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

Masoud Reyhani Hamedani,Sang-Wook Kim

doi:10.3390/app11010162

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.

Highlights

Nowadays, graphs are becoming increasingly important since they are natural representations to encode relational structures in many domains, where nodes represent the domain’s objects and links to their pairwise relationships [1,2,3,4,5,6,7]
In Section 4.2.2, for each dataset, we find the best values of d for which the embedding methods show their highest accuracies in similarity computation of nodes
We apply the similarity measures to our five datasets on eight iterations; for each similarity measure with a dataset, we find out the best iteration on which the similarity measure shows its highest accuracy

Summary

Introduction

Graphs are becoming increasingly important since they are natural representations to encode relational structures in many domains (e.g., app’s function-call diagrams, brain-region functional activities, bio-medical drug molecules, protein interaction networks, citation networks, and social networks), where nodes represent the domain’s objects and links to their pairwise relationships [1,2,3,4,5,6,7]. Computing the similarity score between two nodes based on the graph structure is a fundamental task in a wide range of applications such as recommender systems, spam detection, graph clustering [8,9], web page ranking, citation analysis, social network analysis, k-nearest neighbor search [1,9], synonym expansion (i.e., search engine’s query rewriting and text simplification), and lexicon extraction (i.e., automatically building bilingual lexicons from text corpora) [10].

Methods

Results

Discussion

Conclusion