.
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.
The DTW distance. For backtrack
=
TRUE
, a list with:
distance
: The DTW distance.
index1
: x
indices for the matched elements in the warping path.
index2
: y
indices for the matched elements in the warping path.
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")
).
It also includes symmetric optimizations to calculate only half a distance matrix when
appropriateâ€”only one list of series should be provided in x
. If you want to avoid this
optimization, call dist
by giving the same list of series in both x
and y
.
In order for symmetry to apply here, the following must be true: no window constraint is used
(window.size
is NULL
) or, if one is used, all series have the same length.
The elements of the local cost matrix are calculated by using either Manhattan or squared
Euclidean distance. This is determined by the norm
parameter. When the squared Euclidean
version is used, the square root of the resulting DTW distance is calculated at the end (as
defined in Ratanamahatana and Keogh 2004; Lemire 2009; see vignette references). This can be
avoided by passing FALSE
in sqrt.dist
.
The DTW algorithm (and the functions that depend on it) might return different values in 32 bit installations compared to 64 bit ones.
An infinite distance value indicates that the constraints could not be fulfilled, probably due to
a too small window.size
or a very large length difference between the series.
## Not run: # ==================================================================================== # Understanding multivariate DTW # ==================================================================================== # The variables for each multivariate time series are: # tip force, x velocity, and y velocity A1 <- CharTrajMV[[1L]] # A character B1 <- CharTrajMV[[6L]] # B character # Let's extract univariate time series A1_TipForce <- A1[,1L] # first variable (column) A1_VelX <- A1[,2L] # second variable (column) A1_VelY <- A1[,3L] # third variable (column) B1_TipForce <- B1[,1L] # first variable (column) B1_VelX <- B1[,2L] # second variable (column) B1_VelY <- B1[,3L] # third variable (column) # Looking at each variable independently: # Just force dtw_basic(A1_TipForce, B1_TipForce, norm = "L1", step.pattern = symmetric1) # Corresponding LCM proxy::dist(A1_TipForce, B1_TipForce, method = "L1") # Just x velocity dtw_basic(A1_VelX, B1_VelX, norm = "L1", step.pattern = symmetric1) # Corresponding LCM proxy::dist(A1_VelX, B1_VelX, method = "L1") # Just y velocity dtw_basic(A1_VelY, B1_VelY, norm = "L1", step.pattern = symmetric1) # Corresponding LCM proxy::dist(A1_VelY, B1_VelY, method = "L1") # NOTES: # In the previous examples there was one LCM for each *pair* of series. # Additionally, each LCM has dimensions length(A1_*) x length(B1_*) # proxy::dist won't return the LCM for multivariate series, # but we can do it manually: mv_lcm <- function(mvts1, mvts2) { # Notice how the number of variables (columns) doesn't come into play here num_obs1 <- nrow(mvts1) num_obs2 <- nrow(mvts2) lcm <- matrix(0, nrow = num_obs1, ncol = num_obs2) for (i in 1L:num_obs1) { for (j in 1L:num_obs2) { # L1 norm for ALL variables (columns). # Consideration: mvts1 and mvts2 MUST have the same number of variables lcm[i, j] <- sum(abs(mvts1[i,] - mvts2[j,])) } } # return lcm } # Let's say we start with only x velocity and y velocity for each character mvts1 <- cbind(A1_VelX, A1_VelY) mvts2 <- cbind(B1_VelX, B1_VelY) # DTW distance dtw_d <- dtw_basic(mvts1, mvts2, norm = "L1", step.pattern = symmetric1) # Corresponding LCM lcm <- mv_lcm(mvts1, mvts2) # still 178 x 174 # Sanity check all.equal( dtw_d, dtw::dtw(lcm, step.pattern = symmetric1)$distance # supports LCM as input ) # Now let's consider all variables for each character mvts1 <- cbind(mvts1, A1_TipForce) mvts2 <- cbind(mvts2, B1_TipForce) # Notice how the next code is exactly the same as before, # even though we have one extra variable now # DTW distance dtw_d <- dtw_basic(mvts1, mvts2, norm = "L1", step.pattern = symmetric1) # Corresponding LCM lcm <- mv_lcm(mvts1, mvts2) # still 178 x 174 # Sanity check all.equal( dtw_d, dtw::dtw(lcm, step.pattern = symmetric1)$distance # supports LCM as input ) # By putting things in a list, # proxy::dist returns the *cross-distance matrix*, not the LCM series_list <- list(mvts1, mvts2) distmat <- proxy::dist(series_list, method = "dtw_basic", norm = "L1", step.pattern = symmetric1) # So this should be TRUE all.equal(distmat[1L, 2L], dtw_d) # NOTE: distmat is a 2 x 2 matrix, because there are 2 multivariate series. # Each *cell* in distmat has a corresponding LCM (not returned by the function). # Proof: manual_distmat <- matrix(0, nrow = 2L, ncol = 2L) for (i in 1L:nrow(manual_distmat)) { for (j in 1L:ncol(manual_distmat)) { lcm_cell <- mv_lcm(series_list[[i]], series_list[[j]]) # LCM for this pair manual_distmat[i, j] <- dtw::dtw(lcm_cell, step.pattern = symmetric1)$distance } } # TRUE all.equal( as.matrix(distmat), manual_distmat ) ## End(Not run)
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