 # Dynamic Time Wrapping for time series with more than 1 variable of interest

Hi there,

I have been exploring 'dtw' package to calculate the distance between multiple time series.

This stackflow post gives a wonderful working example of how to use dtw package for univariate time series data:

Here they have a dataframe that looks as this:

``````#data: 8 observations, 3 cars
file.ID2 <- c("Cars_03", "Cars_03", "Cars_03",
"Cars_03", "Cars_03", "Cars_03", "Cars_03", "Cars_03", "Cars_04",
"Cars_04", "Cars_04", "Cars_04", "Cars_04", "Cars_04", "Cars_04",
"Cars_04", "Cars_05", "Cars_05", "Cars_05", "Cars_05", "Cars_05",
"Cars_05", "Cars_05", "Cars_05")
speed.kph.ED <- c(129.3802848,
129.4022304, 129.424176, 129.4461216, 129.4680672, 129.47904,
129.5009856, 129.5229312, 127.8770112, 127.8221472, 127.7672832,
127.7124192, 127.6575552, 127.6026912, 127.5478272, 127.4929632,
134.1095616, 134.1205344, 134.1315072, 134.1534528, 134.1644256,
134.1753984, 134.1863712, 134.197344)

df <- data.frame(file.ID2, speed.kph.ED)
df
``````

Here we have 3 univariate time series (one for each type of car) that has 1 variable of interest: `speed.kph.ED`

Per suggested by the accepted answer, here is the procedure to calculate distance between 3 cars using dtw:

``````library(dtw)
library(purrr)
library(dplyr)

# Split your data frame into a list by file.ID2
ds <- split(df, df\$file.ID2)
ds

# Use expand.grid to make all combinations of your names, file.ID2 and your values
Names <- expand.grid(unique(df\$file.ID2), unique(df\$file.ID2))
Values <- expand.grid(ds, ds)

# purrr:map_dbl iterates through all row-combinations of Values and returns a vector of doubles
Dist <- map_dbl(1:nrow(Values), ~dtw(x = Values[.x,]\$Var1[]\$speed.kph.ED, y = Values[.x,]\$Var2[]\$speed.kph.ED)\$distance)

library(dplyr)
ans <- Names %>%
mutate(distance = Dist)

ans

``````

Now, I am wondering what if I have other two variables in this dataframe that I also want to take into consideration?

Let's say I created these 2 extra variables `score.kph.ED` and `rating.kph.ED` :

``````score.kph.ED <- c(1:24)
rating.kph.ED <- c(25:48)

df <- data.frame(file.ID2, speed.kph.ED, score.kph.ED, rating.kph.ED)
df
``````

That is, now, the distance between the 3 cars are calculated not only based on `speed.kph.ED`, but also based on `score.kph.ED` and `rating.kph.ED`.

How can I modify the existing code so that I can achieve this goal?

Thanks so much for your help!