# Spectral Clustering for Discrete Distributions

arXiv: https://arxiv.org/abs/2401.13913 · HTML: https://mlsanity.com/paper/2401.13913/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 25 Jan 2024.

## Builds on (most cited first, 15 of 15)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Wasserstein Embedding for Graph Learning](https://mlsanity.com/paper/2006.09430/) (2020)
- [Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbations](https://mlsanity.com/paper/2008.09165/) (2020)
- [Fast Discrete Distribution Clustering Using Wasserstein Barycenter with Sparse Support](https://mlsanity.com/paper/1510.00012/) (2015)
- [Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view](https://mlsanity.com/paper/2102.07943/) (2021)
- [Discrete Wasserstein Barycenters: Optimal Transport for Discrete Data](https://mlsanity.com/paper/1507.07218/) (2015)
- [Large-Scale Subspace Clustering via k-Factorization](https://mlsanity.com/paper/2012.04345/) (2020)
- [A Simple Approach to Automated Spectral Clustering](https://mlsanity.com/paper/2107.12183/) (2021)
- [Projection Robust Wasserstein Barycenters](https://mlsanity.com/paper/2102.03390/) (2021)
- [Laplacian-based Cluster-Contractive t-SNE for High Dimensional Data Visualization](https://mlsanity.com/paper/2207.12214/) (2022)

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

- [Relative Wasserstein Spatial Depth for Cluster Number Selection in Distributional Data](https://mlsanity.com/paper/2610.09153/) (2026)

## Abstract (arXiv)

The discrete distribution is often used to describe complex instances in machine learning, such as images, sequences, and documents. Traditionally, clustering of discrete distributions (D2C) has been approached using Wasserstein barycenter methods. These methods operate under the assumption that clusters can be well-represented by barycenters, which is seldom true in many real-world applications. Additionally, these methods are not scalable for large datasets due to the high computational cost of calculating Wasserstein barycenters. In this work, we explore the feasibility of using spectral clustering combined with distribution affinity measures (e.g., maximum mean discrepancy and Wasserstein distance) to cluster discrete distributions. We demonstrate that these methods can be more accurate and efficient than barycenter methods. To further enhance scalability, we propose using linear optimal transport to construct affinity matrices efficiently for large datasets. We provide theoretical guarantees for the success of our methods in clustering distributions. Experiments on both synthetic and real data show that our methods outperform existing baselines.