Adapting Stochastic Block Models to Power-Law Degree Distributions

Area of Science:

• Network Science
• Statistical Modeling
• Data Analysis

Background:

• Stochastic Block Models (SBMs) are standard for network community detection.
• Real-world networks often exhibit complex features like power-law degree distributions, which standard SBMs cannot handle.
• Existing models struggle to accurately represent the scale-free properties of many real-world networks.

Purpose of the Study:

• To propose a novel variant of SBM, the Power-Law Degree SBM (PLD-SBM).
• To explicitly model the power-law degree characteristic found in real-world networks.
• To improve the accuracy of community detection in complex networks.

Main Methods:

• Introduced degree decay variables into the SBM framework.
• Utilized an exponential prior to preserve scale-free network features.
• Employed variational E-step inference to correct SBM biases.

Main Results:

• The proposed PLD-SBM approximately preserves the scale-free feature of real networks.
• PLD-SBM corrects inherent biases in standard SBMs through degree decay factors.
• Experiments on synthetic and real-world datasets (Adolescent Health Data, political blogs network) demonstrated superior cluster prediction accuracy.

Conclusions:

• PLD-SBM is an effective extension of SBM for networks with power-law degree distributions.
• The model enhances community detection accuracy by accounting for varying node degrees.
• PLD-SBM offers a more robust approach to analyzing complex network structures.