A Matrix Approach to Implicit Relationship Finding in Large-Scale Knowledge Bases

Relationships between entities in a Knowledge Base (KB) are not always explicitly expressed. In addition, entities may implicitly exist within explicit ones. These phenomena are very common when it comes to large-scale KBs. Finding implicit relationships in a KB can make the original KB more meaningful and enhance its potential in real world applications. In this paper, we focus on the problem of finding implicit-relationship networks in large-scale KBs. Since a network can be mathematically expressed as a matrix, the process of reasoning for implicit relationship finding can be transformed to matrix computation. Considering that there are many advantages for matrix computation instead of logic based and graph based reasoning (such as scalability for storing and processing relationships), by realizing the mathematical nature of KBs, we use matrix transformation and computation to investigate the problem of implicit relationship finding. We give several illustrative real world examples using large-scale KBs to validate this framework. In addition, we also investigate the potential problems of scalability on matrix storage, as well as the cost for computation and time. Based on the proposed approach and the consideration on the scalability issue, we develop the MIRF and MIRF-L algorithms which can efficiently process this kind of problem if the rules in concrete cases can be clearly expressed.