# Community Detection in Weighted Multilayer Networks with Ambient Noise

arXiv: https://arxiv.org/abs/2103.00486 · HTML: https://mlsanity.com/paper/2103.00486/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 100 references that are in the map.
- First posted on arXiv 24 Feb 2021.

## Builds on (most cited first, 30 of 30)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Community detection in networks: A user guide](https://mlsanity.com/paper/1608.00163/) (2016)
- [Hierarchical Variational Models](https://mlsanity.com/paper/1511.02386/) (2015)
- [Inference for multiple heterogeneous networks with a common invariant subspace](https://mlsanity.com/paper/1906.10026/) (2019)
- [Statistical clustering of temporal networks through a dynamic stochastic block model](https://mlsanity.com/paper/1506.07464/) (2015)
- [On a 'Two Truths' Phenomenon in Spectral Graph Clustering](https://mlsanity.com/paper/1808.07801/) (2018)
- [Learning Latent Block Structure in Weighted Networks](https://mlsanity.com/paper/1404.0431/) (2014)
- [Modern temporal network theory: A colloquium](https://mlsanity.com/paper/1508.01303/) (2015)
- [Community detection in multi-relational data with restricted multi-layer stochastic blockmodel](https://mlsanity.com/paper/1506.02699/) (2015)
- [Latent space models for multiplex networks with shared structure](https://mlsanity.com/paper/2012.14409/) (2020)
- [Network classification with applications to brain connectomics](https://mlsanity.com/paper/1701.08140/) (2017)
- [Joint Embedding of Graphs](https://mlsanity.com/paper/1703.03862/) (2017)
- [Clustering Network Layers With the Strata Multilayer Stochastic Block Model](https://mlsanity.com/paper/1507.01826/) (2015)
- [Nonparametric weighted stochastic block models](https://mlsanity.com/paper/1708.01432/) (2017)
- [Spectral Clustering of Signed Graphs via Matrix Power Means](https://mlsanity.com/paper/1905.06230/) (2019)
- [Modeling sequences and temporal networks with dynamic community structures](https://mlsanity.com/paper/1509.04740/) (2015)
- [Multilayer stochastic block models reveal the multilayer structure of complex networks](https://mlsanity.com/paper/1411.1098/) (2014)
- [Mutual Information in Community Detection with Covariate Information and Correlated Networks](https://mlsanity.com/paper/1912.05375/) (2019)
- [Weighted Multiplex Networks](https://mlsanity.com/paper/1312.6720/) (2013)
- [Estimating network structure from unreliable measurements](https://mlsanity.com/paper/1803.02427/) (2018)
- [A testing based extraction algorithm for identifying significant communities in networks](https://mlsanity.com/paper/1308.0777/) (2013)
- [Informative core identification in complex networks](https://mlsanity.com/paper/2101.06388/) (2021)
- [Enhanced detectability of community structure in multilayer networks through layer aggregation](https://mlsanity.com/paper/1511.05271/) (2015)
- [Gaussian Mixture Models for Stochastic Block Models with Non-Vanishing Noise](https://mlsanity.com/paper/1911.01855/) (2019)
- [Stochastic Block Models for Multiplex networks: an application to networks of researchers](https://mlsanity.com/paper/1501.06444/) (2015)
- [A testing-based approach to the discovery of differentially correlated variable sets](https://mlsanity.com/paper/1509.08124/) (2015)
- [Intertemporal Community Detection in Human Mobility Networks](https://mlsanity.com/paper/1906.04582/) (2019)
- [Role Detection in Bicycle-Sharing Networks Using Multilayer Stochastic Block Models](https://mlsanity.com/paper/1908.09440/) (2019)
- [Bayesian inference of network structure from unreliable data](https://mlsanity.com/paper/2008.03334/) (2020)

## Abstract (arXiv)

We introduce a novel model for multilayer weighted networks that accounts for global noise in addition to local signals. The model is similar to a multilayer stochastic blockmodel (SBM), but the key difference is that between-block interactions independent across layers are common for the whole system, which we call ambient noise. A single block is also characterized by these fixed ambient parameters to represent members that do not belong anywhere else. This approach allows simultaneous clustering and typologizing of blocks into signal or noise in order to better understand their roles in the overall system, which is not accounted for by existing Blockmodels. We employ a novel application of hierarchical variational inference to jointly detect and differentiate types of blocks. We call this model for multilayer weighted networks the Stochastic Block (with) Ambient Noise Model (SBANM) and develop an associated community detection algorithm. We apply this method to subjects in the Philadelphia Neurodevelopmental Cohort to discover communities of subjects with co-occurrent psychopathologies in relation to psychosis.