Functional dependencies in relational databases: a lattice point of view
Discrete Applied Mathematics - Special issue on combinatorial problems in databases
Horn approximations of empirical data
Artificial Intelligence
Efficient mining of association rules using closed itemset lattices
Information Systems
Generating non-redundant association rules
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
A partition-based approach towards constructing Galois (concept) lattices
Discrete Mathematics
Fast Algorithms for Mining Association Rules in Large Databases
VLDB '94 Proceedings of the 20th International Conference on Very Large Data Bases
Computations with Finite Closure Systems and Implications
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
Minimum covers in the relational database model (Extended Abstract)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Mining Bases for Association Rules Using Closed Sets
ICDE '00 Proceedings of the 16th International Conference on Data Engineering
Theory of Relational Databases
Theory of Relational Databases
Translating between Horn representations and their characteristic models
Journal of Artificial Intelligence Research
A parallel algorithm for lattice construction
ICFCA'05 Proceedings of the Third international conference on Formal Concept Analysis
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Formal concept analysis (FCA) has a significant appeal as a formal framework for knowledge discovery not least because of the mathematical tools it provides for a range of data manipulations such as splits and merges. We study the computation of the canonical basis of a context starting from the bases of two apposed subcontexts, called factors. Improving on a previous method of ours, we provide here a deeper insight into its pivotal implication family and show it represents a relative basis. Further structural results allow for more efficient computation of the global basis, in particular, the relative one admits, once added to factor bases, an inexpensive reduction. A method implementing the approach as well as a set of further combinatorial optimizations is shown to outperform NextClosure on at least one dataset.