On the irredundant generation of knowledge spaces
Journal of Mathematical Psychology
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
A partition-based approach towards constructing Galois (concept) lattices
Discrete Mathematics
Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
MapReduce: simplified data processing on large clusters
OSDI'04 Proceedings of the 6th conference on Symposium on Opearting Systems Design & Implementation - Volume 6
A local approach to concept generation
Annals of Mathematics and Artificial Intelligence
DEXA '07 Proceedings of the 18th International Conference on Database and Expert Systems Applications
Distributed Algorithm for Computing Formal Concepts Using Map-Reduce Framework
IDA '09 Proceedings of the 8th International Symposium on Intelligent Data Analysis: Advances in Intelligent Data Analysis VIII
Analyzing Social Networks Using FCA: Complexity Aspects
WI-IAT '09 Proceedings of the 2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology - Volume 03
An Improved Incremental Algorithm for Constructing Concept Lattices
WCSE '09 Proceedings of the 2009 WRI World Congress on Software Engineering - Volume 04
Twister: a runtime for iterative MapReduce
Proceedings of the 19th ACM International Symposium on High Performance Distributed Computing
Two basic algorithms in concept analysis
ICFCA'10 Proceedings of the 8th international conference on Formal Concept Analysis
Efficient mining of association rules based on formal concept analysis
Formal Concept Analysis
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While many existing formal concept analysis algorithms are efficient, they are typically unsuitable for distributed implementation. Taking the MapReduce (MR) framework as our inspiration we introduce a distributed approach for performing formal concept mining. Our method has its novelty in that we use a light-weight MapReduce runtime called Twister which is better suited to iterative algorithms than recent distributed approaches. First, we describe the theoretical foundations underpinning our distributed formal concept analysis approach. Second, we provide a representative exemplar of how a classic centralized algorithm can be implemented in a distributed fashion using our methodology: we modify Ganter's classic algorithm by introducing a family of $\mbox{MR}^\star$ algorithms, namely MRGanter and MRGanter+ where the prefix denotes the algorithm's lineage. To evaluate the factors that impact distributed algorithm performance, we compare our $\mbox{MR}^{*}$ algorithms with the state-of-the-art. Experiments conducted on real datasets demonstrate that MRGanter+ is efficient, scalable and an appealing algorithm for distributed problems.