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  • $\begingroup$ It seems that several unrelated methods are being tried arbitrarily $\endgroup$ Commented Apr 1, 2017 at 3:08
  • $\begingroup$ Yes it is the case, I tried to explore the problem and just posted what I tried, but I didn't find a correct path to the solution $\endgroup$ Commented Apr 1, 2017 at 3:15
  • $\begingroup$ This is an interesting problem with infinitely many solutions. There are some trivial symmetries (e.g. you can't distinguish forward vs. backward), but more troublesome ones too. For example, in your plot, say a trajectory hits the clump of points in the middle, then starts going around the loop. How many times does it go around before emerging again or stopping? Adjacent points might not be part of the same pass, but subsequent passes (or even doubling back). So, some strong constraints will be necessary to solve the problem. $\endgroup$ Commented Apr 1, 2017 at 6:32
  • $\begingroup$ Right now it sounds like you have a fuzzy idea of what a solution would look like. A good first step would be to figure out how to make that mathematically precise so it can be turned into an algorithm. Thinking about the physical process that generated the data could also help. For example, if you know some bounds on the speed/acceleration of the object (or other information about how it behaves) and the time interval between sensor readings, it may give you some useful constraints. $\endgroup$ Commented Apr 1, 2017 at 6:49
  • $\begingroup$ I think the best approach here is pre-smoothing before applying isomap. A few methods are possible. I would suggest fitting a Gaussian mixture model with say 20-50 components, then using the centers of the mixture components as input to the isomap. I have no idea how to restrict the curvature though. A very interesting problem. $\endgroup$ Commented Apr 1, 2017 at 7:11