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I have a length 200000 time series of six dimensional data describing the evolution of a chaotic dynamical system. I am exploring ways to partition the state space of the data into minimally interacting regions; I want the least transitions from cluster to another in my time series. Other than not being interested in the trivial case of only 1 cluster I have no restrictions on cluster number though I expect it to be small (K<6 say). The purpose of this is to try and identify quasi-stable basins of attraction in the chaotic system.

I have tried Hidden Markov Models with both Gaussian and Gaussian Mixture emissions, but they do not well capture the very non-gaussian structure of my data in phase space. I have also tried using DBSCAN with some success but since it didnt treat data as a time series, the parameters had to be very carefully tuned to get good results, which left me dissatisfied.

Do any other approaches leap to mind?

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You can trivially modify DBSCAN (see GDBSCAN) to take time into account rather than dropping the precious time information.

I.e. neighbors are those points that are within a time difference of dt, and that have a minimum similarity.

Apart from that, classic "change in mean" analysis techniques for time series come to my mind. Maybe also changepoint detection.

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