Partitioning large data to scale up lattice-based algorithm

Partitioning large data to scale up lattice-based algorithm...

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Partitioning large data to scale up lattice-based algorithm Huaiguo Fu, Engelbert Mephu Nguifo CRIL-CNRS FRE2499, Universit´e d’Artois Rue de l’universit´e SP 16, 62307 Lens cedex. France fu,mephu @cril.univ-artois.fr Abstract Concept lattice is an effective tool and platform for data analysis and knowledge discovery such as classification or association rules mining. The lattice algorithm to build for- mal concepts and concept lattice plays an essential role in the application of concept lattice. We propose a new effi- cient scalable lattice-based algorithm: ScalingNextClosure to decompose the search space of any huge data in some partitions, and then generate independently concepts (or closed itemsets) in each partition. The experimental results show the efficiency of this algorithm. 1. Introduction Concept lattice structure [6, 8] has shown to be an ef- fective tool for data analysis and knowledge discovery. It has been applied to machine learning, data mining and in- formation retrieval, etc. Concept lattice can derive concep- tual structures from data. It studies how objects can be hier- archically grouped together according to their common at- tributes. It can generate formal concepts from the data to reveal the relations between objects and attributes. So con- cept lattice is a natural framework for data mining. Its char- acteristics are very suitable for data mining. For example, a closed itemset (or the intent of a formal concept) is a max- imal itemset for association rules [11]. So the problem of finding frequent itemsets from data for association rules can be reduced to finding frequent closed itemsets with closed itemset lattice or concept lattice. The lattice algorithm to build formal concepts and con- cept lattice plays an essential role in the application of con- cept lattice. Several algorithms were proposed to generate concepts or concept lattices of a data context, for exam- ple: Bordat [2], Ganter (NextClosure algorithm) [5], Chein [3], Norris [9], Godin [7] and Nourine [10], etc. Experimen- tal comparisons of performance of existing algorithms show that NextClosure algorithm is the best for large and dense data [8, 4]. But the problem is that it still takes very high expensive time cost to deal with huge data. So in this pa- per, we propose a new efficient lattice-based algorithm Scal- ingNextClosure that decomposes the search space of any huge data in some partitions, and then generates indepen- dently concepts or closed itemsets in each partition. The new algorithm is a kind of decomposition algorithm of concept lattice. All existing decomposition algorithms for generating concept lattices use an approach of context decomposition, that are different from ours. Our new algo- rithm uses a new method to decompose the search space. It can freely decompose the search space in any set of parti- tions if there are concepts in each partition, and then gener- ate them independently in each partition. So this algorithm can be used to analyze huge data and to generate formal concepts. Moreover for this algorithm, each partition only
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