In applications such as paleontology and medical genetics the 0-1 data has an underlying unknown order (the ages of the fossil sites, the locations of markers in the genome). The order might be total or partial: for example, two sites in different parts of the globe might be ecologically incomparable, or the ordering of certain markers might be different in different subgroups of the data. We consider the following problem. Given a table over a set of 0-1 variables, find a partial order for the rows minimizing a score function and being as specific as possible. The score function can be, e.g., the number of changes from 1 to 0 in a column (for paleontology) or the likelihood of the marker sequence (for genomic data). Our solution for this task first constructs small totally ordered fragments of the partial order, then finds good orientations for the fragments, and finally uses a simple and efficient heuristic method for finding a partial order that corresponds well with the collection of fragments. We describe the method, discuss its properties, and give empirical results on paleontological data demonstrating the usefulness of the method. In the application the use of the method highlighted some previously unknown properties of the data and pointed out probable errors in the data.
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