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We have a dataset with six time points and three biological replicates each. Therefore, we have a vector of 18 measurements for each feature, and used hierarchical clustering with Euclidean distance to cluster by the features and cut the tree at a certain point to propose groups of features. This is a simple and sufficient approach for the problem we are addressing. It has been suggested to do bootstrap resampling of the six time points to determine the stability of the feature clustering. Is that valid, because it breaks the relationship between consecutive time points ? Is there a suitable method for this small experiment ?

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Indeed, it breaks the 'time series' aspect. Maybe your time series are more or less random walks? In my opinion, 6 time points is too few... Besides bootstrapping, you can define your own perturbations based on your expertise of the time series. For instance, in finance you can study "multiscale" perturbations (but 6 points is too few for that). You can have a look at this paper for some perturbation ideas.

Actually, you can try to play with your "features" vector (or the population) instead of the 'time'.

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