Eliminating Structural Redundancy Based on Super-node Theory
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摘要: 本体作为指导知识图谱数据构建的上层结构，在知识图谱技术中具有重要意义。本体在发展的过程中会形成结构上的冗余。现有的本体消冗方法无法处理含有等价关系的本体结构，只能针对单一类属关系进行冗余的检测与消除。该文针对含有等价关系的本体提出一种基于超节点理论的消冗算法，首先将相互等价的节点看作超节点，消除单一类属关系之间的的冗余；然后还原等价节点，消除等价关系与类属关系之间的冗余。在计算机生成网络和真实网络上的实验和分析表明，该算法能够准确识别关系冗余，具有较高的稳定性和综合性能。Abstract: Ontology, as the superstructure of knowledge graph, has great significance in knowledge graph domain. In general, structural redundancy may arise in ontology evolution. Most of existing redundancy elimination algorithms focus on transitive redundancies while ignore equivalent relations. Focusing on this problem, a redundancy elimination algorithm based on super-node theory is proposed. Firstly, the nodes equivalent to each other are considered as a super-node to transfer the ontology into a directed acyclic graph. Thus the redundancies relating to transitive relations can be eliminated by existing methods. Then equivalent relations are restored, and the redundancies between equivalent and transitive relations are eliminated. Experiments on both synthetic dynamic networks and real networks indicate that the proposed algorithm can detect redundant relations precisely, with better performance and stability compared with the benchmarks.
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Key words:
- Ontology /
- Equivalent relation /
- Super node /
- Relation redundancy /
- Transitive relationship
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表 1 消冗算法伪代码
输入：本体网络${\text{M}}$ 输出：消冗后的本体网络${\text{R}}$ (1) /*超节点的转化*/ (2) ${\text{Me}} \leftarrow $$t({\text{M}} \!\otimes\! {{\text{M}}^{\rm{T}}})$/*抽取本体网络中的等价关系，存入${\text{Me}}$*/
(3) ${{\rm Mr}_{ij}} \leftarrow $${\rm{bool}}\left(\sum\nolimits_k {({M_{ik}} \cdot {\rm{M}}{{\rm{e}}_{kj}}} + {\rm{M}}{{\rm{e}}_{ik}} \cdot {M_{kj}})\right) - {\rm{M}}{{\rm{e}}_{ij}}$/*将等价 关系转化为类属关系*/(4) /*传递冗余的消除*/ (5) ${\text{R}} \leftarrow {\text{Mr}}$ (6) $D[V\;],I[V\;] = \rm{FEDRR} (G(V,E))$/*用FEDRR算法求出网络中 每个节点的孩子集合$D[V\;]$与后代集合$I[V\;]$*/ (7) for all $v \in V\;$ do (8) for all $s \in I[v] \cap D[v]$ do (9) delete $(s,v,R)$/*置${R_{sv}} = 0$*/ (10) end for (11) end for (12) /*等价-类属冗余的消除*/ (13) ${\text{E}} \leftarrow $${\rm{Equiv(}}{\text{Me}}{\rm{)}}$/*$E$每行表示一种等价关系*/ (14) ${S_{ij}} = {\rm{bool}}\left(\sum\nolimits_k {{E_{ik}} \cdot {R_{jk}} - 1} \right)$/*构造同源冗余*/ (15) ${T_{ij}} = {\rm{bool}}\left(\sum\nolimits_k {{E_{ik}} \cdot {R_{kj}} - 1} \right)$/*构造同目标冗余*/ (16) for $i$ from 1 to n do/*去除矩阵中等价关系与偏序关系之间 的冗余，n是矩阵大小*/ (17) for $j$ from 1 to n do (18) if ${S_{ij}} > 1$ then/*去除同源冗余*/ (19) $\rm{Elim} \_Line({\text{E}}.{\rm{row}} (i),{\text{R}}.{\rm row}(j))$/*只保留节点$j$到 超节点$i$的一条边*/ (20) end if (21) if ${T_{ij}} > 1$ then/*去除同目标冗余*/ (22) ${\rm{Elim\_Line}}({\text{E}}.{\rm{row}}(i),{\text{R}}.{\rm column}(j))$/*只保留超节点 $i$到节点$j$的一条边*/ (23) end if (24) end for (25) end for (26) /*恢复等价关系*/ (27) ${R_{ij}} \leftarrow {\rm{bool}}({R_{ij}} + {\rm{M}}{{\rm{e}}_{ij}})$ 
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表 2 随机生成网络配置参数
网络规模$N$ 网络个数$n$ 最大等价节点对数 冗余边数 配置1 1000 100 500 (100,1000) 配置2 (100,1000) 100 0.5$N$ (1,$N$)
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