# Upper Bounding Barlow Twins: A Novel Filter for Multi-Relational Clustering

arXiv: https://arxiv.org/abs/2312.14066 · HTML: https://mlsanity.com/paper/2312.14066/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 21 Dec 2023.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [Self-supervised Heterogeneous Graph Neural Network with Co-contrastive Learning](https://mlsanity.com/paper/2105.09111/) (2021)
- [Deep Graph Clustering via Dual Correlation Reduction](https://mlsanity.com/paper/2112.14772/) (2021)
- [Attributed Graph Clustering via Adaptive Graph Convolution](https://mlsanity.com/paper/1906.01210/) (2019)
- [HDMI: High-order Deep Multiplex Infomax](https://mlsanity.com/paper/2102.07810/) (2021)
- [Multi-view Contrastive Graph Clustering](https://mlsanity.com/paper/2110.11842/) (2021)
- [Deep Fusion Clustering Network](https://mlsanity.com/paper/2012.09600/) (2020)
- [Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspective](https://mlsanity.com/paper/2106.07115/) (2021)
- [An Attention-based Collaboration Framework for Multi-View Network Representation Learning](https://mlsanity.com/paper/1709.06636/) (2017)
- [Beyond Homophily: Reconstructing Structure for Graph-agnostic Clustering](https://mlsanity.com/paper/2305.02931/) (2023)
- [High-order Multi-view Clustering for Generic Data](https://mlsanity.com/paper/2209.10838/) (2022)

## Built on by (most cited first, 12 of 12)

- [On the Benefits of Attribute-Driven Graph Domain Adaptation](https://mlsanity.com/paper/2502.06808/) (2025)
- [CDC: A Simple Framework for Complex Data Clustering](https://mlsanity.com/paper/2403.03670/) (2024)
- [When Heterophily Meets Heterogeneous Graphs: Latent Graphs Guided Unsupervised Representation Learning](https://mlsanity.com/paper/2409.00687/) (2024)
- [Beyond Redundancy: Information-aware Unsupervised Multiplex Graph Structure Learning](https://mlsanity.com/paper/2409.17386/) (2024)
- [Balanced Multi-Relational Graph Clustering](https://mlsanity.com/paper/2407.16863/) (2024)
- [Homophily Enhanced Graph Domain Adaptation](https://mlsanity.com/paper/2505.20089/) (2025)
- [Cooperation of Experts: Fusing Heterogeneous Information with Large Margin](https://mlsanity.com/paper/2505.20853/) (2025)
- [Simplified PCNet with Robustness](https://mlsanity.com/paper/2403.03676/) (2024)
- [Unveiling Mode Connectivity in Graph Neural Networks](https://mlsanity.com/paper/2502.12608/) (2025)
- [Effective Clustering for Large Multi-Relational Graphs](https://mlsanity.com/paper/2508.17388/) (2025)
- [SiMilarity-Enhanced Homophily for Multi-View Heterophilous Graph Clustering](https://mlsanity.com/paper/2410.03596/) (2024)
- [Beyond the Academic Monoculture: A Unified Framework and Industrial Perspective for Attributed Graph Clustering](https://mlsanity.com/paper/2603.20829/) (2026)

## Abstract (arXiv)

Multi-relational clustering is a challenging task due to the fact that diverse semantic information conveyed in multi-layer graphs is difficult to extract and fuse. Recent methods integrate topology structure and node attribute information through graph filtering. However, they often use a low-pass filter without fully considering the correlation among multiple graphs. To overcome this drawback, we propose to learn a graph filter motivated by the theoretical analysis of Barlow Twins. We find that input with a negative semi-definite inner product provides a lower bound for Barlow Twins loss, which prevents it from reaching a better solution. We thus learn a filter that yields an upper bound for Barlow Twins. Afterward, we design a simple clustering architecture and demonstrate its state-of-the-art performance on four benchmark datasets.