There have already been questions similar to yours,
but the answers haven't been too detailed.
Here's a breakdown of what you need to know,
in the specific case of R.
Calculating cross-distance matrices
The proxy package is made specifically for the calculation of cross-distance matrices.
You should check its vignette to know which measures are already implemented by it.
An example of its use:
set.seed(1L)
sample_data <- matrix(rnorm(50L), nrow = 5L, ncol = 10L)
suppressPackageStartupMessages(library(proxy))
distance_matrix <- proxy::dist(sample_data, method = "euclidean",
upper = TRUE, diag = TRUE)
print(distance_matrix)
#> 1 2 3 4 5
#> 1 0.000000 2.636027 3.834764 5.943374 3.704322
#> 2 2.636027 0.000000 2.587398 4.515470 2.310364
#> 3 3.834764 2.587398 0.000000 4.008678 3.899561
#> 4 5.943374 4.515470 4.008678 0.000000 5.059321
#> 5 3.704322 2.310364 3.899561 5.059321 0.000000
Note: in the context of time series,
proxy treats each row in a matrix as a series,
which can be confirmed by the fact that sample_data above is a 5x10 matrix and the resulting cross-distance matrix is 5x5.
Using the DTW distance
The dtw package implements many variations of DTW,
and it also leverages proxy.
You could calculate a DTW distance matrix with:
suppressPackageStartupMessages(library(dtw))
dtw_distmat <- proxy::dist(sample_data, method = "dtw",
upper = TRUE, diag = TRUE)
print(distance_matrix)
#> 1 2 3 4 5
#> 1 0.000000 2.636027 3.834764 5.943374 3.704322
#> 2 2.636027 0.000000 2.587398 4.515470 2.310364
#> 3 3.834764 2.587398 0.000000 4.008678 3.899561
#> 4 5.943374 4.515470 4.008678 0.000000 5.059321
#> 5 3.704322 2.310364 3.899561 5.059321 0.000000
Using custom distances
One nice thing about proxy is that it gives you the option to register custom functions.
You seem to be interested in the normalized version of DTW,
so you could do something like this:
ndtw <- function(x, y = NULL, ...) {
dtw::dtw(x, y, ..., distance.only = TRUE)$normalizedDistance
}
pr_DB$set_entry(
FUN = ndtw,
names = "ndtw",
loop = TRUE,
distance = TRUE
)
ndtw_distmat <- proxy::dist(sample_data, method = "ndtw",
upper = TRUE, diag = TRUE)
print(ndtw_distmat)
#> 1 2 3 4 5
#> 1 0.0000000 0.4046622 0.5075772 0.6789465 0.5290478
#> 2 0.4046622 0.0000000 0.3630849 0.4866252 0.3612722
#> 3 0.5075772 0.3630849 0.0000000 0.5678698 0.3303344
#> 4 0.6789465 0.4866252 0.5678698 0.0000000 0.5078112
#> 5 0.5290478 0.3612722 0.3303344 0.5078112 0.0000000
See the documentation of pr_DB for more information.
Other DTW implementations
The dtwclust package
(which I made)
implements a basic but faster version of DTW which can use multi-threading and also leverages proxy:
suppressPackageStartupMessages(library(dtwclust))
dtw_basic_distmat <- proxy::dist(sample_data, method = "dtw_basic", normalize = TRUE)
print(dtw_basic_distmat)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0000000 0.4046622 0.5075772 0.6789465 0.5290478
#> [2,] 0.4046622 0.0000000 0.3630849 0.4866252 0.3612722
#> [3,] 0.5075772 0.3630849 0.0000000 0.5678698 0.3303344
#> [4,] 0.6789465 0.4866252 0.5678698 0.0000000 0.5078112
#> [5,] 0.5290478 0.3612722 0.3303344 0.5078112 0.0000000
The dtw_basic implementation only supports two step patterns and one window type,
but it is considerably faster:
suppressPackageStartupMessages(library(microbenchmark))
microbenchmark(
proxy::dist(sample_data, method = "dtw", window.type = "sakoechiba", window.size = 5L),
proxy::dist(sample_data, method = "dtw_basic", window.size = 5L)
)
Unit: microseconds
expr min lq mean
proxy::dist(sample_data, method = "dtw", window.type = "sakoechiba", window.size = 5L) 5279.124 5621.742 6070.069
proxy::dist(sample_data, method = "dtw_basic", window.size = 5L) 657.966 710.418 776.474
median uq max neval cld
5802.354 6348.199 10411.000 100 b
752.282 814.037 1161.626 100 a
Another multi-threaded implementation is included in the parallelDist package,
although I haven't personally tested it.
Multivariate or multi-dimensional time series
A single multivariate series is commonly a matrix where time spans the rows and the multiple variables span the columns.
DTW also works for them:
mv_series1 <- matrix(rnorm(15L), nrow = 5L, ncol = 3L)
mv_series2 <- matrix(rnorm(15L), nrow = 5L, ncol = 3L)
print(dtw_distance <- dtw_basic(mv_series1, mv_series2))
#> [1] 22.80421
The nice thing about proxy is that it can calculate distances between objects contained in lists too,
so you can put several multivariate series in lists of matrices:
mv_series <- lapply(1L:5L, function(dummy) {
matrix(rnorm(15L), nrow = 5L, ncol = 3L)
})
mv_distmat_dtwclust <- proxy::dist(mv_series, method = "dtw_basic")
print(mv_distmat_dtwclust)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.00000 27.43599 32.14207 36.42211 31.19279
#> [2,] 27.43599 0.00000 20.88470 23.88436 29.73219
#> [3,] 32.14207 20.88470 0.00000 22.14376 29.99899
#> [4,] 36.42211 23.88436 22.14376 0.00000 28.81111
#> [5,] 31.19279 29.73219 29.99899 28.81111 0.00000
Your case
Regardless of what you choose,
you can probably use proxy to get your result,
but since you haven't provided your whole data,
I can't give you a more specific example.
I presume that dtwclust::dtw_basic(control[, 1:4], lead[, 1:4], normalize = TRUE) would give you the distance between one pair of series,
assuming you're treating each one as a multivariate series with 4 variables.
