# Cluster "by part" instead of "as a whole"?

A definition before I start:

A trajectory $t$ of length $n$ is here defined as a series of 2D coordinates $$\{(x_1,y_1), (x_2, y_2),..., (x_n, y_n)\}$$ Now I have a set comprised of such trajectories denoted by set $T=\{t_1, t_2,...,t_n\}$.

Take $t_1$ and $t_2$ as an example: let's say a segment of $t_1$ denoted by $S_{t_1}$ overlaps with a part of $t_2$ denoted by $S_{t_2}$. But for the other parts, they do not overlap.

All the trajectories may have such a "partially-overlapping" relationship with the others.

Obviously in this case, we cannot treat every trajectory as a whole, find a distance metric and finally cluster them. We have to sort of cluster the trajectories by part instead of as a whole.

Is there any already-existed clustering technique that does the job?

Any suggestions or pointers are very much welcomed.

• Are those pairs of coordinates indexed by time? If so, are the time intervals and origin the same?
– chl
Commented Oct 6, 2013 at 10:25
• @chl No, they are not. Time is not relevant here. Thanks! Commented Oct 6, 2013 at 11:45