# Hierarchical Clustering of Hyperspectral Images using Rank-Two Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/1310.7441 · HTML: https://mlsanity.com/paper/1310.7441/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2013.

## Built on by (most cited first, 11 of 11)

- [Multiscale Clustering of Hyperspectral Images Through Spectral-Spatial Diffusion Geometry](https://mlsanity.com/paper/2103.15783/) (2021)
- [Hyperspectral Remote Sensing Benchmark Database for Oil Spill Detection with an Isolation Forest-Guided Unsupervised Detector](https://mlsanity.com/paper/2209.14971/) (2022)
- [Unsupervised Segmentation of Hyperspectral Remote Sensing Images with Superpixels](https://mlsanity.com/paper/2204.12296/) (2022)
- [Block Alternating Bregman Majorization Minimization with Extrapolation](https://mlsanity.com/paper/2107.04395/) (2021)
- [Unsupervised Diffusion and Volume Maximization-Based Clustering of Hyperspectral Images](https://mlsanity.com/paper/2203.09992/) (2022)
- [A consistent and flexible framework for deep matrix factorizations](https://mlsanity.com/paper/2206.10693/) (2022)
- [On the Robustness of the Successive Projection Algorithm](https://mlsanity.com/paper/2411.16195/) (2024)
- [Co-Separable Nonnegative Matrix Factorization](https://mlsanity.com/paper/2109.00749/) (2021)
- [Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence](https://mlsanity.com/paper/2410.07786/) (2024)
- [The Nondecreasing Rank](https://mlsanity.com/paper/2509.00265/) (2025)
- [Hyperspectral Unmixing Hierarchies](https://mlsanity.com/paper/2604.16969/) (2026)

## Abstract (arXiv)

In this paper, we design a hierarchical clustering algorithm for high-resolution hyperspectral images. At the core of the algorithm, a new rank-two nonnegative matrix factorizations (NMF) algorithm is used to split the clusters, which is motivated by convex geometry concepts. The method starts with a single cluster containing all pixels, and, at each step, (i) selects a cluster in such a way that the error at the next step is minimized, and (ii) splits the selected cluster into two disjoint clusters using rank-two NMF in such a way that the clusters are well balanced and stable. The proposed method can also be used as an endmember extraction algorithm in the presence of pure pixels. The effectiveness of this approach is illustrated on several synthetic and real-world hyperspectral images, and shown to outperform standard clustering techniques such as k-means, spherical k-means and standard NMF.