Bias-adjusted spectral clustering in multi-layer stochastic block models.

Area of Science:

• Network Science
• Statistical Modeling
• Bioinformatics

Background:

• Community structure estimation is challenging in sparse multi-layer networks.
• Individual layers may lack sufficient signal for robust analysis.
• Aggregating information across layers is key to overcoming sparsity.

Purpose of the Study:

• To develop a method for estimating common community structures in multi-layer stochastic block models.
• To demonstrate the effectiveness of aggregating signal using sum-of-squared adjacency matrices.
• To address the challenges posed by very sparse network layers.

Main Methods:

• Utilizing sum-of-squared adjacency matrices to aggregate signal across network layers.
• Implementing a novel bias-removal step to counteract noise in sparse regimes.
• Developing new tail probability bounds for matrix linear combinations and quadratic forms.

Main Results:

• The proposed method effectively estimates community structures even in very sparse multi-layer networks.
• The bias-removal step is shown to be essential for performance in sparse scenarios.
• Novel theoretical bounds provide analytical support for the method's efficacy.

Conclusions:

• Summing squared adjacency matrices is a viable strategy for signal aggregation in sparse multi-layer networks.
• Bias removal is critical for accurate community detection when noise dominates signal.
• The method shows promise for applications in gene co-expression network analysis.