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I am interested in classifying vectors of time series $x_t=(x_{1,t},\ldots,x_{n,t})$. In addition these vectors are subject to the restrictions $\forall i,t$: $0 \leq x_{i,t} \leq 1$ and $\forall t$: $\sum_{i=1}^n x_{i,t}=1$. So the $x_{i,t}$ are actually percentage values. The vectors come from several groups and given a new vector of time series, I want to classify from which group this new vector might come from.

I know a little bit about dynamic time warping, but this doesn't deal with vectors. And even more, I got the additional structure of the problem which stems from the above mentioned restrictions.

Does anybody know a method to do this?

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You say "I know a little bit about dynamic time warping, but this doesn't deal with vectors" But a time series is just a vector, right? The constraint you have is just one type of normalization, but and Mueen and Keogh point out, you must normalize for DTW [a].

It is not clear that DTW is needed here, could you use Eucldian distance (which is really a special case of DTW, with a warping window of zero)

[a] https://www.cs.unm.edu/~mueen/DTW.pdf

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