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I'm using AgglomerativeClustering to group time-series with Dynamic Time Warping (DTW) as a metric. I get distance matrix and pass it to clustering.

#dtwMetric is the callable that accepts two observations
dist_m = sklearn.metrics.pairwise.pairwise_distances(data_frame, metric=dtwMetric)

agg = AgglomerativeClustering(n_clusters=10, affinity='precomputed', 
                              linkage='complete')

labels = agg.fit_predict(dist_m)

Then I can get a cluster label for each observation (time-series) in my data frame.

I need to get SARIMAX forecasting later for each cluster using only one (the "most centered") time-series from cluster, so I suppose I don't want an "average" series per cluster but one of my initial observations.

How do I select the "most centered" time-series for each cluster?

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Find the one with the smallest average distance to all others.

It's called the medoid, and it is used by well known algorithms such as PAM.

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  • $\begingroup$ Thanks @Anony-Mousse . Since i was using LB Keogh version (faster) of DTW and this function is non-commutative, I ended up with getting smallest average distance to all others as an average of sum of distances using all possible permutations. E.g if I have [1, 2, 3] in a cluster, then the distance for 1 is calculated as an average of d(1,2) + d(1,3) + d(2,1) + d(3,1). $\endgroup$ – lavrik Apr 27 '18 at 14:25
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    $\begingroup$ The proper way is to use the lower bounding property. So max(d(1,2),d(2,1)) is still a lower bound. You can find the candidate with the smallest lower bound, computer the exact DTW, and repeat this until there is no candidate with a lower bound less than the best refined you have found. $\endgroup$ – Anony-Mousse Apr 28 '18 at 6:07
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    $\begingroup$ Do not use LB Keogh as a substitute for DTW. It is a lower bound and should be used as such. The asymmetry will also mess with the clustering before. In fact, I don't think you should use LB_Keogh with clustering at all. You will likely need all exact distances for a reliable result. $\endgroup$ – Anony-Mousse Apr 28 '18 at 6:15
  • $\begingroup$ Thanks for you comments @Anony-Mousse. Pure DTW was computed much more slower. I think windowed version of DTW may help. $\endgroup$ – lavrik May 1 '18 at 11:29

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