The problem of segmenting linearly ordered data is frequently encountered in time-series analysis, computational biology, and natural language processing. Segmentations obtained independently from replicate data sets or from the same data with different methods or parameter settings pose the problem of computing an aggregate or consensus segmentation. This Segmentation Aggregation problem amounts to finding a segmentation that minimizes the sum of distances to the input segmentations. It is again a segmentation problem and can be solved by dynamic programming. The aim of this contribution is (1) to gain a better mathematical understanding of the Segmentation Aggregation problem and its solutions and (2) to demonstrate that consensus segmentations have useful applications. Extending previously known results we show that for a large class of distance functions only breakpoints present in at least one input segmentation appear in the consensus segmentation. Furthermore, we derive a bound on the size of consensus segments. As show-case applications, we investigate a yeast transcriptome and show that consensus segments provide a robust means of identifying transcriptomic units. This approach is particularly suited for dense transcriptomes with polycistronic transcripts, operons, or a lack of separation between transcripts. As a second application, we demonstrate that consensus segmentations can be used to robustly identify growth regimes from sets of replicate growth curves.

High-throughput methods are producing an ever increasing flood of-omics data that yield a more and more detailed and rich genomic annotation. Combining these data into coherently behaving regions lies at the heart of functional genome annotation efforts. The segmentation problem, which addresses the task of subdividing an ordered sequence of data into homogeneous, approximately constant intervals, therefore has rapidly gained practical importance in computational biology, with a strong emphasis on multi-dimensional data tracks. We suggest a new segmentation method based on decomposition thresholding, and local optimum differentiation, which detects significant breakpoints in the data to identify segment boundaries.