Unbalanced Optimal Transport Dictionary Learning for Unsupervised Hyperspectral Image Clustering

TL;DR

The deployment of spectral clustering on the learned representation results in an effective approach for the unsupervised learning of labels, by utilizing unbalanced Wasserstein barycenters to learn a lower-dimensional representation of the underlying data.

Abstract

Hyperspectral images capture vast amounts of high-dimensional spectral information about a scene, making labeling an intensive task that is resistant to out-of-the-box statistical methods. Unsupervised learning of clusters allows for automated segmentation of the scene, enabling a more rapid understanding of the image. Partitioning the spectral information contained within the data via dictionary learning in Wasserstein space has proven an effective method for unsupervised clustering. However, this approach requires balancing the spectral profiles of the data, blurring the classes, and sacrificing robustness to outliers and noise. In this paper, we suggest improving this approach by utilizing unbalanced Wasserstein barycenters to learn a lower-dimensional representation of the underlying data. The deployment of spectral clustering on the learned representation results in an effective approach for the unsupervised learning of labels.

Figures (2)

• Figure 1: Pictured here is the balanced (left) and unbalanced (right) barycentric interpolation between two Gaussian distributions with the same variance using $\tau = 0.5$ and $\epsilon = 0.001$. Notice that the unbalanced barycenters do not obey strict mass conservation, but still take the general shape of the reference distributions.
• Figure 2: This image shows the in-painting process of a trial run of the Salinas A data set with $24$ atoms, $\tau = 1000$, and $\epsilon = 0.1$ achieving an accuracy before in-painting of $89\%$. We note that the bottom right corner of the image accounts for the majority of the mislabeling, and that this issue is common under unsupervised labeling schemes.