# Structure Amplification on Multi-layer Stochastic Block Models

arXiv: https://arxiv.org/abs/2108.00127 · HTML: https://mlsanity.com/paper/2108.00127/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 38 references that are in the map.
- First posted on arXiv 31 Jul 2021.

## Builds on (most cited first, 10 of 10)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Knowledge Graph Embedding for Link Prediction: A Comparative Analysis](https://mlsanity.com/paper/2002.00819/) (2020)
- [Single Image Reflection Removal through Cascaded Refinement](https://mlsanity.com/paper/1911.06634/) (2019)
- [Heat kernel based community detection](https://mlsanity.com/paper/1403.3148/) (2014)
- [Strong Consistency, Graph Laplacians, and the Stochastic Block Model](https://mlsanity.com/paper/2004.09780/) (2020)
- [Hidden Community Detection in Social Networks](https://mlsanity.com/paper/1702.07462/) (2017)
- [Revealing Multiple Layers of Hidden Community Structure in Networks](https://mlsanity.com/paper/1501.05700/) (2015)
- [Hidden Community Detection on Two-layer Stochastic Models: a Theoretical Perspective](https://mlsanity.com/paper/2001.05919/) (2020)
- [Local Network Community Detection with Continuous Optimization of Conductance and Weighted Kernel K-Means](https://mlsanity.com/paper/1601.05775/) (2016)
- [Link Prediction and Unlink Prediction on Dynamic Networks](https://mlsanity.com/paper/2101.06919/) (2021)

## Abstract (arXiv)

Much of the complexity of social, biological, and engineered systems arises from a network of complex interactions connecting many basic components. Network analysis tools have been successful at uncovering latent structure termed communities in such networks. However, some of the most interesting structure can be difficult to uncover because it is obscured by the more dominant structure. Our previous work proposes a general structure amplification technique called HICODE that uncovers many layers of functional hidden structure in complex networks. HICODE incrementally weakens dominant structure through randomization allowing the hidden functionality to emerge, and uncovers these hidden structure in real-world networks that previous methods rarely uncover. In this work, we conduct a comprehensive and systematic theoretical analysis on the hidden community structure. In what follows, we define multi-layer stochastic block model, and provide theoretical support using the model on why the existence of hidden structure will make the detection of dominant structure harder compared with equivalent random noise. We then provide theoretical proofs that the iterative reducing methods could help promote the uncovering of hidden structure as well as boosting the detection quality of dominant structure.