属性拓扑的并行概念计算算法

Parallel Concept Computing Based on Bottom-Up Decomposition of Attribute Topology

随着并行计算时代的到来,形式概念的并行计算成为形式概念分析领域的研究热点之一.以属性拓扑为基本表示形式,通过属性拓扑的图特性进行并行概念计算算法设计.首先,根据属性拓扑中属性的伴生关系对属性拓扑进行自下而上的分解,将一个整体拓扑分解为若干个子拓扑;其次,根据属性间的相关关系去除各子拓扑间的概念耦合,保证不同子拓扑在概念计算层面的各自独立性,以避免后期合并运算的大规模时间消耗;最后,在各子拓扑上进行概念计算,并将各子拓扑概念直接累加可得原始背景的全部概念集合.实验结果表明:所提方法不但可以无重复地计算全部概念,而且可以根据硬件平台情况提高计算效率,减少概念计算所需时间.

With the arrival of parallel computing era, parallel computing of formal concepts has become a hot issue in the field of formal concept analysis. This paper proposes a parallel concept computing algorithm by means of the graph characteristics of an attribute topology used in representing formal context. First, according to the parent relations, the bottom-up decomposition of attribute topology is conducted to generate sub-topologies. Then, concept-couplings among sub-topologies are removed based on the correlations in attribute-pairs in order to ensure the independence of the sub-topologies when carrying out concept computing and then to avoid large time consumption of the merging operation in later stage. Finally, all the concepts without repetition can be calculated by accumulating directly all the concept-sets eomputed in different sub-topologies. The experiment shows that the approach proposed in this paper can not only obtain all the concepts without repetition, but also improve the computational efficiency in accordance with the hardware platform and reduce the time required for the concept calculation.