# A graph representation based on fluid diffusion model for data analysis: theoretical aspects and enhanced community detection

arXiv: https://arxiv.org/abs/2112.04388 · HTML: https://mlsanity.com/paper/2112.04388/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 45 of its 140 references that are in the map.
- First posted on arXiv 7 Dec 2021.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 45)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Multimodal Machine Learning: A Survey and Taxonomy](https://mlsanity.com/paper/1705.09406/) (2017)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [SpectralNet: Spectral Clustering using Deep Neural Networks](https://mlsanity.com/paper/1801.01587/) (2018)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [A Review of Feature Selection Methods Based on Mutual Information](https://mlsanity.com/paper/1509.07577/) (2015)
- [Deep Learning for Community Detection: Progress, Challenges and Opportunities](https://mlsanity.com/paper/2005.08225/) (2020)
- [Attributed Social Network Embedding](https://mlsanity.com/paper/1705.04969/) (2017)
- [Covariate-assisted spectral clustering](https://mlsanity.com/paper/1411.2158/) (2014)
- [Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks](https://mlsanity.com/paper/1502.04381/) (2015)
- [Learning Latent Block Structure in Weighted Networks](https://mlsanity.com/paper/1404.0431/) (2014)
- [Analysis of spectral clustering algorithms for community detection: the general bipartite setting](https://mlsanity.com/paper/1803.04547/) (2018)
- [Community detection, link prediction, and layer interdependence in multilayer networks](https://mlsanity.com/paper/1701.01369/) (2017)
- [Learnable Manifold Alignment (LeMA) : A Semi-supervised Cross-modality Learning Framework for Land Cover and Land Use Classification](https://mlsanity.com/paper/1901.02838/) (2019)
- [Fluid Communities: A Competitive, Scalable and Diverse Community Detection Algorithm](https://mlsanity.com/paper/1703.09307/) (2017)
- [Kernel-based Graph Learning from Smooth Signals: A Functional Viewpoint](https://mlsanity.com/paper/2008.10065/) (2020)
- [Community Detection in Networks with Node Features](https://mlsanity.com/paper/1509.01173/) (2015)
- [Forman-Ricci Curvature for Hypergraphs](https://mlsanity.com/paper/1811.07825/) (2018)

## Built on by (most cited first, 1 of 1)

- [Improving embedding of graphs with missing data by soft manifolds](https://mlsanity.com/paper/2311.17598/) (2023)

## Abstract (arXiv)

Representing data by means of graph structures identifies one of the most valid approach to extract information in several data analysis applications. This is especially true when multimodal datasets are investigated, as records collected by means of diverse sensing strategies are taken into account and explored. Nevertheless, classic graph signal processing is based on a model for information propagation that is configured according to heat diffusion mechanism. This system provides several constraints and assumptions on the data properties that might be not valid for multimodal data analysis, especially when large scale datasets collected from heterogeneous sources are considered, so that the accuracy and robustness of the outcomes might be severely jeopardized. In this paper, we introduce a novel model for graph definition based on fluid diffusion. The proposed approach improves the ability of graph-based data analysis to take into account several issues of modern data analysis in operational scenarios, so to provide a platform for precise, versatile, and efficient understanding of the phenomena underlying the records under exam, and to fully exploit the potential provided by the diversity of the records in obtaining a thorough characterization of the data and their significance. In this work, we focus our attention to using this fluid diffusion model to drive a community detection scheme, i.e., to divide multimodal datasets into many groups according to similarity among nodes in an unsupervised fashion. Experimental results achieved by testing real multimodal datasets in diverse application scenarios show that our method is able to strongly outperform state-of-the-art schemes for community detection in multimodal data analysis.