I have a long segment/array (e.g. 100000 samples) as input. Regardless of the method, I need to output a partition of this segment into $k$ sub-segments, which do not overlap, and whose union can but doesn't have to be the entire segment. For instance, for the segment
[0, 1000], a valid output can be the list
[[0, 10], [20, 50], [500, 900], [950, 970]].
I have a ground truth of the "correct" partition, for example:
[[0, 15], [25, 40], [400, 650], [950, 975]]. Notice the number and length of the "truth" segments don't have to even resemble the number and length of the actual segments.
Given that I have the ground-truth, what would be a suitable loss function to solve this problem?
Currently, I don't have any special requirements from that error function, so I would just like one that makes sense, a trivial one is fine too, as I can't come up even with that.
If some error functions for such a problem exist, please let me know of them, or even what that problem is called, so I can search for something.