Liu Shihu, Liu Yingjie, Yang Chunsheng, Deng Li
School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650504, China.
Entropy (Basel). 2022 Aug 19;24(8):1154. doi: 10.3390/e24081154.
Many similarity measure algorithms of nodes in weighted graph data have been proposed by employing the degree of nodes in recent years. Despite these algorithms obtaining great results, there may be still some limitations. For instance, the strength of nodes is ignored. Aiming at this issue, the relative entropy of the distance distribution based similarity measure of nodes is proposed in this paper. At first, the structural weights of nodes are given by integrating their degree and strength. Next, the distance between any two nodes is calculated with the help of their structural weights and the Euclidean distance formula to further obtain the distance distribution of each node. After that, the probability distribution of nodes is constructed by normalizing their distance distributions. Thus, the relative entropy can be applied to measure the difference between the probability distributions of the top important nodes and all nodes in graph data. Finally, the similarity of two nodes can be measured in terms of this above-mentioned difference calculated by relative entropy. Experimental results demonstrate that the algorithm proposed by considering the strength of node in the relative entropy has great advantages in the most similar node mining and link prediction.
近年来，通过利用节点的度，人们提出了许多加权图数据中节点的相似度度量算法。尽管这些算法取得了很好的效果，但仍可能存在一些局限性。例如，节点的强度被忽略了。针对这一问题，本文提出了基于距离分布的节点相似度度量的相对熵。首先，通过综合节点的度和强度来给出节点的结构权重。其次，借助它们的结构权重和欧几里得距离公式计算任意两个节点之间的距离，以进一步获得每个节点的距离分布。之后，通过对节点的距离分布进行归一化来构建节点的概率分布。因此，可以应用相对熵来度量图数据中最重要节点的概率分布与所有节点的概率分布之间的差异。最后，可以根据通过相对熵计算出的上述差异来度量两个节点的相似度。实验结果表明，在相对熵中考虑节点强度所提出的算法在最相似节点挖掘和链接预测方面具有很大优势。
