# A Hybrid Membership Latent Distance Model for Unsigned and Signed Integer Weighted Networks

arXiv: https://arxiv.org/abs/2308.15293 · HTML: https://mlsanity.com/paper/2308.15293/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 70 references that are in the map.
- First posted on arXiv 29 Aug 2023.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Network Representation Learning: A Survey](https://mlsanity.com/paper/1801.05852/) (2017)
- [Community Interaction and Conflict on the Web](https://mlsanity.com/paper/1803.03697/) (2018)
- [Signed Graph Attention Networks](https://mlsanity.com/paper/1906.10958/) (2019)
- [NetSMF: Large-Scale Network Embedding as Sparse Matrix Factorization](https://mlsanity.com/paper/1906.11156/) (2019)
- [SDGNN: Learning Node Representation for Signed Directed Networks](https://mlsanity.com/paper/2101.02390/) (2021)
- [Exploiting Social Network Structure for Person-to-Person Sentiment Analysis](https://mlsanity.com/paper/1409.2450/) (2014)
- [Distributed Representations of Signed Networks](https://mlsanity.com/paper/1702.06819/) (2017)
- [POLE: Polarized Embedding for Signed Networks](https://mlsanity.com/paper/2110.09899/) (2021)
- [On Mixed Memberships and Symmetric Nonnegative Matrix Factorizations](https://mlsanity.com/paper/1607.00084/) (2016)
- [Finding large balanced subgraphs in signed networks](https://mlsanity.com/paper/2002.00775/) (2020)
- [Piecewise-Velocity Model for Learning Continuous-time Dynamic Node Representations](https://mlsanity.com/paper/2212.12345/) (2022)
- [A Hierarchical Block Distance Model for Ultra Low-Dimensional Graph Representations](https://mlsanity.com/paper/2204.05885/) (2022)
- [Characterizing Polarization in Social Networks using the Signed Relational Latent Distance Model](https://mlsanity.com/paper/2301.09507/) (2023)
- [HM-LDM: A Hybrid-Membership Latent Distance Model](https://mlsanity.com/paper/2206.03463/) (2022)
- [Balance in Signed Bipartite Networks](https://mlsanity.com/paper/1909.06073/) (2019)
- [Stochastic block model and exploratory analysis in signed networks](https://mlsanity.com/paper/1501.00594/) (2015)
- [Exponential Family Graph Embeddings](https://mlsanity.com/paper/1911.09007/) (2019)

## Abstract (arXiv)

Graph representation learning (GRL) has become a prominent tool for furthering the understanding of complex networks providing tools for network embedding, link prediction, and node classification. In this paper, we propose the Hybrid Membership-Latent Distance Model (HM-LDM) by exploring how a Latent Distance Model (LDM) can be constrained to a latent simplex. By controlling the edge lengths of the corners of the simplex, the volume of the latent space can be systematically controlled. Thereby communities are revealed as the space becomes more constrained, with hard memberships being recovered as the simplex volume goes to zero. We further explore a recent likelihood formulation for signed networks utilizing the Skellam distribution to account for signed weighted networks and extend the HM-LDM to the signed Hybrid Membership-Latent Distance Model (sHM-LDM). Importantly, the induced likelihood function explicitly attracts nodes with positive links and deters nodes from having negative interactions. We demonstrate the utility of HM-LDM and sHM-LDM on several real networks. We find that the procedures successfully identify prominent distinct structures, as well as how nodes relate to the extracted aspects providing favorable performances in terms of link prediction when compared to prominent baselines. Furthermore, the learned soft memberships enable easily interpretable network visualizations highlighting distinct patterns.