Segmentations with Rearrangements

Sequence segmentation is a central problem in the analysis of sequential and time-series data. In this paper we introduce and we study a novel variation to the segmentation problem: in addition to partitioning the sequence we also seek to apply a limited amount of reordering, so that the overall representation error is minimized. Our problem formulation has applications in segmenting data collected from a sensor network where some of the sensors might be slightly out of sync, or in the analysis of newsfeed data where news reports on a few different topics are arriving in an interleaved manner. We formulate the problem of segmentation with rearrangements and we show that it is an NP-hard problem to solve or even approximate. We then proceed to devise effective algorithms for the proposed problem, combining ideas from linear programming, dynamic programming, and outlier-detection algorithms in sequences. We perform extensive experimental evaluation on synthetic and real datasets that demonstrates the efficacy of the suggested algorithms.