# Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/2104.12289 · HTML: https://mlsanity.com/paper/2104.12289/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 70 references that are in the map.
- First posted on arXiv 25 Apr 2021.

## Builds on (most cited first, 11 of 11)

- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)
- [Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization](https://mlsanity.com/paper/1908.01402/) (2019)
- [A block inertial Bregman proximal algorithm for nonsmooth nonconvex problems with application to symmetric nonnegative matrix tri-factorization](https://mlsanity.com/paper/2003.03963/) (2020)
- [Deep Approximately Orthogonal Nonnegative Matrix Factorization for Clustering](https://mlsanity.com/paper/1711.07437/) (2017)
- [Joint Reconstruction and Low-Rank Decomposition for Dynamic Inverse Problems](https://mlsanity.com/paper/2005.14042/) (2020)
- [A Review of Nonnegative Matrix Factorization Methods for Clustering](https://mlsanity.com/paper/1507.03194/) (2015)
- [A Block Coordinate Descent-based Projected Gradient Algorithm for Orthogonal Non-negative Matrix Factorization](https://mlsanity.com/paper/2003.10269/) (2020)
- [Four algorithms to solve symmetric multi-type non-negative matrix tri-factorization problem](https://mlsanity.com/paper/2012.05963/) (2020)
- [Sequential Dimensionality Reduction for Extracting Localized Features](https://mlsanity.com/paper/1505.06957/) (2015)
- [A Survey on Surrogate Approaches to Non-negative Matrix Factorization](https://mlsanity.com/paper/1808.01975/) (2018)
- [SPRING: A fast stochastic proximal alternating method for non-smooth non-convex optimization](https://mlsanity.com/paper/2002.12266/) (2020)

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

- [Supervised topological data analysis for MALDI mass spectrometry imaging applications](https://mlsanity.com/paper/2302.13948/) (2023)

## Abstract (arXiv)

Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not necessarily be reconstructed well by standard clustering methods. Motivated by applications in hyperspectral imaging, we introduce in this work clustering models based on orthogonal nonnegative matrix factorization, which include an additional total variation (TV) regularization procedure on the cluster membership matrix to enforce the needed spatial coherence in the clusters. We propose several approaches with different optimization techniques, where the TV regularization is either performed as a subsequent postprocessing step or included into the clustering algorithm. Finally, we provide a numerical evaluation of all proposed methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionisation imaging measurement, which leads to significantly better clustering results compared to classical clustering models.