On Investigating Both Effectiveness and Efficiency of Embedding Methods in Task of Similarity Computation of Nodes in Graphs

Abstract

One of the important tasks in a graph is to compute the similarity between two nodes; link-based similarity measures (in short, similarity measures) are well-known and conventional techniques for this task that exploit the relations between nodes (i.e., links) in the graph. Graph embedding methods (in short, embedding methods) convert nodes in a graph into vectors in a low-dimensional space by preserving social relations among nodes in the original graph. Instead of applying a similarity measure to the graph to compute the similarity between nodes a and b, we can consider the proximity between corresponding vectors of a and b obtained by an embedding method as the similarity between a and b. Although embedding methods have been analyzed in a wide range of machine learning tasks such as link prediction and node classification, they are not investigated in terms of similarity computation of nodes. In this paper, we investigate both effectiveness and efficiency of embedding methods in the task of similarity computation of nodes by comparing them with those of similarity measures. To the best of our knowledge, this is the first work that examines the application of embedding methods in this special task. Based on the results of our extensive experiments with five well-known and publicly available datasets, we found the following observations for embedding methods: (1) with all datasets, they show less effectiveness than similarity measures except for one dataset, (2) they underperform similarity measures with all datasets in terms of efficiency except for one dataset, (3) they have more parameters than similarity measures, thereby leading to a time-consuming parameter tuning process, (4) increasing the number of dimensions does not necessarily improve their effectiveness in computing the similarity of nodes.