document: Nestedness and segmented nestedness Consider each row of a 0-1 dataset as the subset of the columns for which the row has an 1 . Then a dataset is nested , if for all pairs of rows one row is either a superset or subset of the other . The concept of nestedness has its origins in ecology , where approximate versions of it has been used to model the species distribution in different locations . We argue that nestedness and its extensions are interesting properties of datasets , and that they can be applied also to domains other than ecology . We first define natural measures of nestedness and study their properties . We then define the concept of k-nestedness : a dataset is ( almost ) k-nested if the set of columns can be partitioned to k parts so that each part is ( almost ) nested . We consider the algorithmic problems of computing how far a dataset is from being k-nested , and for finding a good partition of the columns into k parts . The algorithms are based on spectral partitioning , and scale to moderately large datasets . We apply the methods to real data from ecology and from other applications , and demonstrate the usefulness of the concept .
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