document: Fragments of order High-dimensional collections of 0 -- 1 data occur in many applications . The attributes in such data sets are typically considered to be unordered . However , in many cases there is a natural total or partial order ≺ underlying the variables of the data set . Examples of variables for which such orders exist include terms in documents , courses in enrollment data , and paleontological sites in fossil data collections . The observations in such applications are flat , unordered sets ; however , the data sets respect the underlying ordering of the variables . By this we mean that if A ≺ B ≺ C are three variables respecting the underlying ordering ≺ , and both of variables A and C appear in an observation , then , up to noise levels , variable B also appears in this observation . Similarly , if A1 ≺ A2 ≺ ... ≺ Al-1 ≺ Ai is a longer sequence of variables , we do not expect to see many observations for which there are indices i ( j ( k such that Ai and Ak occur in the observation but Aj does not . In this paper we study the problem of discovering fragments of orders of variables implicit in collections of unordered observations . We define measures that capture how well a given order agrees with the observed data . We describe a simple and efficient algorithm for finding all the fragments that satisfy certain conditions . We also discuss the sometimes necessary postprocessing for selecting only the best fragments of order . Also , we relate our method with a sequencing approach that uses a spectral algorithm , and with the consecutive ones problem . We present experimental results on some real data sets ( author lists of database papers , exam results data , and paleontological data ) .
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