J. Wijsen, R. Ng, and T. Calders. Discovering roll-up dependencies. In Proc. ACMSIGKDD Int. Conf. Knowledge Discovery and Data Mining, pages 213--222, San Diego, CA, 1999. 13  Home/Search   Document Details and Download   Summary   Related Articles   Check

....us to use Boolean operators between attributes. Boolean dependencies can be extended from simple equality comparison of values to compare whether the values belong to the same equivalence class. This makes it possible to define constraints between value groups, e.g. age age group. Wijsen et al. [WNC99] study generalising temporal dependencies for non temporal dimensions. They generalise temporal functional dependencies into rollup dependencies and illustrate their usability in conceptual modelling and data mining. The rollup dependencies can be used in modelling generalisation hierarchies if ....

Wijsen, J., Ng, R., and Calders, T.: Discovering roll-up dependencies, The Fifth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD

....by a domain expert or automatically generated by a clustering algorithm. Although the system was originally developed to mine relational databases, rather than OLAP, multidimensional ones, it can be used to mine multidimensional data. Another system integrating data mining and OLAP is proposed by [20]. This system discovers Roll Up Dependencies, which are a kind of generalization of functional dependencies for hierarchical attributes. Yet another related work is described by [12] In this project, if the data cube already contains relevant precomputed aggregations, they are used to render ....

Wijsen, J.; Raymond, T.N.; Calders, T. (1999) Discovering Roll-Up Dependencies. Proc. 5th ACM SIGKDD Int. Conf. Knowledge Discovery & Data Mining, 213-222. ACM, 1999.

....surface can be partitioned into continents, countries, states, and so on. Also recently, there has been a lot of research focusing almost exclusively on time granularity [3] Demonstrably, time granularity has useful applications in temporal dependency theory [19, 21, 20] and temporal data mining [4, 24]. Clearly, generalization hierarchies in OLAP serve a role similar to that of time granularity in temporal databases. A natural and important question then is: what precisely are the differences commonalities (if any) between both concepts This basic question has many facets, including the ....

....selected from I without replacement, satisfy t 1 Q;U t 2 , given they already satisfy t 1 P;U t 2 . The task then is to mine RUDs that satisfy a certain threshold confidence. We have finished a C implementation for mining RUDs. The first experiments are promising, and are reported in [24]. More details about the complexity of mining RUDs can be found in [22] 4 Adding Inequality 4.1 Introductory Examples Recall that a fiscal year runs from July 1 to June 30. Clearly, civil) years and fiscal years are not comparable by , i.e. YEAR k FISCALYEAR. Some weeks span two civil years, ....

J. Wijsen, R. Ng, and T. Calders. Discovering roll-up dependencies. In Proc. ACMSIGKDD Int. Conf. Knowledge Discovery and Data Mining, pages 213--222, San Diego, CA, 1999. 13

....schemas of T WEEK L LOCATION ordered by Theta . For example, D MONTH D YEAR L VORONOI is not irreducible, because MONTH YEAR; the same partition is defined by the irreducible generalization schema D MONTH L VORONOI . The proof of the following theorem can be found in [22]: Theorem 1 Let S be a schema. The set of all irreducible generalization schemas of S, ordered by Theta , is a complete lattice. The set of all generalization schemas of S, ordered by Theta , will be called the roll up lattice of S. A roll up lattice is shown in Figure 3. It should be stressed ....

....A sound and complete axiomatization for reasoning about RUDs is given next. Definition 5 The axioms for reasoning about RUDs are as follows (P; Q; R are generalization schemas over a given schema) RUD P Q if P Theta Q (2) P Q RUD PR QR (3) P Q and Q R RUD P R (4) In [22], we proved the following result. Theorem 2 Let Sigma be a set of RUDs and let oe be a single RUD (all over the same schema) Sigma RUD oe iff Sigma j= RUD oe. The axioms are almost Armstrong s axioms [1] the only difference is that axiom (2) refers to Theta , whereas the corresponding ....

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J. Wijsen and R. Ng. Discovering roll-up dependencies. Technical report, The University of British Columbia, Dept. of Computer Science, 1998. Also available at http://www.uia.ua.ac.be/u/jwijsen/.

.... the a priori algorithm has subsequently been generalized to levelwise search [10] As a matter of fact, the a priori trick is applicable in many other data mining tasks, such as the discovery of keys, inclusion dependencies, functional dependencies, episodes [9, 10] and other kinds of rules [15]. With the advent of data mining primitives in query languages, it is interesting and important to explore to which extent the a priori technique can be incorporated into next generation query optimizers. During an invited tutorial at ICDT 97, Heikki Mannila raised an interesting and important ....

J. Wijsen, R. Ng, and T. Calders. Discovering roll-up dependencies. In Proc. ACM SIGKDD Int. Conf. Knowledge Discovery and Data Mining, pages 213--222, San Diego, CA, 1999. 12

....support of the binary association rule 1 2 1 4 is 4 7 . The con dence is 4 5 . 2 There are multiple similarities between association rules and binary association rules. Both rules give frequent dependencies that hold within the tuples themselves. Unlike for example roll up dependencies [16] or approximate dependencies [9] 10] that describe relations between di erent tuples, association rules and binary association rules relate properties of attributes. In association rule mining, frequent itemsets can be considered as a conjunction of unary predicates. In this setting, binary ....

J. Wijsen, R. Ng, and T. Calders. Discovering roll-up dependencies. In Proc. ACM SIGKDD , 1999. 21 A Approximation of the number of partial orders

....2 3 . The con dence is 1. 3 r(i) denotes the i th component of r; e.g. a; b; c) 2) b. There are multiple similarities between association rules and binary association rules. Both rules give frequent dependencies that hold within the tuples themselves. Unlike for example roll up dependencies [9], that describe relations between di erent tuples, association rules and binary association rules relate properties of attributes. In association rule mining, frequent itemsets can be considered as a conjunction of unary predicates. In this setting, binary association rules are a straightforward ....

J. Wijsen, R. Ng, and T. Calders. Discovering roll-up dependencies. In Proc. ACM SIGKDD , 1999.

....focused on one particular generalization hierarchy called time granularity [3] This hierarchy captures the partitioning of years into months, months into days, and so on. Demonstrably, time granularity has useful applications in temporal dependency theory [16, 17, 18] and temporal data mining [4, 20]. This focus on temporal aspects raises some interesting and important questions concerning the peculiarity of the time dimension. Does temporal dependency theory carry over to non temporal dimensions, like space What is so typical about the temporal dimension that justifies its special ....

....every month belongs to a single year. We also say that a month rolls up to its year. On the other hand, WEEK and MONTH are not comparable by because months do not divide evenly into weeks, nor vice versa. The level PRICE BRACKET denotes a set of consecutive price intervals, for example, 1 10] [11 20], 21 30] and so on. We have PRICE PRICE BRACKET, and a price rolls up to its containing price bracket. Roll up dependencies (RUDs) extend functional dependencies (FDs) by allowing attributes to be compared for equality at a specified level. For example, we may find that the tax rate does ....

[Article contains additional citation context not shown here]

J. Wijsen, R. Ng, and T. Calders. Discovering roll-up dependencies. In Proc. ACM SIGKDD Int. Conf. Knowledge Discovery and Data Mining, San Diego, CA, 1999.

....contains A L and A L 0 with L 6= L 0 then L k L 0 . 1 For example, D MONTH D YEAR C REGION is not irreducible, because MONTH YEAR; the same partitioning is defined by the irreducible generalization schema D MONTH C REGION . The proof of the following theorem can be found in [19]. Theorem 1. Let S be a schema. The set of all irreducible generalization schemas of S, ordered by Theta , is a complete lattice. The set of all irreducible generalization schemas of S, ordered by Theta , is called the roll up lattice of S. A roll up lattice is shown in Fig. 3. Our notion of ....

....A sound and complete axiomatization for reasoning about RUDs is given next. Definition 5. The axioms for reasoning about RUDs are as follows (P; Q; R are generalization schemas over a given schema) RUD P Q if P Theta Q (3) P Q RUD PR QR (4) P Q and Q R RUD P R (5) In [19], we proved the following result. Theorem 2. Let Sigma be a set of RUDs and let oe be a single RUD (all over the same schema) Sigma RUD oe iff Sigma j= RUD oe. 1 We write L k L 0 iff neither L L 0 nor L 0 L. Gamma Gamma Gamma Gamma Gamma Gamma Gamma Gamma ....

J. Wijsen and R. Ng. Discovering roll-up dependencies. Technical report, The University of British Columbia, Dept. of Computer Science, 1998. Also available at http://www.uia.ua.ac.be/u/jwijsen/.

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