Mining association rules between sets of items in large databases
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
Privacy-preserving data mining
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
A condensed representation to find frequent patterns
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Discovering Frequent Closed Itemsets for Association Rules
ICDT '99 Proceedings of the 7th International Conference on Database Theory
A Tight Upper Bound on the Number of Candidate Patterns
ICDM '01 Proceedings of the 2001 IEEE International Conference on Data Mining
Concise Representation of Frequent Patterns Based on Disjunction-Free Generators
ICDM '01 Proceedings of the 2001 IEEE International Conference on Data Mining
Approximation of Frequency Queris by Means of Free-Sets
PKDD '00 Proceedings of the 4th European Conference on Principles of Data Mining and Knowledge Discovery
Mining All Non-derivable Frequent Itemsets
PKDD '02 Proceedings of the 6th European Conference on Principles of Data Mining and Knowledge Discovery
Why to Apply Generalized Disjunction-Free Generators Representation of Frequent Patterns?
ISMIS '02 Proceedings of the 13th International Symposium on Foundations of Intelligent Systems
Concise Representation of Frequent Patterns Based on Generalized Disjunction-Free Generators
PAKDD '02 Proceedings of the 6th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining
Privacy preserving mining of association rules
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
Upper Bound on the Length of Generalized Disjunction-Free Patterns
SSDBM '04 Proceedings of the 16th International Conference on Scientific and Statistical Database Management
Data Mining and Knowledge Discovery
Transaction databases, frequent itemsets, and their condensed representations
KDID'05 Proceedings of the 4th international conference on Knowledge Discovery in Inductive Databases
Key roles of closed sets and minimal generators in concise representations of frequent patterns
Intelligent Data Analysis
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Recent studies demonstrate the usefulness of condensed representations as a semantic compression technique for the frequent itemsets. Especially in inductive databases, condensed representations are a useful tool as an intermediate format to support exploration of the itemset space. In this paper we establish theoretical upper bounds on the maximal size of an itemset in different condensed representations. A central notion in the development of the bounds are the l-free sets, that form the basis of many well-known representations. We will bound the maximal cardinality of an l-free set based on the size of the database. More concrete, we compute a lower bound for the size of the database in terms of the size of the l-free set, and when the database size is smaller than this lower bound, we know that the set cannot be l-free. An efficient method for calculating the exact value of the bound, based on combinatorial identities of partial row sums, is presented. We also present preliminary results on a statistical approximation of the bound and we illustrate the results with some simulations.