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ICDE '95 Proceedings of the Eleventh International Conference on Data Engineering
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ADL '00 Proceedings of the IEEE Advances in Digital Libraries 2000
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STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Finding partial orders from unordered 0-1 data
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Efficiently Mining Frequent Closed Partial Orders
ICDM '05 Proceedings of the Fifth IEEE International Conference on Data Mining
Post sequential patterns mining: a new method for discovering structural patterns
Intelligent information processing II
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Discovering Frequent Closed Partial Orders from Strings
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Compressing large boolean matrices using reordering techniques
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Finding Total and Partial Orders from Data for Seriation
DS '08 Proceedings of the 11th International Conference on Discovery Science
Learning to order: a relational approach
MCD'07 Proceedings of the 3rd ECML/PKDD international conference on Mining complex data
Finding trees from unordered 0–1 data
PKDD'06 Proceedings of the 10th European conference on Principle and Practice of Knowledge Discovery in Databases
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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).