Classifying compositional vectors of time series

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?