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I've a sequence of time ordered set of points: for each $t=1...T$ I have a set of points $(x_{t,i},y_{t,i})$. I need to cluster them together in space-time. I don't know however a priori the number of clusters. What approach do you suggest? My goal is to understand whether the event at time, let's say, $t_1$ belongs to some of other past cluster or forms a new one.

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Why not adding time as a third dimension and use a standard clustering algorithm? I.e. create new "points" $(x_i,y_i,t_i)$ and use k-means or DBSCAN. With this way you can also use a custom scaling/normalization to adjust the weight of the the time dimension.

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