Relative Entropy of Distance Distribution Based Similarity Measure of Nodes in Weighted Graph Data

• Published in: Entropy (Basel, Switzerland) Switzerland), 2022-08, Vol.24 (8), p.1154
• Main Authors: Liu, Shihu, Liu, Yingjie, Yang, Chunsheng, Deng, Li
• Format: Article
• Language: English
• Subjects: Algorithms; distance distribution; Distribution (Probability theory); Entropy; Euclidean geometry; link prediction; Mathematical analysis; Mining; Nodes; relative entropy; Similarity; similarity measure; Similarity measures; weighted graph data
• ISSN: 1099-4300; 1099-4300
• 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 d 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.