r - Clustering time series - Distance betweens time series

Question

I'm running hierarchical clustering to time series where I have N time series, where each has 24 observations, i.e, each time series represents a day measured every hour. I'm using the TSClust and the diss function to compute the dissimilarity matrix. But what I don't understand is how the distance is giving a unique value. With measures such as DTWarp, we should get a "path" between the two-time series instead of a single value. For example, the following:

      > x <- cumsum(rnorm(100))
      > y <- cumsum(rnorm(100))
      > diss.DTWARP(x, y)
      
      [1] 257.2109

Doesn't the DTW (and Frechet distance for example) gives a "path" instead of a value? How is this value obtained?

If the distance between each time series is a unique value, then the clustering will only have in account the distance on a daily basis instead of an hour basis, and each of my time series has 24 values.

EDIT: For example, if a time series X has its maximum value at lunchtime and minimum at night and another time series Y is the opposite (maximum at night and minimum at lunchtime) does the diss function take that (hours) into account? I want to cluster my time series accordingly to their behaviour, that's why I'm using DTW, but since I get no path, only one value, I guess the behaviour is not accounted for?

Answer 1

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