# Graph Laplacian mixture model

arXiv: https://arxiv.org/abs/1810.10053 · HTML: https://mlsanity.com/paper/1810.10053/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2018.

## Built on by (most cited first, 8 of 8)

- [Joint Network Topology Inference via a Shared Graphon Model](https://mlsanity.com/paper/2209.08223/) (2022)
- [Graph Laplacian Learning with Exponential Family Noise](https://mlsanity.com/paper/2306.08201/) (2023)
- [Multiview Graph Learning with Consensus Graph](https://mlsanity.com/paper/2401.13769/) (2024)
- [Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation](https://mlsanity.com/paper/2207.14019/) (2022)
- [LogSpecT: Feasible Graph Learning Model from Stationary Signals with Recovery Guarantees](https://mlsanity.com/paper/2305.01379/) (2023)
- [Position-Sensing Graph Neural Networks: Proactively Learning Nodes Relative Positions](https://mlsanity.com/paper/2105.11346/) (2021)
- [Kernel-based Joint Multiple Graph Learning and Clustering of Graph Signals](https://mlsanity.com/paper/2310.19005/) (2023)
- [Graph-Dictionary Signal Model for Sparse Representations of Multivariate Data](https://mlsanity.com/paper/2411.05729/) (2024)

## Abstract (arXiv)

Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in settings where all available data relate to the same graph. This is, however, not always the case, as data is often available in mixed form, yielding the need for methods that are able to cope with mixture data and learn multiple graphs. We propose a novel generative model that represents a collection of distinct data which naturally live on different graphs. We assume the mapping of data to graphs is not known and investigate the problem of jointly clustering a set of data and learning a graph for each of the clusters. Experiments demonstrate promising performance in data clustering and multiple graph inference, and show desirable properties in terms of interpretability and coping with high dimensionality on weather and traffic data, as well as digit classification.