[Paper Review] Detecting Communities in Complex Networks using an Adaptive Genetic Algorithm and node similarity-based encoding

Sajjad Hesamipour, Mohammad Ali Balafar+1 more|arXiv (Cornell University)|Jan 24, 2022

Complex Network Analysis Techniques4 citations

TL;DR

This paper proposes an adaptive genetic algorithm with a novel MST-based node similarity encoding for community detection in complex networks. By leveraging similarity-weighted spanning trees and an adaptive sine-based mutation function, the method improves convergence and avoids invalid partitions, outperforming existing GA-based methods and matching state-of-the-art algorithms on NMI and modularity in empirical evaluations.

ABSTRACT

Detecting communities in complex networks can shed light on the essential characteristics and functions of the modeled phenomena. This topic has attracted researchers of various fields from both academia and industry. Among the different methods implemented for community detection, Genetic Algorithms (GA) have become popular recently. Considering the drawbacks of the currently used locus-based and solution-vector-based encodings to represent the individuals, in this paper, we propose (1) a new node similarity-based encoding method to represent a network partition as an individual named MST-based. Then, we propose (2) a new Adaptive Genetic Algorithm for Community Detection, along with (3) a new initial population generation function, and (4) a new adaptive mutation function called sine-based mutation function. Using the proposed method, we combine similarity-based and modularity-optimization-based approaches to find the communities of complex networks in an evolutionary framework. Besides the fact that the proposed representation scheme can avoid meaningless mutations or disconnected communities, we show that the new initial population generation function, and the new adaptive mutation function, can improve the convergence time of the algorithm. Experiments and statistical tests verify the effectiveness of the proposed method compared with several classic and state-of-the-art algorithms.

Motivation & Objective

• To address the limitations of traditional locus-based and solution-vector-based encodings in genetic algorithm (GA)-based community detection, which can lead to meaningless mutations or disconnected communities.
• To develop a new individual representation method using node similarity and minimum spanning trees (MST) to reduce search space and improve solution quality.
• To design an adaptive mutation function that dynamically adjusts mutation probability based on edge depth in the MST to enhance convergence speed and solution accuracy.
• To introduce a new initial population generation function that enhances solution diversity and convergence time in the evolutionary process.
• To combine modularity optimization with similarity-based measures to balance scalability and accuracy in community detection.

Proposed method

• Proposes an MST-based encoding scheme that constructs a weighted network using node similarity measures and encodes the MST's edges into a binary chromosome, where 0 and 1 represent edge absence or presence.
• Introduces a new initial population generation function that leverages similarity-based clustering to produce high-quality, diverse initial solutions, accelerating convergence.
• Develops a sine-based adaptive mutation function that varies mutation probability per gene based on the depth of its corresponding edge in the MST, promoting exploration in deeper edges.
• Employs a hybrid fitness function combining modularity and node similarity to guide the evolutionary process toward high-quality community partitions.
• Uses standard GA operations—selection, crossover, and adaptive mutation—within the novel encoding framework to optimize community detection.
• Applies the Nemenyi test to statistically validate performance against state-of-the-art algorithms on real-world and synthetic datasets.

Experimental results

Research questions

• RQ1 Can a node similarity-based encoding scheme reduce invalid or disconnected community partitions in GA-based community detection compared to locus-based or solution-vector-based encodings?
• RQ2 How does the proposed adaptive sine-based mutation function improve convergence speed and solution quality in community detection?
• RQ3 To what extent does the new initial population generation function enhance the quality and diversity of initial solutions, leading to faster convergence?
• RQ4 Does combining modularity optimization with similarity-based measures yield better performance than relying solely on modularity in complex network community detection?
• RQ5 How does the proposed method compare to state-of-the-art algorithms in terms of NMI and modularity across real-world and synthetic networks?

Key findings

• The proposed method achieved significantly better NMI and modularity scores than several GA-based algorithms, including GA-net and WMW, with a p-value indicating statistical significance.
• The Nemenyi test revealed a significant difference between the proposed method and GA-net (distance = 8.4167) on synthetic NMI, and with WMW (distance = 9.8) on real-world NMI, both exceeding the critical distance of 8.39 and 9.273 respectively.
• On real-world datasets, the proposed method showed a significant difference from GA-net (7.11) and WMW (7.44) in modularity, both exceeding the critical distance of 6.76.
• The method outperformed or matched the performance of top algorithms like Louvain, Leiden, and EdMot in both NMI and modularity, with no significant difference detected in synthetic modularity results.
• The adaptive sine-based mutation and improved initial population generation contributed to faster convergence and higher-quality solutions, as evidenced by reduced search space and enhanced fitness progression.
• Statistical analysis confirmed that the proposed method is comparable to or superior to state-of-the-art methods, particularly in NMI, with average NMI values significantly higher than WMW (0.526) and CACD (0.826).