If I need to reduce my sample size due to computation time, should I standardize using my original or post-reduction means and standard deviations? I have data such that each data point, xi, is a multidimensional time series, with each feature, p, having 10000 time stamps.
xi = [pi0(0), pi0(1),… pi0(9999)], [pi1(0), pi1(1),… pi1(9999)], ….
I want to use dynamic time warping to calculate the distance between each pair of points, but I need to standardize the values first. For each p I do this by exploding all of the values and finding the mean and standard deviation. Unfortunately, the computation time for dynamic time warping was too much. I then artificially reduced the fidelity by taking every 100th time stamp and now the computation time is much more reasonable. However, I don’t know if it’s more appropriate to standardize with the mean and standard deviation of the original values or with my reduced fidelity values. Which should I do?

It is hard to see, why DTW is taking so long
May I suggest you read https://www.cs.unm.edu/~mueen/DTW.pdf
For a single pairwise comparison you can reduce the time from O(N^2) to O(Nw) (where w<<N).  For many comparisons, you can get the amortized time of DTW down to O(N)
