Is it appropriate to use Ward's linkage as the method for linkage function for hierachical clustering of time series data?

Dear all,

I am using hierarchical clustering to cluster several time-series data with unequal length. For my case, considering each time-series data as one observation doesn't make any sense. Therefore, I calculated DTW (dynamic time warping) distance pairwisely among those time series data to form a dissimilarity matrix which has same form as the output of pdist function. Then I use this dissimilarity matrix as the input of linkage function, chosing 'ward' as the method. Compared to other commonly used method such as 'single', 'average', 'complete', it seems 'ward' gives more interpretable clustering result.

When I carefully checked "linkage" documentation (https://www.mathworks.com/help/stats/linkage.html#d120e444115), it clearly mentioned that 'ward' is appropriate for Euclidean distances only. And after I took a close look about the defination of Ward' linkage, which needs to calculate the centroids of clusters.

Here follows my questions.

First, I just called linkage(dissimilarity matrix, 'ward'), how could this algorithm to calclulate the centroids? For the unequal length of time series data, even centroids could not be well defined.

Second, is it make sense to use ward method for my case?

Any reply will be greatly appreciated.

Best regard,

Xiaoqun Yu