# Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds

arXiv: https://arxiv.org/abs/1303.2221 · HTML: https://mlsanity.com/paper/1303.2221/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2013.

## Built on by (most cited first, 13 of 13)

- [Graph Sparsification via Mixture of Graphs](https://mlsanity.com/paper/2405.14260/) (2024)
- [Supra-Laplacian Encoding for Transformer on Dynamic Graphs](https://mlsanity.com/paper/2409.17986/) (2024)
- [A common variable minimax theorem for graphs](https://mlsanity.com/paper/2107.14747/) (2021)
- [Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization](https://mlsanity.com/paper/2205.00626/) (2022)
- [Embedding Graphs on Grassmann Manifold](https://mlsanity.com/paper/2205.15068/) (2022)
- [Policy Augmentation: An Exploration Strategy for Faster Convergence of Deep Reinforcement Learning Algorithms](https://mlsanity.com/paper/2102.05249/) (2021)
- [Multilayer Graph Approach to Deep Subspace Clustering](https://mlsanity.com/paper/2401.17033/) (2024)
- [Advanced Unsupervised Learning: A Comprehensive Overview of Multi-View Clustering Techniques](https://mlsanity.com/paper/2512.05169/) (2025)
- [Multilayer Graph Clustering with Optimized Node Embedding](https://mlsanity.com/paper/2103.16534/) (2021)
- [Multi-view graph structure learning using subspace merging on Grassmann manifold](https://mlsanity.com/paper/2204.05258/) (2022)
- [Information Fusion: Scaling Subspace-Driven Approaches](https://mlsanity.com/paper/2204.12035/) (2022)
- [Discriminative community detection for multiplex networks](https://mlsanity.com/paper/2410.00724/) (2024)
- [A Spectral Framework for Tracking Communities in Evolving Networks](https://mlsanity.com/paper/2412.07378/) (2024)

## Abstract (arXiv)

Relationships between entities in datasets are often of multiple nature, like geographical distance, social relationships, or common interests among people in a social network, for example. This information can naturally be modeled by a set of weighted and undirected graphs that form a global multilayer graph, where the common vertex set represents the entities and the edges on different layers capture the similarities of the entities in term of the different modalities. In this paper, we address the problem of analyzing multi-layer graphs and propose methods for clustering the vertices by efficiently merging the information provided by the multiple modalities. To this end, we propose to combine the characteristics of individual graph layers using tools from subspace analysis on a Grassmann manifold. The resulting combination can then be viewed as a low dimensional representation of the original data which preserves the most important information from diverse relationships between entities. We use this information in new clustering methods and test our algorithm on several synthetic and real world datasets where we demonstrate superior or competitive performances compared to baseline and state-of-the-art techniques. Our generic framework further extends to numerous analysis and learning problems that involve different types of information on graphs.